WORLD METEOROLOGICAL ORGANIZATION
OPERATIONAL HYDROLOGY REPORT No. 30
HYDROLOGICAL ASPECTS OF COMBINED EFFECTS OF STORM SURGES AND HEAVY RAINFALL ON RIVER FLOW
SECRETARIAT OF THE WORLO METEOROLOGICAL ORGANIZATION-GENEVA-SWITZERLANO 1988 © 1988, World Meteorological Organization ISBN 92 - 63 - 10704-1
NOTE
The designations employed and the presentation of material in this publication do not imply the expression of any opinion whatsoever on the part of the Secretariat of the World Meteorological Organization concerning the legal status of any country, territory, city or area. or of its authorities, or concerning the delimitation of its frontiers or boundaries. CONTENTS
FOREWORD •...... •...... •...... VI SUMMARY (English, French, Russian, Spanish) ...... •...•... VII
1. GENERAL CONSIDERATIONS ...... •... 1 1.1 Introduction ...... ••.•...... 1 1.2 Definition of storm surge .•...... 2 1.3 Historical incidences of catastrophic storm surges . 2 1.4 Causes of storm surges ....•...... •...•..•..... 2 1.5 Marine effects ...... •....•...•..••••....•..•...... 2 1.6 Tropical cyclones ...... •.•....•... 4 1.7 Extra-tropical cyclones .•.•••.•...... •.•...... 4 1.8 Fluvial effects ...... •.••.•...... 4
2. STORM SURGE DATA ACQUISITION ...... ••...... 6 2.1 Introduction ...... •...... 6 2.2 Operational meteorological data ...... ••...•.. 6 2.3 Operational tide and surge data •...•.....•....•...... 7 2.4 Water surface elevations of bays and estuaries . 7 2.5 Bathymetric characteristic of river bays and estuaries 7 2.6 Coastal plane topography ...... •...... 8 2.7 Stages and discharges in rivers .•...•...... 8 2.8 Wind velocity and direction and its temporal distribution 8 2.9 Precipitation and its areal and temporal distribution .•.... 9 2.10 Methods of observation ..•...... •...... •..•...... 9 2.10.1 Tidal staff ...... •.• 9 2.10.2 Tidal gauge •...... •...... 9 2.10.3 Crest gauge ...... ••....•.•...... •...... 10 2.10.4 Remote recording tide gauge or tide telemeter . 10 2.10.5 Meteorological instruments ...... ••...... 10
3. FLOOD MODELLING IN TIDAL AREAS - THE DETERMINISTIC APPROACH 11 3.1 Introduction ...... •...... •.. 11 3.2 The deterministic approach ...... •...... 11 3.3 Model structure ...... •....•.....•.•...••.•.•...... 11 3.4 Open sea models ...... •...... ; . 11 3.4.1 Mathematical basis ...... •..... 12 3.4.2 Implementation of ocean models ...... •....•..•.•...... 13 3.5 Bays and estuaries . 14 3.6 River models ...... •...... •..•.... 14 3.6.1 General considerations of river flooding .•....•...... 15 3.6.2 Possibilities for hydraulic modelling of tidal and fluvial river flooding ...... • 15 3.6.3 Examples of methods using numerical integration of the hydraulic equations ...•....•...... •....•...... 16
4. FLOOD MODELLING IN TIDAL AREAS - THE EMPIRICAL APPROACH 25 4.1 Introduction •...... 25 4.2 Merits and problems of the empirical approach •...... 25 4.3 Empirical models for coastal surge calculation •...... 25 4.4 River surges .. 27 IV CONTENTS
4.4.1 General considerations ..._...... 27 4.4.2 Combined effect of surge and river flow...... 27 4.4.3 Modelling possibilities ...... •...... •.....•...... 28 4.5 Physically based formulae 31 4.5.1 Introduction ...... •...... •...... •...... •.•. •• .... 31 4.5.2 River flows in the interaction zone ...... ••.•...•... 32 4.5.3 Tidal waves in the river ...... •...... •. 32 4.5.4 Interaction of flood and tidal waves •.•...... 32 4.5.5 Illustrative example ..••...... •...... •...•••... 34 4.6 Regression formulae ...... •.....•...... •...... 34 4.6.1 Formula development ...•...... •...... •...... •.....•...... 34 4.6.2 Practical example ...••...... ••.....•.•...... ••....•..... 35
5. RISK EVALUATION OF STORM SURGES IN RIVERS ...••.....•...... 37 5.1 Introduction .. ...•...... •...... •.•...... •••...••....• 37 5.2 Surge frequency at an open coast ...... •.•...... 37 5.3 Flood frequency in tidal rivers .•...... •...... •.....•... 38 5.3.1 Boundary data requirements .••....•...... ••...... •....•.• 38 5.3.2 The approach to the problem ..•.....•...... •..•....•....•• 38 5.3.3 Effect of correlation ...... •...... ••....•.....• 42 5.3.4 Seasonality 42 5.3.5 The time step .•...... •...... ••...... •••...... ••.... 42 5.4 Practical examples ...... •...... •...... ••...... •.•..•.. 43 5.4.1 Steps in the computation ... •...... •...... • 43 5.4.2 The time step ...... •.....•..... 43 5.4.3 Tide distribution .. ..•...... •...... •.•...... •....•..... 44 5.4.4 Discharge distribution ...•...... •...... •.....•.... 44 5.4.5 Modelling the interaction relationship .....•.•.....•...... 44 5.4.6 Integration to obtain frequency distribution of flood levels ...... •...... ••...... •••....•..... 45 5.4.7 Flood frequency for a tidelocked river ...•...... •....•.... 45 5.5 Probable maximum flood ..•...... •.... 45 5.6 Damage assessment and flood insurance ...... •.•....•.....•. 45
6. THE FORECASTING CENTRE •...... •.•...... •....•.... 47 6.1 Introduction .. ..••.....•...... •.••....••...... •. 47 6.2 Location of the forecasting centre ..•...... •. 47 6.3 Choice of model and communication equipment .....•....•..... 48 6.4 Dissemination of forecasts and warnings ....•....•.....•.... 48 6.5 West Gulf Forecasting Centre (WGFC) (USA) ..••...... •....•• 50 6.5.1 Description of the forecasting centre ..•...... ••...•••.... 50 6.5.2 Surge forecasting procedures ...••...... ••....••.....•.... 50 6.5.3 After-the-event analysis of" Hurricane Alicia •...... •....•• 50 6.5.4 Conclusion .• ...... •...... •...... •...... ••..•....•....• 50 6.6 Storm Tide Warning Service (Netherlands) .•...... •.....•.... 51 6.7 Operation Neptune (UK) ..•.•.....•...... ••••...... • 52
7. SELECTED CASE HISTORIES ...... •.•..•....•.•....••.... 53 7.1 Introduction ....• ...... •.....••...... •• .....••••.••••.. 53 7.2 Field survey results and high water information ....•.•....• 53 7.2.1 Tidal gauge records ...... •...... •....•.•..... 53 7.2.2 River flow and level records .....•...... ••.....••...••.... 54 7.2.3 Field survey ...... •..•.....••...... •...... •..•.••• 54 7.2.4 High water measurement ...•...• •.....•••...... •.•..••••...• 55 CONTENTS v
7.3 Flooding on the Brisbane River. Australia (1893-1955) . 55 7.4 Storm surges in Japan (1917-1970) ...... •.•. 59 7.5 Storm surges in Bangladesh (1960-1970) ••...... •...... 59 7.6 Storm surges in the Unites States (1960-1970) . 61 7.7 Storm surges in Hong Kong ...... •..•.•..•...... 62 7.8 Storm surges in the North and Irish Seas (1976-1978) ...••.• 64 7.9 Flooding in Sichuan Province. China (1981) .•...... 65
8. RESEARCH NEEDS AND CONCLUSIONS ...... ••...... •...... 66 8.1 Introduction ....•.••....•.•...... • 66 8.2 Data needs ...... •.....•••...... 66 8.3 Modelling ...... ••....•...... •...... • 66 8.4 Risk assessment and design problems ...•...... 67 8.5 Technology transfer ...... •••...... 68 8.6 Concluding remarks ...... •.....•...... 68
REFERENCES 69 FOREWORD
As r-equested by the WMO Commission for- Hydmlogy (CHy) at its fifth session in 1976, the CHy-V Wor-king Gr-oup on Hydr-ological For-ecasting pr-epar-ed two r-epor-ts, one on hydr-ological aspects of combined effects of stor-m sur-ge and heavy r-ainfall on r-iver- flow end another- on the fr-equency of flooding in r-iver-s subject to sea-stor-m sur-ges and r-ainfall-induced floods. At its sixth session in 1980, the Commission r-eviewed these two r-epor-ts and r-equested its Rappor-teur- on For-ecasting of Combined Stor-m-Sur-ge Flood Effects, Dr- O. Ibidapo-Obe (Niger-ia), to finalize and combine the two r-epor-ts. Accor-dingly, Dr- Ibidapo-Obe prepar-ed a single r-epor-t on the subject; his r-epod also included a r-eview of simple methods for- for-ecasting combined stor-m-sur-ge flood effects as r-equested by CHy-VI.
Th!, pr-esident of CHy r-eviewed the r-epor-t pr-epar-ed by Dr- Ibidapo-Obe and r-ecommended that it should be expanded to include guidance mater-ial on flood modelling in tidal ar-eas and r-isk evaluation of stor-m sur-ges in r-iver-s, as well as mater-ial on forecasting centr-es. The Secr-etar-iat accor-dingly ar-r-anged for- Mr- Max Ber-an (United Kingdom) to pr-epar-e the pr-esent expanded r-epor-t which includes the additional mater-ial, thus ensur-ing a balanced pr-esentation of the subject matter-.
It is with gr-eat pleasur-e that I expr-ess the gr-atitude of WMO to all those who have contr-ibuted to the pr-epar-ation of this r-epor-t, in par-ticular- to the chair-man and member-s of the CHy-V Wor-king Gr-oup on Hydr-ological For-ecasting, to Dr- O. Ibidapo-obe and to Mr- M. Ber-an.
~~~~--_ .•.. ----.-___r ------G.O.P. Obasi Secr-etar-y-Gener-al SUMMARY
This report is concerned with the flood hydrology of those lower reaches of rivers where sea level can influence flood levels. High sea-levels are caused by the astronomic tide or by storm surges or by both acting together. High river discharge can be caused by the same weather system that is responsible for the high sea-level, such as a tropical cyclone, or the two can be quite independent. The phrases "tidally affected river" and "tidal interaction zone" have generally been used in the report to denote the river reach which is under both fluvial and marine influences. This report is intended to complement the WMO publication Present Techniques of Tropical Storm Surge Prediction (WMO-No. 500) by cOI;lcentrating on fluvial and river-based aspects. .
Chapter I of the report includes an introduction to the subject and explains the scope of the report.
Chapter 2 reviews storm-surge data, stages and discharges in rivers, precipitation and its areal and temporal variation, and methods of observation.
Chapter 3 discusses the deterministic approach to flood modelling in tidal areas including model structure, open sea models, bays and estuaries, and river models.
Chapter 4 discusses the empirical approach to flood modelling in tidal areas and includes a review of the merits and problems of the empirical approach, empirical models for coastal surge calculation, river surges, physically based formulae and regression formulae.
Chapter 5 addresses the risk evaluation of storm surges in rivers and reviews surge frequency at an open coast, flood frequency in tidal rivers, probable maximum floods, damage assessment and flood insurance, and includes practical examples.
Chapter 6 includes a short review of forecasting centres and discusses their location, choice of model and communication equipment, and dissemination of forecasts and warnings.
Chapter 7 includes selected case studies from Australia, Bangladesh, China, Hong Kong, Japan, the United Kingdom and the United States of America.
Future research and data requirements, together with the conclusions of the report, are summarized in Chapter 8. VUI SUMMARY
RESUME
Le présent rapport est consacré à l'hydrologie des crues dans la par tie inférieure des cours d'eau où le niveau des crues peut être influencé par celui de la mer. Les fortes élévations du niveau de. la mer sont provoquées par les marées astronomiques, des ondes de tempête, ou la conjonction des deux. Le gonflement des cours d'eau peut être causé par le même système météorologique qui est à l'origine de l'élévation du niveau de la mer, tel qu'un cyclone tropicaL ou en être totalement indépendant. On a en général désigné dans ce rapport la partie du cours d'eau qui est soumis à la fois à une influence pluviale et à une influence maritime par les termes llcours dl eau influencé par la marée" et "zone d'interaction aVec la marée". Ce rapport vise à compléter la publication de l'OMM "Present Technique of Tropical Storm Surge Prediction" (Technique applicable actuellement pour prévoir les ondes de tempête tropicale") (OMM N° 500) en se focalisant Sur les aspects fluviaux et estuariens .
Le chapitre l présente le sujet et définit la teneur du rapport.
Le chapitre 2 traite des données sur les ondes de tempête, des niveaux et des débits des cours d'eau, des précipitations et de leur variation spatio temporelle ainsi que des méthodes d'observation pertinentes.
Le chapitre 3 examine l'application de la démarche déterministe à la modélisation des crues dans les zones soumises à l'influence des marées, notamment en ce qui concerne la structure' du modèle, les modèles de la pleine mer, des baies et des estuaires, des cours d'eau.
Le chapitre 4 examine l'application de la démarche emp~nque à la modélisation des crues dans les zones soumises aux effets de la marée, et com porte un examen des avantages qu'offre et des problèmes que pose cette démarche, des modèles empiriques utilisables pour calculer les contre foulements côtiers, les contre-foulements fluviaux, ainsi que des formules de régression et des formules fondées sur des caractéristiques physiques.
Le chapitre 5 est consacré à l'évaluation du risque d'ondes de tempête dans les cours d'eau à la fréquence des contre-foulements sur une côte ouverte, à la fréquence des crues dans les cours d'eau soumis à l'effet des marées, aux crues maximales probables, à l'évaluation des dommages et à l'as surance contre les crues, le tout illustré par des exemples pratiques.
Le chapitre 6 comporte une courte étude sur les centres de prévision, portant notamment sur leur emplacement, le choix du modèle et de l'équipement de télécommunication, la diffusion des prévisions et des avis.
Le chapitre 7 présente quelques études de cas choisis en Australie, au Japon, au Bangladesh, aux Etats-Unis d'Amérique, à Hong-Kong, au Royaume-Uni et en Chine.
Le chapitre 8 indique brièvement quelles sont les recherches à accom plir et les besoins en données à satisfaire, et résume les conclusions du rapport. SUММдRY IX
РЕЗЮМЕ
Доклад посвящен гидрологии паводков тех низовьев рек, где уровень моря может оказывать влияние на уровни паводков. Высокие уровни моря вы
званы астрономическим приливом или штормовыми нагонами, или и тем и дру гим одновременно. Высокий речной сток может быть вызван тай же системой погоды, что и вызывающей ВЫСОКИй уровень моря совместно с тропическим цик лоном, или оба фактора могут быть независимы. В докладе встречаются вы ражения "река, подверженная воздействию приливав" и "зона взаимодействия приливав", обозначающие участок реки, подвергающийся воздействию как реч ных, так и морских ВЛИЯНИй. Этим докладом предполагается дополнить ПУб ликацию ВМО "Современные методы прогнозирования тропических штормовых на гонов" (публикация ВМО ~ 500), где основное внимание будет уделено аспек там рек и зстуариев. В главе 1 доклада содержится введение в тему и объем доклада. В главе 2 рассматриваются данные штормовых нагонов, уровни и сто ки рек, осадки и их пространственные и временные изменения, а также мето
ды наблюдений. В г лаве 3 обсуждается детерминистический подход к моделированию паводков в районах, подвергающихся воздействию приливав, включая структу
ру моделей, модели открытого моря, модели заливов, зстуариев и рек. В г лаве 4 обсуждается змпирический подход к моделированию павод ков в районах, подвергающихся воздействию приливав, включая обзор преиму ществ и проблем змпирического подхода, змпирические модели расчетов бере говых нагонов, речных нагонов, формулы на физической основе и формулы рег-
рессии. Г лава 5 посвящена оценке риска штормовых нагонов на реках; она рассматривает частотность нагонов на открытом побережье, частотность па
водков на реках, подверженных воздействию приливав, возможные максималь ные паводки, оценку ущерба и страхования от паводков, включая практичес
кие примеры. Г лава 6 включает краткий обзор центров прогнозирования и обсуж- дает вопросы их расположения, выбора моделей и средств коммуникации, а также распространение прогнозов и предупреждений. В главу 7 включены конкретные примеры из практики Австралии, Япо- нии, Бангладеш, Соединенных Штатов Америки, Гонконга, Соединенного Коро
левства и Китая. В главе 8 содержится резюме будущей научно-исследовательской дея тельности и потребностей в данных, а также выводы доклада. x SUMMARY
RESUMEN
El informe trata de la hidrología de las crecidas de aquellos tramos inferiores de los ríos en que el nivel del mar puede influir en los niveles de las crecidas. La elevación del nivel del mar está causada por la marea astro nómica, por las mareas de tempestad o por ambas cosas actuando conjuntamente. La elevación del caudal de los ríos puede estar causada por el mismo sistema meteorológico que es responsable de la elevación del nivel del mar, como suce de con los ciclones tropicales, pero a veces ambos fenómenos son independien tes. Las frases "río afectado por la marea" y "zona de interacción de las ma reas" se han utilizado, en general, en el informe referido al tramo del río que está bajo las influencia fluvial y marina. El presente informe trata de ser El Capítulo 1 del informe es una introducción al tema y una exposición del alcance del informe. El Capítulo 2 examina los datos relativos a las mareas de tempestad, los niveles y caudales de los ríos, las precipitaciones y las variaciones de su extensión y frecuencia, así como los métodos de observación. En el Capítulo 3 se examina el enfoque determinista en la elaboración de modelos de crecidas en zonas de mareas, con inclusión de la estructura de los modelos, modelos de alta mar y modelos de bahías y estuarios y de ríos. En el Capítulo 4 se examina el enfoque empírico en la elaboración de modelos de inundaciones en zonas -de mareas, e incluye un examen de las venta jas y problemas del enfoque empírico, modelos empíricos para el cálculo del oleaje costero, las mareas de los ríos, fórmulas calculadas sobre una base fí• sica y fórmulas de regresión. El Capítulo 5 trata de la elevación de los riesgos de las mareas de tempestad en los ríos y examina la frecuencia de las mareas en una costa abierta, la frecuencia de las crecidas en los ríos afectados por las mareas, las crecidas máximas probables, la evaluación de los daños y el seguro de inundaciones, e incluye ejemplos prácticos. En el Capítulo 6 se hace un breve examen de los centros de predicción meteorológica y se examina su ubicación, elección del modelo y equipo de comu nicación, así como la difusión de los pronósticos meteorológicos y de las alertas. En el Capítulo 7 se ofrece una selección de casos concretos de Australia, el Japón, Bangladesh, los Estados Unidos de América, Hong Kong, el Reino Unido y China. Las futuras investigaciones y necesidades de datos, junto con las con clusiones del informe, se resumen en el Capítulo 8. CH APT E R 1 GENERAL CONSIDERATIONS 1.1 Introduction The hydrologist is normally concerned with the land phase of the hydrological cycle. However, there are occasions when his interest must extend beyond those strict limits. One such occasion relates to the hydrological conditions encountered on the coastal plain. In these areas the sea can have a major impact through its effect on the physical and chemical conditions in surface and subsurface water bodies. In this report we are concerned with the flooding problem that exists in the upper reaches of estuaries and the lower portions of rivers. In this meeting place between ocean and land, floods occur from a combination of freshwater and marine causes, in particular when a storm surge in the sea coincides with a freshwater flood downriver. Flooding may also occur in creeks and ti'de-locked water courses when freshwater is unable to discharge due to sustained high marine water levels. The report endeavours to be as comprehensive as possible about the problem. Some limited information on the two component causes. river floods and sea surges. is included and references are given to more complete accounts of these topics. The object of the report is to allow hydrologists to recognize affected reaches, to design flood-prevention measures and to develop forecasting and flood warning systems. It is well known that both causative phenomena are initiated by weather conditions; wind and low pressure in the marine case, and rainfall in the freshwater case. Both are modified by the physical natures of the estuary and basin. The degree to which the natural phenomenon is a human problem is of course determined by the level of development on the coastal plain. Unhappily, the affected regions do tend to coincide with important commercial centres. Flat tracts of land with access to good communications by land and sea attract concentrated urban development and industry while the recent depositional history of the area will probably have produced a highly fertile soil, making it attractive for agriculture as well. The sea itself is a source of food, and a shelving coastline is conducive to both an active fishery and an aggravated surge problem. The region of concern often coincides with the lowest point on a river where a bridge or ferry crossing would be practical, a further factor contributing to a high level of development. In global terms the parts of the world where storm surge and flooding conditions are most severe are in the tropical belt where hurricanes are encountered, for example around the Philippines and in the Caribbean. However, other combinations of conditions have resulted in disastrous floods in extra-tropical and temperate regions such as the Bay of Bengal, Japan and the North Sea. In these extra-tropical zones it is likely that flooding is aggravated by other factors, in particular the astronomical tide but also tsunamis, seiche. wind set-up and wave action. 2 CHAPTER 1 1.2 Definition of storm surge A storm surge is often defined as the difference between the observed water level and that which would have occurred at the same place and time in the absence of a storm. It should be noted that this residual can be negative as well as positive, although it is of course only the latter that creates a flooding problem. Note also that the definition implicitly includes higher frequency water-level changes such as waves, seiche, and indeed rainfall flood effects which may accompany the storm surge event. However, this last effect, the fluvial flood enhancement, is excluded from the surge definition in the present report. 1.3 Historical incidences of catastropic storm surges Historically, storm surges have brought disastrous inundations and have been responsible for the majority of deaths in coastal areas affected by storms. In 1953, 2 200 lives were lost in the Netherlands and in England as a result of a surge more than three metres high. In 1959, surges from Typhoon Vera were responsible for nearly 5 000 deaths in Japan. Similarly, in 1969, Hurricane Camille caused a peak surge of nearly eight metres, with accompanying loss of life and property in the USA. In November 1970, more than 200 000 people were drowned during a cyclone in Bangladesh. It should be remarked, however, that high storm surges are not confined to the ocean coasts; for example, the Baltic, a virtually enclosed sea, was affected in 1924 when a four-metre-high surge flooded Leningrad, resulting in the death of 2 000 people. Clearly, the hydrologist must provide himself with a knowledge of past events in his area of concern in order to understand which causative factors pertain and to be able to evaluate the magnitude and risk of an event. 1.4 Causes of storm surges In very general terms a storm surge is induced by a low pressure weather system. This allows the sea-level to rise through barometric suction. The associated wind field "piles up" water through friction at the surface (termed wind set-up), and also creates high waves. Of these two causes it is wind set-up which is the major component. Locally important factors such as Coriolis currents, coastal geometry in plan and in section, and resonance must also be noted. In addition, the same weather conditions can cause flooding in rivers adjacent to the coast, and fluvial and sea-levels interact to aggravate flooding in estuaries and lower river reaches. It is convenient to treat the marine and the fluvial aspects separately. First we consider general aspects of surge-induced high water levels, then proceed to discuss the special features of tropical and extra-tropical surge mechanisms. 1.5 Marine effects (a) !h~ pr~s.§u.!:e_eif~c:!:: In accordance with the law of hydrostatics, the water level in the ocean will rise in regions of low atmospheric pressure and fall in regions of high pressure, so that the total pressure remains constant. GENERAL CONSIDERATIONS 3 This is also known as the inverted barometer effect and one hectopascal of pressure difference causes a difference of approximately one centimetre of sea-level. The equilibrium is achieved under the following conditions: (i) There are no rapid changes in the intensity of the atmospheric pressure system; (ii) The pressure systems are not moving; and (iii) The ocean is sufficiently deep and large so that there will be no restriction to the flow of water in attaining equilibrium. (b) !h~ ~f~e~t_o~ ~i~d_s~r~s~e~: The intensity of the frictional stress produced by winds blowing over a water surface depends on the wind speed and the roughness of the sea surface. The roughness of the sea surface is itself a function of the wind speed. The wind equation can be expressed as where: As = surface shear stress; PA = density of air; K = constant; V = wind speed. Over shallow waters this wind stress generates a current the direction of which is almost parallel to the wind. Any obstruction to the flow of this current will cause the water to become "piled up". Consequently, the coastal sea-level will tend to rise with on-shore winds and fall with off-shore winds. By considering the balance between wind stress and the restoring force of gravity, the following formula has been proposed for wind set-up based upon observations of differences between tide gauges in the Baltic Sea: 2 liT] = c FV / h where: liT] = level difference; F = wind fetch; V = mean wind speed along the direction of the two gauges; h = mean sea depth; c = an empirical constant. (c) !h~ ~f~e~t_o~ ~h~ ~a!:t!:!' ~ !:o~a~iQn: In the absence of this effect the water movement would be parallel to the wind direction. The influence of the Coriolis force is to turn the current direction towards the right in the northern hemisphere and towards the left in the southern hemisphere. 4 CHAPTER 1 (d) !h~ ~ffe~t_of ~aves: As waves approach shallow water, of the same order of depth as their own height. they will break. After breaking the water runs up the beach or river and creates "wave set-up"'. Ce) The effect of resonance: Water bodies have their own period of-free osciiiat.ion~ -The impulse of the surge wave or of the low pressure system itself can cause the water body to resonate and high amplitudes can be achieved Ca seiche). This occurs in quite large seas and bays, but also in semi-enclosed water bodies such as harbours, inlets and fjords. (f) !h~ ~ffe~t_of ~o~st.al ge~m§.t!:Y: A coastline which is normal to the line of attack of the surge wave will be most severely affected. Coastal details affect wave movement through mechanisms such as breaking, diffraction and refraction. Cg) 1h§. §.fie~t_of t.h§. ~h~p§. ~f_s!:!o!:elin~s: If an estuary or bay has a wide and deep mouth but becomes progressively narrower towards its head, the effect of convergence as a storm surge propagates further upstream may amplify the surge several times. Moreover, if the head of the estuary or bay is also the leeward end, the pile-up of water due to wind stress may render the surge even more intense. 1.6 Tropical cyclones Tropical cyclones (hurricanes, typhoons) are small intense low-pressure regions characterized by a near circular pressure and windfield form. They follow a largely unpredictable path across the sea and decay rapidly across the ground. They are also accompanied by intense downpours which create local severe flooding. The point at which the maximum barometric component of the surge occurs is beneath the cyclone at landfalL but the maximum of the wind-induced component may not coincide with that location, as it will also depend on the path direction and speed. 1.7 Extra-tropical cyclones In middle and high latitudes marine surges are caused by low-pressure atmospheric conditions which, although much less intense than in tropical cyclones, are an order of magnitUde larger in spatial extent. They tend to be a winter season phenomenon and can affect entire seas, for example the North Sea. The same weather system affects continental regions. Rainfall intensities cannot be equated with those experienced during tropical cyclones, but, again, can affect large catchment areas. 1.8 Fluvial effects The list of surge influences can, if conditions conspire, create flood conditions in estuaries. If the same low~pressure system causes heavy rainfall in the estuary catchment, the flooding can then be much aggravated by fluvial flooding. The fluvial input is a function of catchment factors, in GENERAL CONSIDERATIONS 5 particular the lag time. The longitudinal water surface profile can take many forms; a cusp shape, with a higher level at the estuary mouth than at a short distance upstream, is by no means unusual. Eventually fluvial processes take over and the normal river backwater will dictate a rising trend in the upper estuary and river. CHAPTER 2 STORM SURGE DATA ACQUISITION 2.1 Introduction This chapter provides a checklist of data that are needed for forecasting and for statistical prediction of surge effects in watercourses affected by tides. Detailed descriptions of observational practices and instrwnentation are provided in WMO manuals and other publications. e.g. the Guide to Hydrological Practices (WMO-No. 168 (Vol. 1-1981; Vol. 11-1983» and Present techniques of tropical storm surge prediction (WMO, 1978). As explained in Chapter 1, surge development in rivers is the outcome of complex interactions and requires operational data on meteorological and hydrological as well as tide and surge variables. The surge forecasting centre will itself accwnulate data in the course of time, but this must be supplemented by operational data from meteorologists, navigation authorities and the hydrological staff responsible for the river in question. Statistical information on past surges is perhaps the most difficult to obtain, especially in rivers, but this is precisely the type of information that is most important for design purposes. Topographic information on the estuary and river will also be required to couple the marine and fluvial forcing factors in the river model. and topographic information on surrounding land is needed in order to interpret the effects of past surges and to forecast the impact of future events. 2.2 Operational meteorological data Meteorological charts and diagrams are the main source of information on the development of storm surges. The total weather pattern conveyed by such charts enables the forecaster to build up his experience of surge-causing situations and provides the detailed spatial coverage of pressure data, wind speeds and wind directions which are vital inputs to the forecasting model. It is the forecaster's skill and experience in recognizing the pattern. of past events that will determine the success of forecasts and make up for the inevitable deficiencies in information about the precise location and movement of a given surge event. Nowadays, weather satellites, radar and reconnaissance aircraft provide additional stimulating aids. A system of cloud classification based upon satellite cloud imagery makes it possible to estimate maximwn wind speed and minimwn sea-level pressure. The radius of maximwn wind within a tropical cyclone may be estimated by aerial reconnaissance or by coastal weather radar when the cyclone is within range. The radius of maximwn wind speed is generally of the order of 50 km; when the maximum wind speed exceeds 50 m S-l there will be little difference between the inner radius observed on radar and the radius of maximwn wind speed. However, when the wind speed is between 30 and 40 m S-l. the difference between the radii of maximwn speed and radar eye could be as much as 30 km. For slower wind speeds the difference is of the same order of magnitude as the radius of maximum wind speed. STORM SURGE DATA ACQUISITION 7 2.3 Operational tide and surge data Tidal and surge observations are usually made at such locations as fixed tidal stations along shores, inside bays and on intercoastal waterways. The location of a tidal station should be chosen to satisfy the following conditions: (a) Unhindered communication with the sea with minimum local effects due to freshwater flow or irregular topography; (b) Sufficient depth of water even at extreme low waters; (c) Comparatively solid sea bottom; (d) Location sheltered from storm waves; (e) Minimum effect of littoral drift. It is important to measure regularly the height of the datum for tidal observations by precise levelling of the tidal station to geodetic bench marks. It is desirable for the levelling to be made once a year for primary tidal stations. 2.4 Water surface elevations of bays and estuaries The water surface elevation in a bay or estuary will provide the lower boundary condition in any river model. The level is a combination of factors including tide, sea-level anomaly, forerunner and initial rise. Locations for recording gauges are similar to those for tidal stations. Summary information that is likely to be computed from the record includes the mean low water, sea-level datum and mean high water. Note that the contours and soundings on bathymetric charts conventionally relate to local mean low water and not necessarily to the common datum used by tidal and other stations. It is of course essential to tie in the two sources to a common datum. In the United States, the National Ocean Survey (NOS) provides the mean low-water level in several bays and estuaries. The corresponding source of oceanographic data for UK waters is the Marine Information and Advisory Service (MIASl, which was set up to make oceanographic data, information and advice available to industry and research. The latter data base is held at the Institute of Oceanographic Sciences, Bidston, Birkenhead, UK. 2.5 Bathymetric characteristic of rivers, bays and estuaries This characteristic refers to depths of rivers, bays and estuaries or the continental shelf of an ocean. The spatial distribution of water depths, called the depth field, is one of the most important factors in surge generation. If the depth of river, bay, estuary or ocean is wide and shallow, the coastal region is susceptible to higher surges than in regions where the shelf is narrow and steeper. The offshore bathymetry can give an indication of the storm surge potential. Valuable information on the complex tidal behaviour of bays and estuaries can often be obtained from the verbal records of local inhabitants, especially fishermen. 8 CHAPTER 2 2.6 Coastal plane topography As well as the marine survey, it will be necessary to have accurate survey information on the coastal plain. This should include any impediments to the surge such as coastal protection works, wave walls, and road and railway embankments. Surveys should also include properties at risk, together with the salient levels. Particular note should be made of local information on the extent of past flood events. 2.7 Stages and discharges in rivers The stage of a river is the water surface elevation at a point along a stream, measured above an arbitrary datum. The datum is normally taken as the mean sea-level. The readings that are taken periodically are either by manual or automatic recording gauges. For real-time forecasting there must be some means of transmitting the stage to the forecast centre. If required, the stage is converted to a discharge by a stage discharge relationship (often termed the rating curve). The relationship is calibrated by a regular programme of current meterings of simultaneous flow and stage observations. Such a curve is approximately parabolic, or else linear, on double logarithmic paper. Detailed guidelines on observational practices are to be found in many textbooks and manuals including the WMO Guide to Hydrological Practices. In a tidally affected river the uniqueness of the stage discharge relationship will be lost. However, it is often possible to construct an approximate relationship for a given downstream stage if a sufficient number of current meterings are available and the estuary level is also read simultaneously. Efforts should also be made to derive a roughness coefficient for the river. This will be required for the models to be described in subsequent chapters. Again, techniques for this are to be found in hydrometric manuals such as the WMO Manual on Stream Gauging (WMO-No. 519, 1980). 2.8 Wind velocity and direction and its temporal distribution Because wind is the main generating force in storm surge generation, it represents one of the key data requirements for development and operational use of most models for the prediction of water surface levels in lower reaches of rivers subject to major tidal effects. Wind is defined as the temporally averaged spatial distribution of velocity near the water surface. The wind field for a tropical cyclone can be separated into tangential and radial. The wind distribution in a horizontal plane is a function of the location relative to the centre of the storm. There are two principal means of describing the cyclone's wind field: (a) In terms of central pressure, forward speed, radius to maximum winds and track; and (b) Spatial distribution of wind velocity and pressure. These are developed from information gathered by aircraft, radiosondes and radar. STORM SURGE DATA ACQUISITION 9 2.9 Precipitation and its areal and temporal distribution Tropical cyclones produce large amounts of rainfall. Extra-tropical surges also are associated with rain-producing weather systems. While rain does not have a direct influence on the surge magnitude in the sea. its influence on the river and its coincidence with the sea surge can create critical conditions. Statistical information required for design work is obtained from climatological reports. Information should include depth-duration-frequency data. areal reduction factors and temporal patterns of past major events. For forecasting purposes. rainfall data from raingauges upstream of the surge-affected reach will need to be transmitted to the forecast centre. This may not be possible in tropical cyclone conditions from small flashy catchments but on medium-sized catchments the longer lead time that a rain-based forecast can offer will be found invaluable. 2.10 Methods of observation This again is a brief overview only and concentrates on instruments with which hydrologists may not be familiar. 2.10.1 ------Tidal staff The simplest method to obtain tidal data is the use of a tidal staff. This is a long board or pole standing vertically in the water near the shore. and fastened to a pile or other suitable support. It is graduated upwards from a datum line. The height of the tide is read every hour. or more frequently if necessary. Because the sea surface is always disturbed by wave motions. it is a difficult task to interpolate a smoothed tidal height from the staff readings. A more precise method of tidal observations is the use of an automatic float- or pressure-type tide gauge. Float-type tide gauges are widely used as standard instruments for continuous and accurate observation of tides. Many of them are of the roll type in which the rise and fall of the tide is recorded by a pen moving on a rotating drum. The instrument is installed atop a tidal well. and sea water is conducted into this well by a tube which damps out the wave action. The variation of sea-level in the well is measured by the vertical motion of a float and recorded on a self-recorder. These gauges are soundly structured. have moderate instrumental errors. and are convenient for long-term recording of observations. Pressure-type tide gauges measure variation of sea-level from water pressure variation by a bellows placed on the sea bottom. While it may be possible to avoid using a tidal well. and although it is easier to instal than a float-type gauge. observations by a pressure-type tide gauge are in general slightly less accurate. Details on the operation of tidal gauges are available in the WMO report Present technigues of tropical storm surge prediction. 10 CHAPTER 2 The working portion of this gauge is a glass or vinyl tube 2 cm in diameter, with closed ends. This tube is connected through a small hole to the outer air, and a sheet of tide-test paper is enclosed in the tube. The gauge is fixed to a land object by wires, and the hole is faced landward of the sea in order to avoid unfavourable effects of waves and spray. If seawater floods the tube through the hole, the tide-test paper below the water level will change colour. Data from these gauges are, in practice, post-surge. Because this gauge is simple and inexpensive, a number of them can be set up at various places and at various altitudes to give a detailed pattern of flooding. Remote recording tide gauges of various types (transmitted either by wire or radiol are now operational in several countries. Both analogue and digital transmissions are possible. In Japan, for instance, there are three integrated systems for digitized tidal records at several stations. They are transmitted through a radio channel of 400 11Hz and received at forecasting centres for recording in analogue form on rolls of paper. Some other data, such as wind and wind waves, are also transmitted to centres. The UK class A network is being converted to an interrogable system using telephone-line transmission to a central computer at Bidston near Liverpool. The wind velocity and direction are those experienced near the water surface; therefore, the data that are needed are those unaffected by structures and local land topography. CH APT E R 3 FLOOD MODELLING IN TIDAL AREAS - THE DETERMINISTIC APPROACH 3.1 Introduction This chapter and the next are concerned with surge modelling for tidal rivers and f1uvia11y affected estuaries. In this chapter we focus on the deterministic approach. In Chapter 4 we consider procedures of an empirical and a statistical kind. 3.2 The deterministic approach Deterministic procedures are based on the hydrodynamic equations of unsteady flow applied to the open sea and the connecting bay, estuary or river. These are coupled with a hydrological model for determining the river's response to observed or predicted precipitation and antecedent condition over the river basin. Summary descriptions are offered of types of deterministic models used for surge forecasts, as these are likely to be unfamiliar to hydrologists. Equivalent details of conceptual and hydraulic models for river processes are not included as they will doubtless be familiar to readers of this report. 3.3 Model structure Prediction of the combined effects of upstream-generated floods and open-sea-generated storm surges can be mathematically modelled by analysing the phenomenon in three parts as illustrated in Figure 1. The first part is the open sea, wherein the surge is generated and through which it propagates to the coast; the second part consists of the bay, estuary or river connected to the open sea, and the third part is the drainage basin associated with the river. The combined effects of storm surge and flood occur within the bay, estuary or river. The unsteady flows and/or water surface elevations occurring within each of the three parts must be modelled; however, they may be modelled separately by judicious selection of the upstream and downstream extremities of the bay, estuary or river (portion A-B in Figure 1). Each part will be treated separately. 3.4 Open sea models There are several techniques for surge prediction. In the present state of the art none is capable of solving simultaneously all aspects of the problem, for example the prediction of peak level as well as space and time variation of open water and inland surges. Techniques to be discussed in this chapter range in sophistication from nomographs to full solutions of the controlling partial differential equations. Selection of the appropriate model is a matter for the forecaster who must take account of the skills and data available to him, as well as the range of applicability of the models. 12 CHAPTER 2 NYDROlOGIC .00El ------ BAY, ESTUARY, OR RIVER NYOROOYU ••C .00El OPEN SEA NYOROOYU.IC SURGE .OOEL Figure 1 - Schematic of combined storm surge and flood phenomenon 3.4.1 The effect of storm surges can be described by the two-dimensional vertically integrated hydrodynamic equations of unsteady flow, including atmospheric pressure, wind stress and bottom friction terms. Flather (1981) has expressed the equations in spherical co-ordinate form for use in the United Kingdom continental shelf sea model (CSM): FLOOD MODELLING IN TIDAL AREAS - THE DETERMINISTIC APPROACH 13 a~/at + (l/Rcos$) [a(Du)/aX + a(Dvcos$)/a$] = 0 au/at + (u/Rcos$) (au/aX) + (v/Rcos$) [a(ucos$)/a$] - 2 oosin$.v = - (g/Rcos$) (a~/ax) - (l/pRcos$) (apa/ax + (l/pD) (F s - FB ) av/at + (u/Rcos$) (av/ax) + (viR) (av/a$) + (uZtan$/R) + 2 oosin$.u =- (g/R) (at/a.) - (l/pR) (apa/a.) + (l/pD) (G s - GB) where the notation is: = east-longitude and latitude, respectively; = time; = elevation of the sea surface; u,v = components of the depth-mean current q; D = total depth of water (= h + t); h = undisturbed water depth; R = radius of the Earth; 00 = angular speed of rotation of the Earth; g = acceleration due to gravity; p = density of sea water, assumed uniform; pa = atmospheric pressure on the sea surface; Fs, Gs = components of the wind stress ~s on the sea surface; FB, GB = components of the bottom stress ~B. These equations are analogous to the momentum and continuity equations used in flow routing. Depth averaging is a simplifying assumption applying to cases where current variation with depth is not a significant factor. A bed friction and a surface friction law must be incorporated in the model. The former may be related to the current velocity and the latter to the wind speed. Boundary conditions at the coast must also be imposed and the equations are converted to finite difference form for solution. The main time-varying inputs are the undisturbed water depth, the atmospheric pressure, and the wind-induced surface stress. The astronomical component of tide is described using the most important harmonics. Weather maps or output from an atmospheric model provide the pressure and windfield inputs to the model. 3.4.2 The SPLASH model was developed for the United States National Weather Service as a forecasting model for hurricane-induced surges (Jelesnianski, 1976). The model defines the required tropical cyclone windfield from input parameters of cyclone. Properly smoothed water depths are a pre-prepared input to the calculation. The storm surge and astronomical tide are considered additive for open coast forecasts. However, the actual output consists of separate surge residual and normal water surface elevation, thus allowing maximum flexibility for recombination by the model user. This model has been specialized into nomogram form for landfalling storms. They are based on standard tropical cyclone and bay parameters and allow very quick assessment of the peak surge level. Routine storm surge forecasting in the UK by the Storm Tide Warning Service employs a numerical model developed by the Institute of Oceanographic 14 CHAPTER 3 Sciences (Flather (1981), Proctor and Flather (1983». The climatic inputs are taken from atmospheric model outputs. The numerical solutions are presented in the form of forecast tide and surge residuals for specified ports around the UK coast. Submodels allow the details of bays to be modelled at appropriate grid sizes and time steps. The SSURGE model was developed for use in the design of coastal protection projects. It is also based upon the hydrodynamic eguations and reguires tropical cyclone parameters as input. The grid size and bay geometry are more flexible than those permitted in the SPLASH model. The United States Federal Insurance Administration (FIA) surge model was developed for flood insurance purposes and differs from the SSURGE model in its coastline description. Bathystrophic models use a simplified form of the governing eguations in which the continuity relation can be omitted. They are generally used for design purposes. More complex three-dimensional models have also been used for studies where the vertical distribution of current is important. However, the effect can safely be neglected for predictions of storm surge elevation. 3.5 Bays and estuaries For a river emptying directly into the sea (e.g. the Mississippi), the hydrograph at the mouth including astronomical tide, predicted by a continental shelf model (or by some other method), becomes the boundary input (Fread, 1974). Where the stream empties into a bay or estuary, modification of the oceanic storm surge within the bay must be taken into account. The state of the art is to do this with a two-dimensional vertically integrated hydrodynamic model using a separately computed ocean storm tide hydrograph as boundary input (Reed and Bodine, 1968). A model of this type was also developed for Apalachicola Bay, Florida (Overland, 1975). A "one and one-half" dimension model was developed later for the Cape Fear River, North Carolina (Overland and Myers, 1976). Researchers are working on complete interactive models in which estuary and bay effects are allowed to influence nearby ocean water levels. The SLOSH model (Jelesnianski. 1981) is an example of such a model designed for continental shelves, inland terrain and inland water bodies. Limited accuracy only is possible over inland terrain due to the complexity of natural and man-made impediments such as dunes, ridges and railway embankments. The above-cited models are designed to predict water levels. Many other models for various bays have been developed, primarily for evaluation of circulation. The basic physics for circulation models and water level models is, of course, the same; but different approximations and linearization steps are generally applied to focus on the desired result in an economical manner. The more comprehensive models of either type could be adapted to the other. Hinwood and Wallis (1975a and b) have published papers on the classification and review of models of tidal waters. 3.6 River models All rivers have a transition zone between an upstream point where river level is determined by river discharge, to a lower point where sea-level is predominant. Between these points the analysis of flooding reguires a joint treatment of the two phenomena. In the following paragraphs we FLOOD MODELLING IN TIDAL AREAS - THE DETERMINISTIC APPROACH 15 introduce some general considerations relating to the joint phenomena, and also some possibilities for deterministic modelling of the interaction. The construction of conceptual models of the rainfall-runoff process is not considered in detail, as this topic is very adequately covered elsewhere (WMO, 1975) • 3.6.1 An important distinction arises between the tropical and extra-tropical situations; although much more intense, the rainfall floods ar~s~ng from tropical cyclones are much more limited in extent than the low-pressure systems associated with extra-tropical surges. Thus, only small regions adjacent to landfall will respond, but this response will very probably coincide with the most severe portion of the surge. If coincidence occurs in the larger, longer 1ag-time basins affected by extra-tropical low pressure. systems, it is probable that the cause of the flood was due to an earlier event. Thus, we can list the following sets of conditions as critical for joint fluvial and surge flooding: (a) In small islands subject to hurricanes, such as the Philippines, Japan and the West Indies, where river response times are short; (b) Where antecedent conditions have predisposed a larger river to flood and this coincides with a sea surge. This can occur in both tropical and extra-tropical locations. As an example of the former, a stationary front often lies over Japan in September and early October; the saturated conditions and regular rainfalL often intensified by a typhoon, lead to regular coincidences of floods and surges; (c) Where human activities have shortened the lag time. Examples are reclamation of the swampy areas in the flatter coastal reaches of a river, or urbanization creating a rapidly responding subcatchrnent. 3.6.2 ~o~s~b~l~t~e~ fOE ~YQr~uli£ ~oQel1~ng ~f_t~d~l_a~d_flu~i~l Ei~eE f1~Qi~g Steady state models have often been applied to tida11y affected river reaches using the bay level as the lower boundary condition. However, this is only a partial solution to a problem which includes dynamic aspects deriving from rapidly changing downstream conditions, due to the astronomical component of tide, as well as the considerable mass transfer of water under tidal and surge influence. Another very simple approach is to add the surge residual as a constant extra level to the river's normal surface water surface profile. This too can be inadequate as, depending upon the form of the river, the surge may be amplified or attenuated. 16 CHAPTER 3 3.6.3 ~x~m21§. Qf_m§.t!!os!s_u.§.i!!g_n~.§.ric~l_i!!t.§.gEa.!:.iQn_o!: the !!ys!r~uli~ .§.q~a!=iQn.§. Advanced techniques use numerical integration of the hydraulic equations. Examples from Japan and USA follow. (a) Japanese example The form of the equation appropriate to the tidally affected river is: l/[g(D+h)].(aMx/at) + ah/ax + (l/pg)(ap/ax) - (T sx - Tbx)/[g(D+h)] = 0 l/[g(D+h)].(aMy/at) + ah/ay + (l/pg) (ap/ay) - (T sy - Tby)/[g(D+h)] =0 ah/at + aMx/ax + aMy/ay = q where: M = the mass transport or the discharge at the unit width; h = the water level; P = the atmospheric pressure; Ts = the wind stress; Tb '" the bottom friction; D = the depth of water; q = the local inflow per unit water surface; x and y = horizontal axes. In the lower reach of the river, only the x component is available. The first two equations are equations of motion, where the first term is the inertia force, the second the surface gradient, the third the atmospheric pressure (suction) gradient, the last the tangential stresses including the surface and bottom stresses (frictions). The third equation is an equation of continuity, where the first term is the time increment of the water level, the second and third terms are mass convergence and the right-hand side is the local inflow (sink or source). The given terms are the boundary conditions such as p, the pressure distribution of a cyclone; Ts , the wind distribution with a known wind stress coefficient; q, the inflow determined by the discharge of the flood generated upstream. As the initial condition, Mu My and h are given at t=o, Tb is a function of M and (D+h). The unknown parameters Mu My and h will be solved at every instant. The bay, the estuary or the lower reach of the river is divided into segments as shown in Figure 2. Mu My and h are obtained step by step at each segment, by a digital computer or an analogue computer. (b) United States National Weather Service method The National Weather Service (NWS) provides real-time forecasts of the unsteady flows and water surface elevations FLOOD MODELLING IN TIDAL AREAS - THE DETERMINISTIC APPROACH 17 in such coastal rivers as the Mississippi, Columbia, Sabine, Neches and Trinity. To compute stages and discharges, a one-dimensional, implicit hydrodynamic model (DWOPER) is used. Subsequent sub-sections present a brief description of the DWOPER model and how it utilizes a river-ocean interfacial boundary to account for ocean effects. Model applications, efficiency and calibration are also discussed. ~~:4..11, ,!la", ir" Illl'" ,, II.~" li • ".'" " " ~, 't , t7 .. JI )2 ~ ,. "1'l AI" <4\ " " " ~ ~.. • 4~ ~ ..., ...... 51U5ol~'i~' ~ SI 51 59 &0 ,. .... " ~ , ~ 0 6B 119,,TO ., iIlOr ~ " .~ ...... , ..~ U !t/VII! .. .. • 0 .. .. ~ .ll • • " '" Pacific Ocean Figure 2 - Computational meshes in Tokyo Bay The DWOPER model is a generalized one-dimensional hydrodynamic model developed by Fread (1974, 1979, 1980) for use in river systems where simple storage routeing methods are inadequate due to the effects of backwater, tides, and mild channel bottom slopes. The basis for the model is a finite difference solution of the one-dimensional equations of unsteady flow consisting of the conservation of mass and momentum equations. These are: 18 CHAPTER 3 aQ/ax + a(A+Ao)/at - q = 0 where: 2 2 4 3 SE = (n 'Q'Q)/(2.2l A R / ); Se = (K./2g) [a (Q/A)2/8x]; WE = Cw (V r cos 00)2 in which: x = distance along the longitudinal axis of the waterway; t = time; Q = discharge; A = active cross-sectional area; Ao = inactive (off-channel storage) cross-sectional area; q = lateral inflow (+) or outflow (-); g = the gravity acceleration constant; h = water surface elevation; B = wetted topwidth of the cross section; V x = the velocity of the lateral inflow in the x-direction of the main channel flow; SE = friction slope computed from Manning's equation; n = the Manning roughness coefficient; R = hydraulic radius approximated by (A/B); Se = the local loss slope; Ke = an expansion (-) or contraction (+) coefficient; WE = the wind term; Cw = non-dimensional wind coefficient; Vr = the velocity of the wind (Vw) relative to the velocity of the channel flow; 00 = the angle between the wind direction and channel flow direction. In the implicit finite difference solution the continuous x-t solution domain in which solutions of hand Q are sought is represented by a rectangular net of discrete points. The net points (nodes) may be at equal or unequal intervals along the t and x axes. Each node is identified by a subscript (i) which designates the x position and a superscript (j) for the time line. A four-point weighted, implicit difference approximation is used to transform the nonlinear partial differential equations of unsteady flow into nonlinear algebraic equations. The four-point weighted difference approximations are: K = 0.5 8 (Kl+ 1 + Kl:l) + 0.5 (1-8) (Kl + Kl+1) FLOOD MODELLING IN TIDAL AREAS - THE DETERMINISTIC APPROACH 19 whe ...e: K = a dummy pa...amete ...... ep... esenting any variable in the above diffe... entia1 equations; e = a weighting facto ... va...ying f ...om 0.5 to 1; i = a subscript denoting the sequence numbe ... of the cross section of /lx reach; and j = a supe...script denoting the sequence numbe ... of the time line in the x-t solution domain. In DWOPER, the upst eam bounda...y may be a specified discha...ge 0 ... wate ... su face elevation (WSEL) hyd...og...aph fo... each rive.... On the main stem, the downst... eam bounda...y condition may be a WSEL hyd...og...aph, discha...ge hydrog...aph, 0 ... a known ... e1ationship between the WSEL and discha...ge, such as a ...ating cu...ve. In the case of a ...ating cu...ve bounda...y condition, the ...ating may be single valued 0 ... it may also be a loop ating cu...ve gene...ated inte...na11y f ...om c ...oss section and oughness p...operties of the downstream bounda...y and the instantaneous wate... su...face slope at the p ...evious time step. In addition to the va... ious bounda...y conditions, DWOPER has a numbe of featu... es which make it applicable to a va... iety of natu a1 ... ive... systems fo ea1-time fo... ecasting. It is designed to accommodate i egu1a... c ...oss sections located at unequal distances along a single mu1tip1e-... each rive... 0 seve...a1 such rive... s fo ...ming a dendritic 0'" fi ...st o ...de... t ee-type configu...ation. It allows fo...... oughness pa...amete...s to va...y with location and WSEL 0... discha...ge. Tempo ...a11y va...ying inflows, wind effects, bridge effects, off-channel sto...age, levee ove...topping and/o... c ... evasse flow a ...e included among its featu... es. An efficient automatic ca1ib...ation p ...ocedu e fo... dete...mining optimum Manning n-WSEL 0'" discha...ge e1ationships f ...om obse...ved data is also provided as an option in DWOPER (Fread and Smith, 1978). Data handling requi...ements fo... day-to-day ... ive... forecasting a ... e minimal due to extensive data management features (Smith, 1978) utilizing disk sto...age. Howeve ... , preparation of the data fo... river system configu...ation, c ...oss sections, and the like must be determined and the data p ...ovided as input. Also, stage and discha...ge data for the boundary and initial wo ...k cannot be avoided; however, the data management module does substantially ... educe the time and effort ... equi ... ed to use the model on a day-to-day operational basis. The data initially provided 20 CHAPTER 3 to simulate a particular river system are stored on disks, and only the updated information for boundary conditions need be provided before making a new simulation. In coastal rivers, the channels tend to have very flat slopes of less than 1 in 2 500 and wide floodplains which are usually protected by levees. When a flood wave is routed down the channel and the tidal effects are minimal, as in rivers flowing into the Gulf of Mexico, the effects of the ocean tide may be ignored and the flood wave dissipates rapidly as it propagates into the ocean. Real-time forecasting for this condition occurs for a reach of the lower Mississippi River extending from Vicksburg to a section in the Gulf of Mexico which is 37 km below the Head of Passes. The downstream boundary condition of a specified time history of elevation should be for a section so located that the river flood does not significantly affect it. Thus, the downstream boundary for the Mississippi River is located approximately 16 km into the Gulf. "The boundary condition is considered to be a constant water elevation (mean sea-level) with time. If this condition were imposed for a river section at the Head of Passes, the flood wave at sections in the upstream vicinity would be underpredicted. To help control flooding on the Mississippi River, three division control structures are used to divert water from the main channel. DWOPER has the capability of modelling the flow diverted from the channel. Moreover, this reach of the lowr Mississippi River is contained within levees for most of the length, although some overbank flows occur along portions of the upper 336 km. The average channel bottom slope is a very mild 1:35 000. A total of 42 croos sections located at unequal intervals ranging from 3 to 50 km were used to describe the 736-km reach. The reach was first automatically calibrated by DWOPER for the 1969 spring flood using a 24-hour time step. The RMS error varied from 5 to 11 cm with an average value of 8 cm. Several historical floods from the period 1959-1971 were then simulated using the calibrated Manning n values obtained from the 1969 flood. The RMS error for all the floods was 14 cm. DWOPER is currently being used for real-time forecasting on the 209-km reach of the lower Columbia River below Bonneville Dam, including the 40-km tributary reach of the lower Willamette River. A schematic of the river system is shown in Figure 3. The downstream boundary for this system is a tide hydrograph. These tides are obtained from a predicted tide table produced by the National Ocean Service. During a forecast period the tide values are updated manually to reflect current observations. FLOOD MODELLING IN TIDAL AREAS - THE DETERMINISTIC APPROACH 21 This reach of the Columbia has a very flat slope and the tidal effect extends as far upstream as the tailwater of Bonneville Dam during periods of low flow. Reversals in discharge during low flow are possible as far upstream as Vancouver. A total of 25 cross sections located at unequal distance intervals ranging from 0.8 to 20 km are used to describe the river system. One-hour time steps are used in simulations. (IIVEI IM 234.1) 10UEVIlLE OAM 1 2 ..•... nllEIIALE 1 .. • 4 • • WasllUUl 5 ...c • 1 el"EI IM 171.1) VUCllnl 7 1 'IITUI. .IE••I Cl TV FAllS 1 / (IIVEI IM 11.2) 1 =:H~-+---f---"--I 11 1 4 2 1 11 Cll••IIA 12 • WILUIETTE IIIVEI 11 IAIIIEI 14 .. ..•... 11 • • • elllEl I .....) WUIA 11 ...c • 17 11 11 (IIIEI I. 21.1) TllalE PlIIT 2. Figure 3 - Schematic lower Columbia-Willamette River System CH APT E R 4 FLOOD MODELLING IN TIDAL AREAS - THE EMPIRICAL APPROACH 4.1 Introduction Like the deterministic models discussed in the previous chapter, empirical procedures have as their object the calculation of surge levels within rivers, estuaries and coasts. The two approaches differ in that empirical procedures do not explicitly represent the physical processes governing water behaviour in the river and estuary systems. Instead, use is made of the observational data that must be available at the sites of interest to calibrate a predictive relationship between surge level and observable causative factors such as minimum pressure and river discharge. The empirical relationships can be purely statistical, such as a regression equation, or they can be simplified versions of physical relationships. Both types are described in the sections which follow. 4.2 Merits and problems of the empirical approach Most practical forecasting procedures in use today make use of empirical relationships established between the peak level at the site of interest and observable meteorological factors. This popularity is due to their ability to provide forecasts of adequate accuracy without the need for mathematical skills of a high order, for expensive and possibly unreliable computer resources, and for exhaustive hydrographic and hydraulic surveys. Empirical models are also well suited to statistical studies needed for design purposes because their simplicity makes it feasible to make multiple determinations of results from different input conditions. In fact, in the current state of the art, the deterministic model still is no more accurate than an empirical model. However, the deterministic model provides a more complete answer to the surge prediction problem. The full spatial and temporal profiles of surge levels are provided. This could not be achieved with the empirical approach,nNor is an empirical model as portable or capable of accomodating changes to the characteristics of the water body; it would need recalibration for each new site and for each new set of conditions. In principle; all that the deterministic model needs is to be "fed" the physical constants and boundary condition relating to the new site. In practice, calibration is essential and the "feeding" of new constants represents a major investment in survey data. 4.3 Empirical models for coastal surge calculation As with the deterministic approach it is necessary to estimate the coastal surge which can then act as the lower boundary condition for the river surge calculation. The majority of practical surge-warning systems employ the empirical approach. For example the United Kingdom Storm Tide Warning Service (STWS) started after the disastrous North Sea surges (see section 7.8) by 26 CHAPTER 4 applying regression relationships with peak levels at selected reference ports on the North Sea coast using observed pressure and wind speed as dependent variables. Although much improved since then, the same basic philosophy is used in current forecasts even though, since 1978, the forecast centre has operated in parallel a fully deterministic ocean and atmospheric model. As well as this UK procedure a number of others will help to illustrate the approach and to highlight data requirements as well as limitations . Ca) !:!o!!g_KQng !!a~bQu£: Prediction equations as quoted in WMO (1978) were used to forecast maximum surge(s) from maximum gust, 10- and 60-minute wind speeds and minimum sea-level pressure (P). The last, for example, took the form S = 87.16 + 0.085P. After 1977 the SPLASH model replaced this simple approach. (b) ~a£a!!: Practice varies from district to district. Complex models based upon standard patterns of typhoon (tropical cyclone) track are used in the more populated areas, but simple models are applied elsewhere. For example, use is made of an expression of the form S = A(po-p)+Bv2 cose where the (Po-p) term relates to pressure differential, v is wind speed, and cose adjusts for the inclination of the bay or inlet to the wind direction. Theoretically, A should lie close to unity, but coefficient B is found to be very variable and site specific and so needs calibrating from local data. (c) ~ay Qf_B~ngal: A somewhat similarly structured relationship has been employed for surge forecasting in this high-risk area. In this instance the coefficients were fixed by repeated application of a numerical model. Inaccuracies in this area have been ascribed to the interaction between tide and surge so the superposition assumption does not strictly hold. (d) ~h~lipl2i!!e.§.: Numerical models have been applied to some important coastlines and have been used to calibrate the simple expression: where Sp is the initial estimate from a nomogram for standard typhoon (tropical cyclone) conditions and Fb and Fm are correction factors to allow for wind direction and for shoaling. Of these, the shoaling factor must be determined for each bay and is achieved by regression equations with 12 point depths at fixed intervals perpendicular to the coast. The latitude also enters the equation. To date, this procedure has been used to assess surge risk and for coastal defence measures and has not been used in an operational forecast. FLOOD MODELLING IN TIDAL AREAS - TIlE EMPIRICAL APPROACH 27 (e) ~e~ign__s~rge~ fo~ ~u~t~a!i~: Sylvester and Mitchell (1977) present an interesting application of the use of empirical formulae to derive design maxima for the entire continental coastline. The basic formulae could be described as semi-empirical in that, although they are not full solutions of the hydrodynamic equations, neither are they dependent upon local calibration except at the final validation stage. The authors make the very cogent point that the sophistication of the model should be commensurate with the quality of the wind data being used. The coastline of Australia is segmented into 41 reaches and each is designated a representative shelf profile in terms of its breadth and ocean and coastal ,depths. Distinctions had to be drawn between coasts subject to tropical and extra-tropical storm surges, and maximum parameter values were inserted into governing expressions for design-surge maxima. These resemble the Colding formula (section 1.5) but take account of the shelf geometry. Some coastal stretches require detailed attention. Of interest here is the analysis of two south coast gulfs. These are triangular in plan and wedge-shaped in section and were treated using Keulegan' s (1952) amplification factor formula. The maximum surge at the head of Spencer's Gulf was computed to be 410 cm compared with 65 cm at the mouth. The final stage in the analysis consisted of a comparison between derived surge and observed historical surges in the same segments. 4.4 River surges 4.4.1 ------General considerations Few examples are to be found of studies relating specifically to the forecasting or assessment of surge effects in, rivers. As with the deterministic approach it is possible to build a river model adopting as its downstream control the computed coastal or estuary surge level. An empirical approach is possible in which the river stage is related by regression or similar methods to the causative river discharge and downstream surge. It would also be possible to combine the river and estuary models by eliminating the estuary level term and regressing directly on such factors as minimum pressure and maximum wind speed. 4.4.2 Rivers are small compared with the adjacent ocean region. The tidal energy of the river can therefore be regarded as originating in the estuary and arriving at the river mouth as a specifiable boundary condition. The theory that has been applied has related mainly to idealized estuaries and has discussed the surge in terms of standing waves, progressive waves or possible resonance effects. As a general statement, frictional damping becomes the dominant influence in long narrow water bodies of low depth. This is the factor most difficult to assess accurately in hydrodynamic computer models as well as in empirical formulations. 28 CHAPTER 4 It is possible to make a preliminary estimate of the length of river subject to a tidal as well as fluvial influence by examining the water levels during the low-tide period. If water levels fail to respond to upstream floods then the location is tide-dominated. Conversely. river domination can be assumed for a location which displays small response when the flows are moderate. The stretch between these lim~ts is the interaction zone and is the focus of attention of this section. The key to quantifying and modelling this zone depends on being able to define a unique interaction. The simplest form that this can take is shown in Figure 7. This will be recognized as a generalization of the familiar rating curve in which the various curves relate to different downstream estuary levels. This form is ideally expressed for a rapid assessment of the flood level. It must be realized that such a graph is limited in its appl-ication to peak levels; it conveys no information on the build-up or decay. nor on the longitudinal water surface profile. The derivation of the graph requires a good record of river level as well as an estuary gauge and an upstream gauging station. Alternatively. an extended programme of current meterings and coincident level recordings would be needed. This would be exceedingly hard to achieve in a low tidal range region where high marine levels were achieved only during rare storm surges. In general. the regions subject to extra-tropical surges do not suffer this drawback. A more revealing expression of the same information is shown in Figure 8. which shows interaction zone contours as a function of the same variables. This diagram clearly illustrates the diminishing surge and tide influence as one progresses upstream. Figure 9 for the River Severn in the UK shows a more complex pattern in which the control of the shape and spacing of the lines shifts from peak to volumetric influences and back again depending upon the performance of flood plain storages upstream. In the forecasting system for Chester on the River Dee in the UK (Weston. 1979) another variant of the diagram is used in which level in the interaction zone is read off a graph as a function of sea-level with river discharge as a parameter. These forms of the diagram are no less limited by input data than Figure 7; all express an approximate relationship between peak flow and maximum surge or tide level in the estuary. In reality. the level at any instant is the product of the entire recent. history of discharges and estuary movement. Typical accuracies for such diagrams lie in the region of 20 cm to 30 cm and it is likely that these cannot be improved upon within the framework of the model's simple derivation. 4.4.3 Is it possible to circumvent the need for exhaustive data sets to draw interaction diagrams? Even with relatively plentiful data. there will often be a scarcity at high tide and flood levels so some form of model would doubtless be required to extrapolate the curves. Numerical models are one possibility that has already been discussed. Physical modelling is another possibility. but this is increasingly being overtaken by computer models for such purposes. A third idea is to recognize the possible mathematical structure of the interaction curves and then to use multiple non-linear regression to estimate their parameters. A fourth method entails recognizing the physical characteristics of the interaction process. Simplified physically based models can be derived and optimized using limited data. r ~ i ..! 1.1 ;;w ~ • ;= • ~ =~ .._ 4•• ~ w .... :: !2: -:: ....~ =• ~ •••• TIlE LUIU •• IIT,AIr •• In.u UlIE ••••uel UTlI (11.1 I" I ~ ~ .... ::tl 2.1 ~ I 1 01 I I I I I I IIII, , I • 0 M H H " N • IIIC1AIII •• '"E1 .EI.IIf .'.1-1 ... •c'" ~ 200 ~ - se.OOIlNOU. •'" TUIIIlION ZOIE •c » 5111 1_ 15_ , ..... • C.. ...~ ...» 0 ~ ... 2• ..'" 1. VlEElWOK • '" IIYEI IUIIE Z'NE • • 5011 10GOl 11000 , 801• .. E AUUM ~""""''-';;==-'''''''''-7."~...l-l-=-~..L.J....L..J1I VEl lEgliE ZONE 5000 10000 15081 Q DISCHARBE OF THE llVEI IHINE AT LOtlTH IN .2. 5- 1 Figure 8 - Curves of discharge-tide level combinations causing certain stages at gauge stations along the Lower Rhine-Lek-Rotterdan waterway FLOOD MODELLING IN TIDAL AREAS - THE EMPIRICAL APPROACH 31 • ..'" •'" .....~ ...... •... co ;;'" , , ,I , , 3'O~'L-~l-~LJ~JuI~IiJ,;~-Ai"---~_J!,JLJue-WUb2LJlIii.L-,-llIlrJuu o ~ ~ • ~ ~ _ ~ _ ~ ~ ~ 1m ~ .EII...n ••••APH IITU D1IC.UGE IM3/1) Figure 9 - Model inputs which give various levels of the River Severn (ilK) at Gloucester Docks 4.5 Physically based formulae 4.5.1 ------Introduction Rivers tend to taper from a wide point at the mouth, becoming progressively narrower through the interaction zone. The tapering will have an amplifying effect on the tidal or surge wave but this will be counteracted and eventually overtaken by frictional drag. Flow processes are considered first, followed by the wave propogation upstream from the river mouth, and then the two effects recombined. An illustration of the use of the theory is given. 32 CHAPTER 4 4.5.2 Under steady flow conditions and in the absence of tide or surge the effect of the widening channel would be to diminish river levels in the downstream direction. Similarly, variable river flows such as are asssociated with the passage of flood waves will tend to be friction-dominated and will follow the same stage-discharge relationship. This is in accordance with kinematic wave theory. If it can be argued that the long ebb period between successive tides permits the low water levels to return to the steady-state relationship followed by the river alone, then a stage-discharge relationship can be constructed for the interaction zone. The stage at the point of interest is plotted against the lagged river discharge measured at an upstream gauging stat·ion. The lag time is determined from the time of travel of flood wave peaks which in turn can be estimated from the velocity of a kinematic wave (i.e. 1.5 times river velocity). This velocity should preferably be based on the high flow range. 4.5.3 It is common to find that estuary tidal waves are distorted from the relatively symmetric shape of an ocean tide. Surge will further distort the shape. In general, the rising limb is abbreviated and the ebb is prolonged. In some estuaries this is so extreme that the tide steepens into a shock wave or bore. The energy as it enters the river can be specified and its attenuation by friction computed. 4.5.4 The bed level in the river falls only a few metres below the mid-tide level and it is therefore reasonable to restrict the analysis to the positive half of the tidal wave. A shallow water progressive wave propogates at a speed dependent upon water depth and the energy of such a wave travels at precisely the same speed. This equivalence leads to great simplification in the analysis. The tidal wave has to overcome frictional drag and also to climb up on top of the sloping water surface profile which results from the river flow. Therefore, as it moves upstream the tidal wave must increase its potential energy, and yet its total energy is being dissipated by friction. Figure 10 shows a wave in two positions in the river: (a)· at the mouth, and (b) upstream where its mean level is at some height h above datum. The potential energy of an element of the wave of height h above the mean position is ~PE = ~g(n/2+h)b where b is the channel width. Total wave energy is obtained by including the kinetic energy. For a gravity wave the kinetic energy must equal the potential energy measured relative to the n=O plane. The energies at (a) and (b) can be equated to yield E(b) = E(a) - Fb where F is the frictional dissipation per unit area and b is the area of the wave. FLOOD MODELLING IN TIDAL AREAS - THE EMPIRICAL APPROACH 33 ... 0...... !!.. ..•... !! ...... !! ..-< ..;;; "(]) ..•...... :0- •.. 0.." .. ;:l '"' tn ~ <:: ...... , 4.5.5 Professor Quick of the University of British Columbia developed a special case of the above theory to solve a flood frequency problem for a point in the interaction zone of UK rivers. The solution is intended for the case where the astronomical tide dominates although surges can aggravate the marine flood contribution. He assumed that the incoming wave can be approximated by a solitary progressive positive half-wave. The appropriate expression for the energy at a point is E = pgaAb/4 + pghaAb/rr. The half-wave energy is therefore a function of h, the low water profile which results from river flow alone. The wave amplitude, a, is written as X at point (b) and Xa at point (a) and h is written as Y. Hence the energy balance equation is written as pghbb [(X~/4) + (Xb YI1r)] = pgAabaX~/4 - FbbAb and re-arranged as X2 + 4XY/rr = p2X~(l-Kd where p = b.A./bbAb represents Green's wave amplification factor. The replacement of the term 4F/pgpX; by a constant KL can be justified as, although a complex friction factor, it will be found not to vary much for a given estuary; both X and F are proportional to the square of the wave celerity. The final form of the equation for total water level above datum, H, is obtained by solution of the quadratic The formula involves the tide height Xa and the low water river level Y as well as the amplification and friction factors described above. The amplification factor p can be estimated from cross-sectional data for the estuary. The friction factor makes use of the energy equation. Recorded events are used to estimate (l - Kd by least squares. Using this procedure it was possible to explain some 93 per cent of the water level variance at Gainsborough, a tidally affected location on the River Trent with a catchment area of about 8 000 km 2. 4.6 Regression formulae 4.6.1 Some examples of regression formulae were given in section 4.3. These could be developed from observed data or from the output of numerical models. Standard statistical texts should be referred to for information on the theory of least squares regression; here we will discuss issues that relate to the specific application. FLOOD MODELLING IN TIDAL AREAS - THE EMPIRICAL APPROACH 35 The ingredients of the regression relation will be: (a) A dependent variable, presumably the peak surge residual or total maximum water elevation; (b) Independent variables, which may include the observable meteorological quantities, or astronomical and surge residuals in the estuary. They may also include physical parameters such as the friction factor K" of section 4.5.5; (c) Coefficients of the regression equation. Steps in the preparation of a regression relationship are: (a) Identify the dependent variable; normally this is dictated by the application but also by the data that are available; (b) Enter the variables in as near natural a fashion as possible. Transformations should not be used without good justification (as well as entering them individually, interaction between variables can be catered for by including the product of .the variables); (c) Collect enough data to calibrate the equation and estimate its error properties across the range of application, especially high levels. Use Monte Carlo simulation if necessary to supplement error tests by sensitivity tests. A complication that may arise is that the river network upstream of the interaction section may divide. In such cases it may be adequate to include flows from only one of the branches as the other may be highly correlated with it. If continuous records are used it may be tempting to enter very large numbers of events. The time correlation can be a disturbing influence and it is better to reduce the sample size and select events to represent the range of possible combinations. Nor is it necessary to associate maximum surge with maximum discharge. The two are in fact unlikely to coincide and it may be more accurate as well as convenient to use daily mean discharges on the day of occurrence of the surge maximum. If the astronomical tide component dominates the surge then two peaks will probably occur each day. The maximum of the two may be preferred although there is usually a high correlation between the two tides. It is permissible to include current and previous tide and flow variables within the regression equation if significance tests on their contribution suggest it is worthwhile. If the regression is to be used within an operational forecast, it is clearly imperative to use only independent variables that will be available at the forecast centre at the time the forecast is issued. For a study of the River Ouse in the UK, water level recorders were available at four locations down the interaction reach and extras were available in the river estuary. Also available were flow records on each of 36 CHAPTER 4 the two main rivers feeding the reach, the Ouse and the Wharfe. The simple correlation matrix revealed much about the reducing influence of tide upstream (Table 1). TABLE 1 Correlation of water levels in interaction zone with discharge and tide level Interaction zone water level recorders Downstream Upstream Drax Selby Cawood Naburn Discharge .12 .40 .70 .81 Estuary .84 .83 .67 .43 level The distribution of most data showed a slight positive skewness. However, transformation did not obviously improve the error structure and could not be justified on physical grounds. The two flow records were highly correlated and only one was needed in regressions. In the regression equations on the four inteL"action L"each level L"ecoL"ds the incL"easing downstL"eam tidal influence was cleaL"ly reflected in incL"eased regression coefficients. Likewise, the flow L"egL"ession coefficient diminished accoL"ding to expectation. The inteL"action teL"m based upon the simple pL"Oduct of flood dischaL"ge and tide height was significant only at the uppeL"most site (Table 2). In a second L"ound of L"egL"essions the 10w-wateL" level was substituted fOL" flow. This was obtained using the proceduL"e outlined in section 4.5.2. The explained vaL"iance was little affected by this substitution but the inteL"action teL"m gained significance. TABLE 2 Regression on wateL" levels in inteL"action zone Selby Cawood Naburn Log discharge (Q) .74 .98 .93 EstuaL"Y level (X) 1.00 .83 .60 PL"oduct (QX) .0001 .001 .003 Constant -.23 -.24 .63 R2 .88 .89 .82 CH APT E R 5 RISK EVALUATION OF STORM SURGES IN RIVERS 5.1 Introduction Engineers require surge frequency information for flood design purposes in tidally affected rivers just as in inland watercourses or along coasts. Planners recognizing the adverse effects of storm surges have instituted insurance programmes in affected areas. Both need to assess the stage-frequency relationship for the site of interest. An economic evaluation of the consequences of flooding requires knowledge of the extent and period of inundation. If a long water level record is available then this can be analysed to assess directly the frequency of exceedance of any given water level. However, such a condition is rarely achieved and so the statistical distribution of maximum water levels must be derived from the distributions. of causative factors. The considerable body of literature for solving this problem for a coastal site is reviewed briefly; very little has been written, however, about the corresponding problem in tidal rivers. Some advice on an approach to be followed to solve this difficult problem is offered. 5.2 Surge frequency at an open coast The most straightforward case for sea-level prediction occurs at the site of a long-term level record. Even here techniques vary. A fundamental choice exists between whether the full series is to be analysed through, for example, spectral or harmonic methods, or whether the maximum values over a threshold or in a time period are to be fitted to one of the many candidate statistical distributions. In the latter case a distinction can be drawn between methods which treat the data as a single observed data set (Graff, 1979) and methods which attempt to disaggregate the data into an astronomical tide component and a surge component. Separate distributions are fitted to each and the two are then combined to yield the resultant distribution of maximum levels (Pugh and Vassie, 1980). The WMO report on techniques of tropical storm surge prediction (WMO, 1978) provides an entree into the extensive literature on these topics and papers appear frequently in the coastal engineering literature. The WMO report (WMO, 1978) also considers the more likely circumstance where inadequate data exist for the direct estimation of sea-levels requiring the water-level distribution to be deduced from the physically causative factors. One source of variation that is not normally encountered in hydrological investigations of joint events concerns the steps involved in converting regional hurricane probability to the probability of an event at a single site. This arises because hurricane frequency is expressed as the number of cyclones that cross a specified coastline in a year. In order to relate this to the probability at a particular point the direction and spatial profile of surge levels also has to be modelled. This device is not necessary in extra-tropical surge-frequency analysis. Surges are of considerable extent 38 CHAPTER 5 and so occur with sufficient frequency at every point that pressure and windfield data in the surge-generating region can be considered directly. 5.3 Flood frequency in tidal rivers 5.3.1 In the following analysis it is assumed that there exists some means of describing the frequency distribution of high levels in the estuary or at the river mouth and also that the river's flood frequency distribution is known. The estuary problem has been outlined above. In the absence of river flow data, a regional flood frequency relationship can be used based upon a national or regional synthesis of flood data. An example of such a procedure is the UK Flood Studies Report (NERC, 1975) which describes methods that can be applied at an ungauged site using either rainfall runoff or statistical principles. 5.3.2 As in the open coast case the solution to the problem must lie through a joint probability approach. Consider two random variables, for example the level of the sea beyond the influence of river flows, x, and the discharge in the river above the point at which tidal influences can affect it, y. If we can assume that the level at the point of interest, z, is a function of the current values of x and y alone, in other words is unaffected by the previous history of x and y values, then it is possible to construct the distribution of Z from the distribution of x and y. Let the probability density of x be fIx) and of y be g(y). If x and y are independent then the probability of x and y is p(x,y) = fIx) .g(y). If there is any tendency for particular values of x to occur with particular values of y in our example, because high surges tend to occur at a time of year when floods are frequent or because a tropical storm is responsible for both surges and floods, then x and y will not be independent and special measures must be taken. Dependent or not, a bivariate distribution p(x,y) can in principle be found. Figure 11 shows this diagrammatically. This relationship of itself is insufficient to calculate the distribution of consequential Z values. However, by plotting also on Figure 11 loci of equal values of z obtained from the relationship z = h(x,y) which links the level at the point of interest with the two causative factors, the manner of finding the distribution of z is easily seen. The volume below the bivariate surface p(x,y) and beyond any of the 10cL say z = Zl (a constant), is the probability of all combinations of x and y which combine to a value of Z greater than z.. Therefore, this volume is the probability of exceeding z 1. This exercise is repeated for other values of z to construct the probability distribution of z. This scheme can be used even if no closed form function h(x,y) exists for z, for example when z is the result of a non-analytical numerical estuary model. A practical form of solution is to convert to discrete form the x and y distributions. For example, a limited number of, say, 20 values of surge level are adopted to represent the distribution. Their probabilities sum to one and are assigned to each based upon the position of the probability RISK EVALUATION OF STORM SURGES IN RIVERS 39 Bivarlate density p[x,yl Lines of equal z value Region in which z>z1 - .. Probability River discharge x Figure 11 - Definition sketch of method of combining probabilities density that each discrete point represents. The flood discharge distribution is treated similarly. For each pair of x and y values two nlDllbers may be calculated: firstly, the probability of x and y being the product of the two probabilities and secondly, the consequential z value obtained from the function or by running the numerical model. It is a straightforward task to sum these probabilities over any required value of z. Figure 12 shows this scheme. The principle elucidated here is the only correct method of combining probability distributions; all others lead to error. In this connection, one can read of methods which combine, for example, the 0.1 exceedance probability of sea-level (F(x) = 0.9) and flood (G(y) = 0.9) to give what is claimed to be the 0.01 exceedance probability level at the point of interest. Another 40 CHAPTER 5 X, Xz Y:J X4 •••••• Xf River discharge A. Conversion of discharge distribution to discrete form ISimllar procedure for sea level distributionI Y3 · ...•. 9 ...•.. 3 Estuary model Z:hlx,.Yjl Probability Plj: If. 91 B. Sampling scheme for combining discharges and sea levels Exceedance function of Z C. Use of Plj and zfl to form probability· distribution for Z Figure 12 - Probability distribution over any required value of z RISK EVALUATION OF STORM SURGES IN RIVERS 41 scheme entails searching for the particular combination of x and y, maintaining (l-F(x» (l-G(y» at a constant quantity such as 0.01, that maXlmlzes z. Both these schemes lead to underestimates of the true 0.01 probability value of z, as can be seen from Figure 13 where the adopted design point z can be seen to be exceeded with probability 0.01 plus the probability enclosed in other domains. Point on locus at which x z Is a maximum Region over which x>x[0·1J and y>y[0'1J Extra region over which z>z max o':" 11 : ~~~Ilililr ~:§=i=:?' ~....:.- .... " z=zmax .... Locus of points for which j 11- F[x][1-G[yJI = 0'1 ! --p-rO-ba-b-IU-tY-"""';;..J '::R;;:iv=er:::'::di:isc':'h;::a=rge=:--:x:----...L--:-:f:=;-I--...L---- Figure 13 - Fallacy of combining exceedance probabilities 42 CHAPTER 5 5.3.3 In principle, this may readily be accommodated, as has already been indicated in section 5.3.2, by an adjustment to the bivariate distribution of x and y. If this is possible. the calculation then proceeds in exactly the same way as for the independent case. UnfortwLately, however, correlation is only simple to handle in the Normal distribution case and, while the statistical literature does contain examples of bivariate exponentiaL Gamma and Gumbel distributions, these are by no means easy to apply nor in some cases realistic in their geometry. Thus, for practical purposes one would be obliged to transform the two marginal distributions to Normality. In the case of the discrete scheme, section 5.3.2 and Figure 12, correlation appears in the form of a requirement for a different distribution of floods for each value of storm surge level. For example, in the case where tropical storms are responsible for both the higher sea-levels and the higher flood discharges, this would be reflected in higher probabilities in the righthand tail of the set of representative flood values for the corresponding sea surge level values. It may be very difficult to estimate these probabilities from limited data sets. 5.3.4 Correlation that arises through a shared seasonality of the two causative factors is best dealt with by dividing the years up into seasons within which the factors can be regarded as independent. For example, in Northern European waters there are maxima in the astronomical component of sea-levels in March and October. The manner of reconstructing the seasonal distributions back into an annual distribution follows. Considering the year divided into m seasons and by following the recommended procedure, the frequency distribution of levels at the site of interest, z, has been established for each season. The probabilities therefore relate, for example, to the probability of exceeding some threshold level Zo in the ith season Pi. The probability of not exceeding Zo in the ith is (I-Pi) and the probability of not exceeding Zo in any of the m seasons is (l-P,) (l-Pz) ... (l-P,) ... (I-Pm) m = IT (l-P.l. i=l This probability is also the probability of not exceeding Zo during the year. The probability of exceeding zo (or, through its reciprocaL the return period in year units) is m 1 - IT (l-P,) i=l 5.3.5 In associating two variables, x and y, both statistically and through the model to determine z, it is presumed that x and y uniquely determine z. Our prime interest is in the distribution of large values of z. It is RISK EVALUATION OF STORM SURGES IN RIVERS 43 therefore reasonable to consider only those high values of x and y which may contribute to the high values of z. It is not sufficient to consider only the annual or seasonal maximum distributions of x and y because of the high probability that the annual maximum values of sea surge will not coincide with annual maximum river floods. At certain places in the tropics high river flows may in practically every case result from the same cause and occur at the same time as high sea-level. In all other circumstances, however, it is necessary to select a realistic time interval over which it can be reasonably expected that the x and y values really will coincide as in the model, linking them to z which will almost certainly have developed from particular and significant events. In two recent studies, one in the UK (see section 5.4) and one in the Netherlands, a time unit close to one day was selected. 5.4 Practical examples 5.4.1 The steps in assessing flood frequency at a point subject to both marine and fluvial flooding are as follows: (a) Choose a time step for the analysis; (b) Fit a distribution to the estuary tide data at the river mouth (including surge effects); (c) Fit a distribution to the river flows; (d) Model the relationship between the level at the location of interest and the two causative factors; (e) Perform the integration to find the probability of the joint events which combine to exceed the required water level; (f) Convert the probability expresse.d in terms of the analysis time step to annual maximum probability. An outline of how these steps were applied in recent British studies is given in the following paragraphs. 5.4.2 A time step of one day was adopted in a recent study of floods at Gainsborough, which lies within the interaction zone of the River Trent. This was felt to be the time period at which the physical processes could be held to interact and for which sufficient data were available. The important point is that, whatever time step is adopted, it must be matched in the "physical relationship" of step (d) above. Studies which adopt an annual time step and hence use annual maximum statistics for the flow and tide series should relate the maximum water level to these annual maxima and not use the event relationship. The situation with tropical cyclones is made simpler by the near certainty that when a cyclone occurs it will create a flood at landfall and, because they are relatively isolated events, each event can be analysed as a maximum event. In the typical extra-tropical situation the astronomical tide 44 CHAPTER 5 is of first importance and potential flood conditions can exist with every tide. 5.4.3 In the Gainsborough study extensive records were available which allowed an accurate description of the daily maximum tide and surge distribution. The histogram of the data is bimodal and was fitted using a compound Normal distribution using Cohen's (1967) method. It is usually sufficient to assume both elements of the compound distribution have the same variance. Annual maximum tides and surges are often found to be well described by extreme value distributions. 5.4.4 The flow duration curve is the distribution of daily river discharges. This was obtained in the Trent study by analysing the flow records at an upstream site. A lognormal distribution was assumed for this 19-year series. It was extended to higher non-exceedence probabilities using the annual maximum flood distribution. To convert between the two probabilities, use was made of an empirical expression: 365(-10g Pdl = -log Pa + K(log Pal where Pa and Pd are the annual and daily probabilities. The value K represents the degree of daily dependence and in this case was estimated from the two sets of observations. In the absence of site data, K can be estimated from a regression equation on catchment characteristics. 5.4.5 Two approaches were used in the Trent study. Both made use of relationships calibrated on simultaneously recorded values of river flow, tidal' estuary and river level at Gainsborough. This is justified by the adoption of the daily time step. In the first approach a regression between the level at Gainsborough and causative variables was established. A total of 1695 points were used. In order to achieve a more additive form of relationship the flows were transformed through a rating curve to equivalent levels. One day, lagged flows and a product term were also included and with this assistance 92 per cent of the variance could be explained. In the second approach the empirical equation described in section 4.5.4 was used to link Gainsborough level (H) with the estuary level (Xal and the river flow transformed through the low-tide rating curve (Y). Non-linear least squares were used to estimate the combined parameter p(l-K). The variance in the estimated levels explained by this approach was similar to that achieved by regression, but it was attained with only a single parameter and appeared to give more realistic extrapolations. It was therefore adopted as the preferred technique. RISK EVALUATION OF STORM SURGES IN RIVERS 45 5.4.6 Because the tide levels were fitted to the Normal distribution, it was possible to perform part of the integration semi-analytically rather than by converting both variables to discrete form as illustrated in Figure 12. The resultant probabilities relate to the daily time step. In order to convert this to the more familiar annual probability it was necessary to reverse the process described in section 5.4.4. At high return periods this differs little from a direct conversion based upon an assumption of independence. 5.4.7 Thompson and Law (1983) presented a somewhat similar joint probability procedure for the related problem of flood frequency estimation in a river whose mouth was obstructed by a sluice gate. Flood water generated upstream of the gate could therefore escape over part of the tidal cycle only. The purpose of the study was to evaluate the frequency of bank overtopping, due to inadequate capacity in the river to store flood water through the tidelocked period. The authors' approach consisted of an exploration of combinations of tidal and riverflow conditions and the formation of a probability matrix from which the frequency of flood events could be derived. An interesting feature of the analysis was the inclusion of an extra dimension of variability: the lagtime between peak inflow and the time of maximum tide. 5.5 Probable maximum flood A high-risk structure, such as a nuclear power plant, if located close to the coast, should be designed to a higher standard than can safely be evaluated by statistical means. The design basis for nuclear plants is contained in the Safety Series guides published by the International Atomic Energy Agency (IAEA) (1983a and b). Their recommendation is to design flood protection works to withstand the Probable Maximum Storm Surge or Tropical Cyclone. For a river site it would be necessary to combine the marine and fluvial conditions into a severe, but not impossible, design condition. Deterministic models are preferred by the IAEA for this purpose. Different classes of combination are considered in the guides which should be referred to for details. 5.6 Damage assessment and flood insurance Flood protection works to mitigate the effects of flooding from tidally affected rivers should be based upon the costs and benefits of the project. Benefit evaluation must be based upon a knowledge of the area inundated by a flood of a given return period. Hydrodynamic models such as the SSURGE or FIA models (section 3.4.2) are designed for this purpose. However, the problems of modelling in terrain such as is found alongside a tidal river are acute, and it is important to calibrate the model against observed data. Therefore, flood events should always be followed by detailed surveys of inundation extent and flood damage. This can best be done by interviewing or by questionnaire. 46 CHAPTER 5 Non-structural approaches to flood mitigation are popular in some countries. Land-use planning can be used to discourage occupancy of flood-prone areas. Insurance is another possibility, and this has achieved prominence in the United States. The US Federal Insurance Agency makes available government-backed insurance policies to cover flood damage in return for action by a community to minimize the hazard for itself. This programme extends to riverine as well as coastal flooding and, as already stated, has provided the impetus for the development of analytical techniques for risk evaluation. An insurance scheme requires a fund to be set up into which policies are paid and from which withdrawals are made to pay for the damage that occurs. The fund must be capitalized at a sufficient level to cover damages occurring in a random sequence. The stochastic behaviour of the fund, and how to avoid depleting it, have been the subject of investigations by hydrologists (Schaake and Fiering, 1977). CH APT E R 6 THE FORECASTING CENTRE 6.1 Introduction The flood forecasting centre is the office which is responsible for receiving the meteorological and hydrological data and applying the forecasting models which enable future high levels to be estimated. This information is then disseminated to authorities concerned with river and coastal management and also to the preparedness organizations, such as the police, who are responsible for public safety. The main issues to be resolved when setting up a forecasting centre are its physical and institutional location, what forecasting procedures it is to apply, how data are to be supplied to the centre, and what will happen to the flood forecasts thereafter. 6.2 Location of the forecasting centre It is unlikely that a forecasting centre would be justified whose sole function is to forecast floods in tidally affected rivers. Therefore, the decision must be taken whether to locate the centre within the meteorological organization or the engineering authority concerned with river and coastal management. The advantage of basing the centre with the Meteorological Service is that the latter is best placed to receive and process synoptic information, and probably already produces operational forecasts for shipping and other purposes. The disadvantages are that it may not have staff with the necessary skills to perform hydraulic computations and that it is probably physically remote from any given danger area. Despite the need for well-developed communications between the organizations, the optimal solution is probably for the Meteorological Service to supply forecasts of open sea and estuary surge residuals to the local authorities responsible for the particular river. This solution has been applied in the UK where the Storm Tide Warning Service (STWSJ is part of the Meteorological Office where it has immediate access to up-to-date wind forecasts and atmospheric models. Up to 1983 the service was administered by the Ministry of Agriculture and staffed by the Hydrographic Department of the Navy; it was nevertheless located at the Meteorological Office. Coastal and river flood forecasting are the responsibility of the Meteorological Services in both Australia and the United States. In the UK the Regional Water Authorities combine the function of coastal protection and flood forecasting, and so are well placed to make use of the data provided to them. 48 CHAPTER 6 6.3 Choice of model and communication equipment As already intimated in section 4.2, the majority of practical surge forecasting systems use empirical, mostly regression, relationships with wind speed and pressure as predictive variables. This is so in the me although mathematical models are playing an increasing role. The main meteorological inputs to the forecasts are the surface wind and geostrophic winds in the northern North Sea. Because the surge wave must travel down the North Sea, regressions can make use of observed high water levels at points upwind. Two forecasts are issued during each tidal cycle, at 12 hours and six hours before high tide, and for five reference ports on the east coast. Clearly, such a system needs to be tailored to individual circumstances. For example, the importance of astronomical tides varies greatly. In tropical areas other weather phenomena during hurricane landfall are extremely damaging in their own right so the forecast will contain information on wind and rainfall. The river authority, on receipt of the surge residual forecast, will convert this to a water level forecast in the affected river reach. A range of possible methods exists (Chapters 3 and 4). Perhaps the ideal solution is to use prepared nomograms or equations which are simplified solutions of more complex models. Telemetering equipment will greatly enhance the accuracy of the forecasts, both through opening the prospect for updating of the forecast and to feed into staged forecasts for downstream points. Robustness is vital if the equipment is to remain operative through the emergency period. In this respect radio links are to be preferred to telephones. Additional information on practical aspects of issuing hydrological forecasts is included in Chapter 6 of the WMO Guide to Hydrological Practices (WMO-No. 168, 1983); most of the information is relevant to tidal rivers. 6.4 Dissemination of forecasts and warnings Clear lines of communication with interested parties are vital in order for the forecast to be useful. The eastern coast of the UK has been subdivided and, in case of emergency, a coded message is sent summarizing the state of alert in each division. The police, as the primary emergency service, receives the surge forecast from the Storm Tide Warning Service (STWS) by telex. Figure 14 shows the onward lines of contact to other services. The Regional Water Authorities interpret the surge forecast in terms of its likely consequences along the coast and affected rivers. This is retransmitted to the police and through them to all other parties (Roberts, 1983). Some rivers, like the Thames and Hull, have tidal barriers which are closed against high surges. Special-purpose forecasts are issued for these barriers (Horner, 1977). Additional information on the links that are necessary between technical and preparedness organizations is given in the "Disaster prevention and mitigation" series issued by UNDRO 0976 and 1978>' THE FORECASTING CENTRE 49 lONOON WEATHER CENTRE "IQ TELEX POLICE CO\Kl.S and olhw i'll."tH MARITIME TIDAl WARNING - A POLICE Sub division - Herne Bay QJISIQE !VICE to/RS ______CIoso~ !£:!. _ CITY ENGINEER or CHIEF ENGINEER. for overoll responsibility of engine~ advice ------B C 0__ I INeet Lobu •I I MQlaglllW". I H~"""-' I ~.rs I + 0 Figure 14 - Examples of mechanisms for dissemination of storm tide forecasts and warnings 50 CHAPTER 6 6.5 West Gulf River Forecasting Centre (WGRFC) (USA) 6.5.1 This centre is situated at Fort Worth, Texas, USA, and is responsible for issuing river forecasts for streams emptying into the western Gulf of Mexico. Institutionally, the WGRFC is part of the National Weather Service and is allotted a staff of nine people. Data is sent to Fort Worth by a variety of means from local offices concerned with surges, river flow and rainfall. Automated and manual procedures are employed for communication with outstations. Forecasts of river flows are made primarily using a coaxial relationship incorporating an API model whose inputs are API, week of year, storm depth and duration. Increasing use is made of the Sacramento model (Burnash et a1., 1973) and, for larger basins, a quantitative precipitation forecast (QPF) estimate. 6.5.2 Fread's dynamic routeing model (see section 3.6) is employed for forecasting surge effects within 13 streams flowing into the Western Gulf. The input to the model is a two-hourly storm surge hydrograph as output from the SLOSH (see section 3.5), and upstream and lateral inflow hydrographs as described above. Since 1967 when the system was set up, there have been no serious incidents of joint flooding. 6.5.3 The only hurricane to approach critical conditions was Hurricane Alicia in 1983, but the forecast surge level did not achieve the threshold level to require river forecasts. In fact, the actual surge would have activated the system so an analysis was carried out after the event to test the system performance. Figure 15 shows the track of Hurricane Alicia. Affected streams were the San Jacinto, Trinity and Buffalo Bayou Rivers. In the first case the storm surge was found to have added some 1.2 to 1.5 m to the river flood hydrograph. The model would have forecast a peak stage about 0.3 m higher and some six hours earlier than that observed. The Trinity River is further from the hurricane track, and model tests were in approximate accord with the observation of a rapid reversal of flow direction and a stage increase which decayed from 2.5 to 2.8 m at the river mouth to about 64 km upstream. Buffalo Bayou stream is the closest to the storm track and the surge height at its mouth in Galveston Bay was 3.1 to 3.4 m but, due to the heavy local runoff from the Houston agglomeration, no separate surge signal could be distinguished. The peaks of the runoff and surge were supposedly nearly coincident. 6.5.4 -Conclusion-- -- The West Gulf River Forecasting Centre (WGRFC) considers that it will be a number of years before they can verify their procedures because of the small number of events and the small area of significant surge effect. However, in post-mortem analyses the routeing model appeared to achieve adequate accuracy for forecast purposes. THE FORECASTING CENTRE 51 LEGEND 32· o 0000 GMT • 1200 GMT ...... TROPICAL DEPRESSION Cl, ---- TROPICAL STORM \ - HURRICANE \ LOUISIANA \ i \ < 30· T EX ~ S OF MEXICO 28· .....,.... _-0--.....•,5 AUa " AUa 9B' 96' go' 9" 90' Figure 15 - Approximate track of Hurricane Alicia 6.6 Storm Tide Warning Service (Netherland~) The service was set up in 1931 but reorganized and strengthened after the 1953 disaster (see section 7.8). It is located at The Hague and is part of the Tidal Waters Division of the Rijkwaterstaat. It consists of five permanently assigned staff with 25 others available for operational duties during an event. Close liaison is maintained with the Meteorological Service (KNMI) which in fact prepares the initial surge forecast. The forecasting service is involved with the Rhine and Meuse catchments and the Dutch coastal area. Data are at present transmitted by telephone to the forecasting centre. Surge forecasts for coastal stations are issued by KNMI using manual calculations (Weenink, 1958) and digital hydrodynamic models (Tirnrnerman, 1977). Rainfall forecasts are also received from KNMI and input into the newly developed Rhine forecast model (de Ronde, 1984) which is based on rainfall runoff regression. Since 1960, with the closure of the delta by the Haringvliet sluices, there have been no floods due to combined fluvial and tidal causes in the interaction zone. Surge forecasts are nevertheless highly relevant to river management as they are used in controlling these and other structures. 52 CHAPTER 6 6.7 Operation Neptune (UK) This is the name given to the forecasting system operated by the UK North West Water Authority based upon the west coast Storm Tide Warning Service. The latter service was instituted following damaging floods in January 1976 and is modelled upon the similar operation for the east coast (see section 7.8) (Crowther and Ryder, 1985). The technical base of Operation Neptune is the Continental Shelf hydrodynamic model for surge forecasting. Neptune operates from the same office as the Water Authority's river flood forecasting system. This employs 18 raingauge and 54 river gauge outstations linked by microwave. A particular feature of this system is its use of radar for catchment precipitation estimates. River levels and catchment average rainfalls are computed every 15 minutes. Flood forecasts. four hours in advance are produced at the same interval and can be presented in tabular or graphic form. Routeing models are used to combine flood and surge forecasts for estuary sites. Considerable emphasis is given to predetermined lines of communication with police and local administration units in the areas for which warnings are issued. Telex is the preferred medium, but telephone messages are used when there is a rapidly developing situation. CH APT E R 7 SELECTED CASE HISTORIES 7.1 Introduction There is a great dearth of information on the consequences of surges and tides on flooding along rivers away from the immediate coastline. For this reason this chapter commences with a suggested format for obtaining more data on such events. These data will be found to be of fundamental benefit for forecasting, for evaluating flood risk? and for designing protection schemes, as well as for gathering and comparing international experience in coping with the hazard. The case histories that are presented are for the most part for estuary locations rather than for rivers proper. They include cases where storm surge aggravates the tidal problem, in many cases due to tropical storms. These tropical events are termed "hurricanes" in the Atlantic and Gulf of Mexico, "typhoons" in the Pacific, "tropical cyclones" in Australian waters, and "cyclones" in the Bay of Bengal. 7.2 Field survey reports and high water information There is .no internationally accepted format for observations on flood events. The WMO report on storm surge prediction (WMO, 19781 includes a checklist for reporting such events, and this forms the basis for the following headings. 7.2.1 (al Name of the tidal station: (bl Location; (cl Agency; (dl Highest sea-level above the datum line of observation, with the peak value recorded along with the smoothed highest value; (e) Heights of annual mean sea-level and the reference level of land maps above the datum line of observation; (fl Maximum surge for the smoothed variation of sea-level. If the peak value of tide is recorded in (d) and the corresponding value of storm surge is larger than the maximum value for smoothed variation, the value for the peak is also to be noted; (g) Lowest sea-level pressure at the nearest meteorological station (with name and location of the meteorological station); (h) Strongest wind and its direction; (i) Time of occurrence of above extreme values. 54 CHAPTER 7 The following data are also to be reported, if available: (j) Hourly values of sea level during the period of disturbance; (k) Hourly values of storm surges. By collecting the above data from tidal stations in the affected area, the characteristics of peak-surge distribution and time histories of surges can be analysed. Results of the analysis will be included in the report. 7.2.2 River ------flow and level records These will mirror the headings given for tide gauge information omitting items such as (d), (e), (g) and (j). In addition, information should be kept on the current rating curve used for stage-to-flow conversion. Opportunity should be taken to update the interaction diagram such as shown in Chapter 4. 7.2.3 (a) Area of survey; (b) Period of survey; (c) Surveyor(s); (d) Agency in charge of the survey; (e) General explanation on the flooding by storm surges; (f) Table showing the results of high-water mark levelling. One row or column is usually assigned to one high-watermark, and the following data should be noted in a row (column): (i) Time of levelling; (ii) Object of measurement; (iii) Height of high-water mark above bench mark or sea-level; ( iv) Name of bench (iv)' Name of primary mark or other or local station object whose (or) (tidal section) height is pre to be referred cisely known; to; (v) Height of bench (v)' Height of sea mark or other level above object above the (or) annual mean sea reference level level at the of land maps time of levelling; (vi) Corrected height of high-water mark above the reference level or annual mean sea-level; SELECTED CASE HISTORIES 55 (vii) Reliability of the above results; (viii) Time of the highest water level in the period of storm surges. If the surveyor has other useful information, it would be better to note this in separate spaces. 7.2.4 A useful concept for flood reporting and subsequent analysis is the surface envelope of high water generated during the flood event. The surface connects all the peak levels achieved during the event irrespective of their time of occurrence. Gauges are generally restricted to near coastal zones and do not measure water heights inland. Also, they may become inoperative with the passage of a core of high waters, precisely when information is most desirable. Hence, even a dense network of gauges does not guarantee that the resulting measurements would be adequate to define the surface envelope. An economical and effective way to gather additional data is post-storm surveys. The combination of data normally permits a meaningful data base. The main concern of the forecaster is the envelope of high waters. In any data set, readings from discretely positioned gauges will tell the condition of the river or astronomical tide under the envelope of high waters. The data set should be adjusted to separate the level into river flow and envelope astronomical tide. 7.3 Flooding on the Brisbane River, Australia (1893-1955) The Brisbane River is tidal below the water supply weir at Mount Crosby so that the cities of Brisbane and Ipswich are located within the tidal reaches of the main stream and its lower major tributary, the Bremer River. In the past, these reaches have been subject to heavy flooding from the Brisbane River (Piggott, 1966). Due to changes in rainfall profile, only three minor floods have been recorded this century, whereas much larger floods were the rule rather than the exception during the last century. The problem of forecasting flood stages at Brisbane for minor floods, and the rising and falling limbs of major floods, is complicated by the influence of meteorological conditions on the sea-level in Moreton Bay, inflows from both the Bremer River and the local catchment of the lower Brisbane River itself. and by the presence of a marked tidal influence. Consequently, both first flooding stage and duration of flooding cannot be simply determined, and data from a large number of floods are required if the exact relationships involved are to be accurately defined. To satisfy the requirements of flood forecasting, it is necessary then to consider the influence of three separate factors on the river stage at the Brisbane Post Office. These three factors are: (a) Tide; (b) Change in mean level of Moreton Bay caused by meteorological effects; 56 CHAPTER 7 (c) Flood discharge, including local inflow and Bremer River contribution. We now attempt to determine methods of forecasting each factor at least 24 hours in advance of the initial stage of 2.7 m and the peak stage. An empirical approach is adopted which has the advantage of being simple but with acceptable accuracy. The separation of these factors is based on the simple assumption of a linear relationship between them of the form (1) where: Hp = the predicted level of the flood at the Post Office gauge; Hm = a term which includes an allowance for mean sea-level and for changes due to meteorological effects on Moreton Bay; h r = the predicted amplitude of the tide; f r = an empirical tidal attenuation factor which is assumed to be a function of flood discharge, Q; HQ = the contribution to the flood stage due to flood discharge Q past the Post Office. The first step in the investigation was to determine each term in equation (1) where sufficient historical data were available (1893, 1898, 1908, 1931, 1950, 1951, 1954, 1955). Data for Moreton Bay are given in Table 3. TABLE 3 Tidal data Moreton Bay Datum is zero on the Post Office gauge Official high water 2.10 m above datum Mean high water springs 2.04 m " " Mean high water neaps 1.56 m " " Mean low water springs 0.15 m "" Mean sea-level 1.07 m " " Highest recorded tide 2.90 m " " (8/6/1891 and 18/1/1950) SELECTED CASE HISTORIES 57 The height of the predicted tide at any location above a specific datum is given by (2 ) where aD is constant and h r is harmonic in character. It is possible to define the tidal amplitude with comparative accuracy by relatively few terms of the Fourier expansion: h r = E h k cos (kwt + ak) k=l in which k=l represents the diurnal cycle, k=2 the semi-diurnal cycle and so on. Under flood conditions, the discharge dampens the predicted tidal amplitude, so that an attenuation factor is applied to the tide value. This factor has a value of 1.11 under no flood conditions and reduces to zero for flood stages above approximately 6 m on the Post Office gauge. To minimize this error due to damping, a compromise was arrived at by considering the three days about the flood peak as the Fourier period; that is, one hour is equivalent to five degrees. Hp is thus defined as The third, sixth and higher harmonics were considered to be the first approximation to the damped tidal contribution and all other terms were considered to determine the shape of the flood contribution to the hydrograph. 5 Hm + HQ = Ao + XAk cos (5kt + Bk). k = 1 k = 3 The hydrographs of four floods, 1955, 1931, 1893, 1898 and 1893, were analysed. Because the attenuation effect is averaged over three days and harmonics higher than six neglected, the best estimate of the damped tidal contribution was taken as the difference between the estimated value of (Hm + HQ) from the above equation and the corresponding value of Hp from equation 1, as then 5 frhr = Hp - (Aa + XAk cos (5kt + Bk). k = 1 k = 3 58 CHAPTER 7 From the result of these Fourier analyses, a scatter-graph of f r plotted against the estimated sum of Hm and HQ was obtained. Once the form of the scatter-graph has been established, it is possible, by an iterative procedure, to separate from each observed flood hydrograph the values of (Hm + HQ) which, together with the graph, would be necessary to predict exactly the observed flood hydrograph at high and low water. The annual mean sea level in Moreton Bay is 1.1 m on Post Office datum and is subject to small predictable variations throughout the year as indicated in Table 4. TABLE 4 Variation of sea level of Moreton Bay (in cm) Jan Feb Mar Apr May June July Aug 8ept Oct Nov Dec o +3 +6 +9 +9 +6 o -6 -9 -9 -6 -3 Determination of sea-level variations due to meteorological effects in the form HMB = Observed high and low water - Predicted high and low water has been made after smoothing out high water and low water variations in HMB. Although there is most likely interaction between the storm surge and tide, we assume that at the Post Office, only ao (equation 2) is affected. Once the initial surge is established, HMB changes slowly and can be satisfactorily predicted 24 hours in advance. For flood forecasting purposes the trend of the values of the mean of HMB is taken over the Crosby hydrograph without storage. From the comparison of the times of occurrence of peaks at Mount Crosby and the separated HQ at the Post Office, the flood crest 1 travels at a speed of 4.8 km h- • This means that the upstream hydrographs are lagged by the following times: Mount Crosby to the Post Office - 13 h Moggill " 11 " " - 10 h Goudna " 11 11 " 8 h Darra " 11 11 " 5 h. SELECTED CASE HISTORIES 59 The contribution of the Bremer River to the discharge past the Post Office is not easily determined. The river gauge at Ipswich is heavily affected by backwater from the Brisbane River. A correction to the stage at Mount Crosby for the Bremer contribution has been based on an areal rainfall pattern using the parameter: Storm areal rainfall over the catchment of the Bremer Bl=------Storm areal rainfall over the catchment above Mount Crosby 7.4 Storm surges in Japan (1917-1970) In September 1959, a typhoon hit the shores of Japan and resulted in surges at Ise Bay in the central part of Japan. More than 5 000 lives were lost. With maximum deviation of 3.5 m, it was the worst storm surge recorded within the period. The forerunner stage occurred at 1300 hours GMT on 26 September and the resurgence stage was after 0100 hours GMT on 27 September. The longitudinal seiche of the Ise Bay caused the resurgence. In 1965 another storm surge occurred at Oshima Island in Japan. The typhoon was non-homogeneous due to asymmetry in the wind distribution within it. In 1966 storm surges which occurred at the port of Unoki and Isozaki showed that sometimes storm-surge height could be as much as five or seven times static water head. There are many instances of surges exceeding 2.0 m along coastal areas and islands of Japan. Table 5 provides a list of some major surges in Japan. 7.5 Storm surges in Bangladesh (1960-1970) During this decade alone, about 400 000 people died in the exceptionally high tides which swept in along the low-lying northern coast of the Bay of Bengal under the force of tropical cyclones. Table 6 shows the most prominent of these disastrous events. Over half of the lives were lost in the single surge caused by the storm of November 1970. Such loss of life can be prevented only by removal of the population from the area, construction of permanent defenses, or by prediction of and protection against individual storms. The last involves the identification and survey of a severe cyclone. forecast of the development and course of the storm, prediction of the sea-level response, issue of warning and protection of the survivors. A devastating storm struck the north-eastern coast of the Bay of Bengal near Chittagong between 12 and 13 November 1970. A maximum surge was estimated at 1.5 m between 2000 hours GMT on 12 November and 0400 hours GMT on 1 13 November with a speed of about 20 km h- • The maximum surge was reached at Chittagong at about 0100 hours GMT, some two hours before the strongest winds of the storm hit the port. The storm generated a surge which inundated the coastal areas with a water level of 9 m in Chittagong at the time of landfall. There is usually a compliance between surge and tide; it was therefore difficult to extract the surge from the observed tide because in shallow seas there is a nonlinear interaction between the astronomical tide and the meteorological tide. 60 CHAPTER 7 TABLE 5 Storm surges in Japan (1917-1970) Affected Peak Highest Pressure Extreme values Date area surge water (hPa) of wind velocity Location (m) (m) (m S-I) 1.10.17 Tokyo Bay 2.3 3.1 950.4 SSE 40.0 Tokyo 18.7.30 Ariake Sea 2.5 954.6 ENE 30.6 Tomie 21.9.34 Osaka Bay 3.1 3.2 954.3 S 48.4 Osaka 1. 9.38 Tokyo Bay 2.2 978.6 S 31.0 Tokyo 3.9.50 Osaka Bay 2.1 2.5 964.3 NE 3.3.4 Kobe 17.8.56 Ariake Bay 2.4 4.2 968.4 SE 27.0 Saga 26.9.59 Ise Bay 3.6 3.9 958.5 SSE 37.0 Nagoya 16.9.61 Osaka Bay 2.5 2.9 937.3 SSE 33.3 Osaka 25.9.64 Osaka Bay 2.1 2.6 983.5 S 27.1 Sumoto 10.9.65 Osaka Bay 2.2 966.0 SSE 38.8 Sumoto 21.8.70 Tosa Bay 2.4 3.4 962.3 SW 35.8 Ashizuri Several works (WMO. 1978 and Rao. 1973) have dealt with the problem of estimating the surge from the tide for the November 1970 storm; their main results may be summarized as follows: (a) Idealizing a storm by a simple profile of pressure and wind; the surge at the time of landfall could be related to storm intensity and speed; the highest surges were observed for storms· moving towards Bangladesh; (b) The contribution of storm speed was small compared to the effect of storm intensity from the peak surge at landfall; (c) The maximum surge was generally observed about two hours after landfall. It was located about 30 km to the right of the storm centre; (d) The total sea-level elevation depended on the phase of the tidal cycle. The maximum elevation was recorded earlier; it coincided with the time of high water; (e) Superposition of the surge on the astronomical tide led to an overestimate of sea-level elevation by 0.8 m to 1 m. SELECTED CASE HISTORIES 61 TABLE 6 Storm surges on the Chittagong (Bangladesh) coast) Maximum Date Storm observed Astronomical Observed Maximum speed wind speed tide sea-level gauge 1 1 (krnh- ) (krnh- ) (m) (m) (m) 11.10.60 20 87 1.5 6.0 4.5 31.10.60 38 104 0.0 6.6 6.6 9.5.61 38 87 1.2 4.8 3.6 30.5.61 22 87 0.6 29.5.63 40 113 0.3 5.11.65 42 87 1.2 15.12.65 32 87 0.3 13 .11. 70 20 87 1.8 6.0-9.0 4.2-7 7.6 Storm surges in the United States (1960-1970) Storm surges accompanied by Hurricane Camille. reaching a maximum deviation of 7.4 m. were observed on the east coast of the USA in 1969. Although a cyclone moving along the coast may not result in a resonance. a case was recorded on the east coast of the USA which illustrates that the possibility cannot be eliminated. Several Federal agencies involved in storm surge forecasting have developed storm surge models; the reliability of these models was assessed by a Storm Surge Assessment Working Group established by the Hydrology Committee of the US Water Resources Council (1980), The group noticed that: (a) Some models had not been sufficiently tested; (b) Adequate data for testing was not readily available; (c) The models were different in scope and interpretation. so direct comparison of algorithms was difficult. These shortcomings were partly attributed to the fact that the manpower and funding requirements were greater than the resources available. Although storm surges result from several types of storms. only the hurricane was extensively studied and modelled. and the models were restricted to the deterministic type. The models that were assessed by the working group included SPLASH. SSURGE. FIA. and Bathystrophic models. 62 CHAPTER 7 Federal agencies involved in the development of computer programs for modelling both open coast and inland flooding storm surges on US Coastlines are: • Federal Insurance Administration; • Naval Oceanic Research and Development Agency; • National Ocean Survey; • National Weather Service; • US Nuclear Regulatory Commission; • US Army Corps of Engineers; • US Geological Survey. The principal Federal agencies which collect or have available data that may be useful in storm surge modelling include: • National Weather Service; • National Climatic Center; • National Hurricane and Experimental Meteorology Laboratory; • US Geological Survey; • Corps of Engineers; • Geophysical and Solar-Terrestrial Data Center; • Federal Insurance and Hazard Mitigation Agency; • National Ocean Survey. 7.7 Storm surges in Hong Kong It was found that the tides recorded at the North Point Tide Station were representative of the tides in Hong Kong harbour. Consequently, storm surges obtained by analysing the tide records from this station may be taken to be representative of conditions in the harbour during storms. Researchers who have carried out studies of this area include Cheng (1967) and Lau (1980a and b). To obtain storm surges from tide records, a sine curve is fitted between the predicted high and low tides; the difference between this curve and the actual record is taken as the storm surge. Currently, hourly values of tide level are computed which largely obviate the need for interpolation. The various forces which bring about a storm surge are complex so that it is impossible to forecast each one to obtain the total effect. In order to provide guidance for forecasting storm surges, the surges of 1954-1964 were correlated with certain meteorological parameters as measured at the Royal Observatory, namely, the maximum gust, the maximum lO-minute mean wind, the maximum 50-minute mean wind and the minimum sea-leveL and the following regression equations were obtained: SELECTED CASE HISTORIES 63 S = 0.045G - 0.43 (3 ) Coefficient of Correlation = 0.85 where S = storm surge and G = maximum gust recorded by the Royal Observatory Dine's anemometer; S = 0.087W 10 - 0.61 (4) Coefficient of Correlation = 0.88 where S = storm surge and W10 = maximum ID-minute mean wind; S = 0.089W,o- 0.45 (5) Coefficient of Correlation = 0.88 where S = storm surge and W60 = maximum GO-minute mean wind; S = -0.085P + 87.16 (6) Coefficient of Correlation = -0.73 where S storm surge and P = instantaneous minimum sea-level pressure. (All recordings at Royal Observatory) Note that surges caused by storms that landfall to the east of Hong Kong were not used to compute the regression equations but they are plotted on the respective scatter diagrams. Surges associated with a minimum sea-level pressure higher than 1005 hPa were not used in obtaining equation (6). The following is the proposed procedure for forecasting surges in the Hong Kong Harbour: (a) Forecast the following elements for the Royal Observatory for each storm: (i) The maximum gust; (ii) The maximum ID-minute mean wind; (iii) The maximum 60-minute mean wind; and (iv) The instantanous minimum sea level pressure. If there are difficulties in forecasting any of these elements, then they may be omitted; (b) Substitute the above forecast values into equations (3) to (6) to obtain the surge and use the mean of the predicted values as the forecast surge; 64 CHAPTER 7 (c) (i) Plot the isopleths of the surges produced by typhoons at various distances and bearings from Hong Kong; (ii) Plot the forecast track of the typhoon on the graph obtained in (c) (i) above. The surge thus obtained can be used as a check on the value obtained by (b) above; (d) It has been found that on occasions when surges exceeded 0.6 m, the maximum gusts were usually recorded at the Royal Observatory before the maximum surge occurred in the harbour. Hence, if a gust oC for example, 40 m s - 1 has just been recorded one can be fairly certain that a surge at least as high as that corresponding to a maximum gust of 40 m S-l will occur. 7.8 Storm surges in the North and Irish Sea (1976-1978) The coastlines around the North Sea and around the British Isles in general have throughout history had a particular propensity to tidal surges. This is the result of lying in a region of high astronomical tide and a coastal geometry that can enhance the surge effect. The Zuyder Zee in Holland and the fen areas of eastern and southern England were to a great extent formed during the first half of the 13th century as a result of a series of high surges. After flooding of the River Thames in London in 1928, it was agreed that the Meteorological Office should inform the police force of conditions likely to give rise to surges. After the 1953 disaster, in which 300 people were drowned and 24 000 houses damaged, the Storm Tide Warning Service was set up within the British Meteorological Office to warn all interested authorities along the east coast. Instrumental and technological advances have led to much-improved forecast accuracy and in recent years the CSM model described in section 3.4.1 has been used. Coastal defenses and barrier schemes have also followed, the most notable being the Thames Barrier, but several other rivers including the Lea and the Yorkshire Derwent and Hull are also closed against high-tide conditions. The design condition which has been generally adopted is the 1953 level, with some augmentation for wave action. In the case of the Thames Barrier, the la aaa-year return-period event was used, with some explicit allowance for a possible continuation in continental tilting being made. In general, the operation of these barriers is controlled by sea conditions, there being sufficient storage upstream to accommodate a likely fluvial flood. In recent years, surges of a magnitude equal to the 1953 event in recent years have not caused deaths and only very local flooding. Flooding is also experienced along the west coast. For example, the maximum tidal levels experienced in December 1981 in the Bristol Channel were the highest for nearly 100 years. The level at Avonmouth was 8.75 m including a 1.7 m surge. However, the surge did not coincide with fluvial flooding and damage was confined to a coastal strip. The forecast storm surge considerably underestimated the surge height, which underlined the difficulty of forecasting in an area of complex estuary geometry and without benefit of tide gauges upwind of the affected point. SELECTED CASE HISTORIES 65 Like Britain, the Netherlands also experienced a calamitous flood in 1953 when 2 000 people drowned and 195 000 ha of land were flooded. The Dutch Storm Tide Warning Service was reorganized after this event and is now centred at the Rijkswaterstaat in The Hague (see section 6.6). As in Britain, coastal protection schemes now effectively separate fluvial from marine flooding - of particular note is the giant Haringvliet scheme across the Rhine delta. The design standard adopted was a 40 ODD-year return-period surge. 7.9 Flooding in Sichuan Province, China (1981) In July 1981 a flood disaster was reported in the Sichuan Province of China, which was described as the worst since 1949. Over 8 000 people were killed, nearly 100 000 people were injured and over 500 000 people were made homeless. In the same month of that year the Yangtze River was reported to have overflowed its banks causing a very serious flood in which over 4 000 lives were lost and 50 000 housing units were swept away. CH APT E R 8 RESEARCH NEEDS AND CONCLUSIONS 8.1 Introduction In this chapter recent trends in hydrological forecasting are mentioned as well as identifiable gaps in our knowledge and ability to forecast floods in tidally affected rivers. Past forecasting procedures have been based upon either deterministic models or on empirical approximations to deterministic descriptions of tidal river processes. Stochastic models are gaining popularity elsewhere in hydrology and may have an application to tidal rivers, both for forecasting and for risk assessment and design practice. Another very visible trend is the increasing mechanization and computerization which affect data gathering and make more complex and accurate models feasible. The importance of technology transfer and the problems of developing countries are emphasized. 8.2 Data needs Cutting across all research requirements and recommendations for action is the need to improve and increase data gathering. This includes not only the data used operationally in the forecast but also those needed for statistical analysis and to develop the new generation of forecasting models. In a few cases this means no more than tapping existing sources of information such as remotely sensed data, while in most cases it means installing new gauges in estuaries, in rivers upstream of the tidal reach and at salient points within the reach and, in particular, arranging the transmission of those data to the forecasting centre. Also important are topographic surveys of the flood plain and river sections. Post-mortem data should be collected on the effects of every flood. Research is necessary into methods of decoupling water-level observations in the jointly affected river reach so that the individual effects of astronomical tide, surge and river discharge can be assessed. In a river, these will not be additive and the first step in most cases would be to remove the tidal effect by harmonic means. 8.3 Modelling Researchers need little encouragement to pursue mathematical modelling studies, and it is on this front that the most spectacular progress has been made. The deterministic and physically based empirical models that have been constructed have concentrated on the estuary and river basin with relatively little effort directed to the interaction zone. While there is no doubt that the hydrodynamic equations can be generalized to accommodate river conditions, there will then exist a gap between the theoretical model and what is practically achievable. Such gaps have been bridged in the past to allow numerical solutions to be applied to flood routeing, groundwater problems and ocean problems. The task in tidal rivers will be of similar magnitude and will involve sensitivity studies to RESEARCH NEEDS AND CONCLUSIONS 67 show where simplifications and internal stabilities exist. Of particular relevance to the interaction zone is the effect of changes in bed elevation and roughness due to sedimentation. Another area of need relates to the flow over the inundated area. The nature of local relief, the shallow depth, and uncertain flow paths render this a very difficult problem. However, the benefits of this knowledge would be very great. Currently, crude assumptions are often made about the surface envelope of the inundated area, for example, that it runs parallel with the surface-water profile of the river. Requirements for improving the forecasting of tropical cyclones, their path, and the wind and rain intensity at landfall have been identified in numerous reports. In affected regions, one of the main prospects for improvements in river-flow forecasts lies through studies leading to accurate quantative precipitation forecasts The hydrology of tidally affected rivers stands to gain much from the ongoing research into flood-formation processes and the effects of land-use change. Floods have become a more frequent occurrence in some areas because of a reduction in response time of coastal catchments due to deforestation, river canalization, swamp drainage and urbanization. Although this report has emphasized the flood hazard, modelling of interaction-zone processes is equally relevant to other estuary problems such as flow reversal, pollutant circulation and saline intrusion into rivers and adjacent aquifers. In the context of tidally affected rivers, stochastic modelling may be appropriate for forecasting, but more probably for design studies. Use could be made of the Markovian character of the hydrological system on larger rivers and especially of the astronomical component of tide, which can be fully described by harmonic series. This is much more likely to be useful in extra-tropical regions than in the flash-flood regimes of rivers subject to tropical cyclones. Adaptive methods of forecasting make use of past errors to update and recalibrate the forecasting algorithm. Their application to forecasting in tidally affected rivers, either to forecast the causative variables or to forecast the water level in the interaction reach, should be investigated. There is evidence of a time trend in the tidal records of some coasts, leading perhaps to more frequent exceedence of inundation levels. Hydrologists need to be aware of such trends as they will affect design standards. 8.4 Risk assessment and design problems The theory of joint probability is well understood as a statistical principle, but little applied as a practical tool. Research is necessary not only to demonstrate its use but also to extend it to more complicated circumstances. Correlation between the causative elements needs investigation, especially as the governing distributions are not well described by Normal distributions. The correlation structure may also be very different to that often assumed as dependence between flood discharge and surge height will increase as the magnitude of the event increases. Links 68 CHAPTER 8 between the distributions to apply to the same variable measured in different time steps need to be studied, for example daily average and seasonal and annual maximum discharges. Most design studies have concentrated on the relationship between peak values. In the North Sea, for example, it is known that the surge interacts with the astronomical tide in such a way as to avoid addition of the two peaks. Some flood circumstances are volume controlled rather than peak controlled. This occurs especially where storage is involved. Special attention needs to be given to the particular problems of economic evaluations in the tidal river case. Lead times and periods of inundation will differ from those of other flooding causes, and saline water may increase the damage. Institutional responses to flooding have been studied extensively in developed countries. Such studies should be extended to all countries to investigate the potential usefulness of such programmes as flood-proofing and insurance. 8.5 Technology transfer The gap between requirements for techniques and the state of knowledge is matched by the gap that exists between the techniques available in different parts of the world to solve the same problem. WMO's Hydrological Operational Multipurpose Subprogramme (HaMS) exists to bridge this gap. HOMS consists of instrument descriptions, software packages and guidance manuals. Members are invited to contribute components to the HaMS system for such purposes as hydrological forecasting. The HaMS Reference Manual gives information on available components. HOMS is an ideal mechanism for transferring the technology of the advanced countries to the developing regions. Questionnaire responses reveal that. even within countries, large differences can exist in the level of expertise that is being applied to the flooding problem. 8.6 Concluding remarks Intensive research is in progress on deterministic and stochastic modelling for hydrological purposes. Modern methods of forecasting and responding to catastrophe have led in recent years to a reduction in damage in those countries that are in a position to profit from the advances. 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