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Hydrological Forecasting with Radar and the Probability Distributed

Hydrological Model (PDM)

Gbotemi Abraham Adediran

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Hydrological Forecasting with Radar and the Probability Distributed Hydrological Model (PDM)

Copyright © 2010 Gbotemi Abraham Adediran

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ISBN-10: 1-61233-435-0 ISBN-13: 978-1-61233-435-6

Hydrological Forecasting with Radar and the Probability Distributed Hydrological Model (PDM) Gbotemi Abraham ADEDIRAN

i

DEDICATION

To my Dad; Pa Joseph Bamidele Adediran


ii

ACKNOWLEDGEMENT

I thank the Environmental Agency; England and Wales, the Meteorological office UK and

the British Atmospheric Data Council, for providing some of the data sets and models used to

carry out this research work. Most importantly, I thank Dr. Miguel Angel-Rico-Ramirez of

Bristol University UK, for his patience in bringing me to the strange world of hydrological

modelling, and for successfully invoking diligence and excellence in me.


iii

ABSTRACT

Hydrological measurements from traditional rain and flow gauges are regarded as the true

measurement of hydrological occurences on the ground. Data from gauged measurments are

however not very effective in real time hydrological forecasting and modern hydrological

forecasting system is increseingly based on the use of data generated from weather radar.

Furthermore, instead of redering a singular radar based forecast, a more robust probabilistic

forecatings system is percieved to be more realistic.

This work therefore accessed the effeciency of weather radar, a Deterministic Now casting

System (DNS) a Stochastic Now Casting System (SNS) and the Probability distributed

hydrological model (PDM) in measuring and forecasting precipitation and floods at the Brue

catchment in south-western England, UK.

The ability of the radar to measure gauged precipitation in 2007 (regarded as the ground

truth) was evaluated using Normalized Bias (NB) and Normalized Error (NE) statistics as the

objective funtion of evaluation. Radar overestimated precipitation measurements by average

gauges with NB value of 0.41 and a considerably low NE of 0.68. Furthermore, the

effectiveness of a Deterministic nowcasting system (DNS) to forecast radar measured

precipitation at 132 forecast time series of 6hrs forecast lead time was assessed. The DNS

overestimated the radar measured precipitation with a NB value of 0.87 and recorded an

accumulated NE of 1.46. Morover, the effeciencies of 10 esemble precipitation forecats

generated from a Stochastic nowcasting system (SNS) over the singlelar determinisitc

forecasts from the DNS was evaluated at 3 major hydrological events. Some of the ensembles

significantly performed better than the deterministic forecast and brilliantly captured the

radar measured precipitation at most of the forecast time series.


iv

Furthermore, the efficiencies of these sources of precipitation measurement to simulate flows

with the PDM at the Brue catchment were also assessed by integrating the radar based

forecasts with measurements from average gauges. The PDM performed satisfactorily well in

simulating the flows of 17th

January 2007 with an average Nash–Sutcliffe Efficiency Index

(NSE) of 0.65 and the model was judged insensitive to the significantly high precipitation

inputs for the hydrological event of 27th

of May 2007. However, the PDM performed poorly

in simulating flows for the historical storms of 20th

of July 2007; with the model under

estimating flows with bias value of over 250 m3s

−1 for an event popular for its devastating

flooding in the Southwest of England. The model inadequacies was however associated to

poor radar precipitation measurements and forecasts on which flow simulation was based.

This work therefore emphasis the need for developments in hydrological modelling as well as

advancement in weather radar technology to effectively correct radar errors due to radar

calibration, signal attenuation, clutter and anomalous propagation, vertical variation of

reflectivity, range effects, Z-R relationships, variations of drop size distributions, vertical air

motions, beam overshooting the shallow precipitation and sampling issues, that has been

identified to affect radar measurements.


v

Table of Contents

DEDICATION...................................................................................................................... (i)

ACKNOWLEDGEMENT................................................................................................... (ii)

ABSTRACT......................................................................................................................... (iii)

Table of Contents……........................................................................................................... (v)

CHAPTER ONE

1.0 INTRODUCTION

1.1 Background of the Study.................................................................................................. (1)

1.2 Justification of the Study.................................................................................................. (2)

1.3 Research questions and hypothesis................................................................................... (3)

1.4 Aims and Objectives......................................................................................................... (4)

CHAPTER TWO

2.0 LITRATURE REVIEW

2.1 Flood: types, causes and importance................................................................................ (5)

2.2 Principles of Integrated flood management...................................................................... (6)

2.3 Principles of flood forecasting.......................................................................................... (8)

2.4 Historical trends of Hydrological modelling.................................................................... (9)

2.5 Basic Classification of Hydrological Models................................................................. (11)

2.6 Rainfall-runoff models in the UK................................................................................... (13)

2.7 The Probability Moisture Distributed Model (PDM)

(i) Principles.............................................................................................................(14)

(ii) Mathematical Algorithm.....................................................................................(16)

(iii) Error and error correction in PDM......................................................................(23)

(iv) PDM as a computer software...............................................................................(24)

2.8 Measurement of Precipitation with Weather Radar........................................................ (26)

(i) Principles of Radar measurements......................................................................(27)

(ii) Radar error and error corrections........................................................................(28)

2.9 Quantitative Precipitation Forecasting........................................................................... (30)


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CHAPTER THREE

3.0 METHODOLOGY WITH RESULTS

3.1 Hydrological Modelling

(i) Description of the modelled catchment.............................................................. (34)

(ii) Hydrological Data Sets.......................................................................................(34)

(iii) Calibration of the PDM model...........................................................................(38)

(a) Statistics for assessing model calibration.................................................................(49)

(b) Assessments of PDM-Parameters Optimization......................................................(39)

(c) Results of Parameters optimization and Model Calibration......................................(40)

(iv) Validation of the PDM model............................................................................(45)

(a) Results of Model Validation.....................................................................................(45)

3.2 Precipitation Forecasting............................................................................................... (50)

3.2.1 Analysis of precipitation measurements and forecasts

(i) Evaluation of Radar’s ability to measure precipitation......................................(51)

(a) Statistics for the evaluation.......................................................................................(51)

(b) Results.......................................................................................................................(52)

(ii) Evaluation of the ability of the Deterministic Nowcasting system (DNS) to

forecast Radar-measured precipitation...............................................................(54)

(iii) Evaluation of the performance of the DNS and the 10 stochastically generated

probabilistic forecasts from the SNS in forecasting flows for 3 selected

Hydrological

Events..................................................................................................................(58)

3.3 Flood Forecasting.......................................................................................................... (70)

Statistical Analysis......................................................................................................... (71)

(i) Assessment of flood forecasting with DNS and 10 SNS for Hydrological event 1;

2300hrs 17th January 2007, to 1900hr 18th January 2007.................................(72)

(ii) Assessment of flood simulation with PDM for Hydrological event 2; 27th May

2007, from 0500 to 0900hrs)..............................................................................(77)

(iii) Assessment of flood forecasting with DNS and 10 SNS for the extreme

Hydrological event of 20th

July 2007.................................................................(79)

CHAPTER FOUR

4.0 SUMMARY OF RESULTS.......................................................................................... (88)

CHAPTER FIVE

5.0 CONCLUSIONS, RECOMENDATIONS AND LIMITATION................................... (92)

5.1 Research Limitations...................................................................................................... (93)


vii

References............................................................................................................................ (94)

List of Abbreviation

PDM- Probability Distributed Model

DNS-Deterministic Nowcasting System

SNS-Stochastic Nowcasting System

NB-Normalized Bias

NE-Normalized Error

RMSE-Root Mean Square of Error

NSE- Nash–Sutcliffe Efficiency Index

Det- Forecast from Deterministic Nowcasting System and e1, e2 ...e10. - Ten ensemble

forecasts from the Stochastic Nowcasting System.

List of Tables

Table1: Description of standard PDM model parameters (Moore and Bell, 2001) (23)

Table: 2 Calibration Shell of the PDM showing calibrated parameters (41)

Table: 3. PDM Calibration shell showing the calibrated hydrological components and the

RMSE of calibration (42)

Table 4: Selected Hydrological Events (50)

List of figures

Figure 1: A framework for an integrated flood warning system (Moore et al., 2005) (9)

Figure 2: PDM Rainfall-runoff model (From Moore, 2007) (15)

Figure 3: Conceptual description of the PDM (From Cabus, 2008) (15)

Figure 4: The storage capacity distribution function for calculating basin moisture storage, critical capacity, and direct runoff

according to the PDM (Moore, 2007) (19)

Figure 5: The Pareto distribution of storage capacity (Moore, 2007) (20)

Figure 6: Rainfall-runoff relationship for the PDM using Pareto distribution of storage capacity (21)

Figure 7: Outline of PDM model configuration and data requirements (CEH, 2007) (25)

Figure 8: A screen short of the PDM calibration shell (25)

Figure 9: Precipitation measurement with Weather Radar (26)

Figure 10: Performance of forecast skills of Radar nowcasts and NWP over forecast lead time (31)

Figure 11: Location and arrangement of Raingauges at the Brue Catchment (Younger et.al. 2006) (35)


viii

Figure 12: Brue catchment with Lovington-Flow-Gauging Station at the out let of the catchment (36)

Figure 13: A superimposed graphs of Rainfall and flows for the PDM calibration time series (1994 to 1996) (38)

Figure 14: Results of Parameters optimization (40)

Figure 15: Calibration Hydrograph (July 1994 to May 1996) (43)

Figure 16: Calibration Hydrograph (October 1994 to July 1995) (44)

Figure 17: Calibration Hydrograph (August 1995 to May 1996) (44)

Figure 18: Hydrograph of Validation time series (October 2006 to December 2007) (46)

Figure 19: Hydrograph of calibration time series (October 2006 to April 2007) (46)

Figure 20: Hydrograph of Validation time series (May 2007 to December 2007) (47)

Figure 21: Hydrograph of model validation with Radar data (October 2006 to Dec. 2007) (48)

Figure 22: Hydrograph of model validation with Radar data (October 2006 to April 2007) (48)

Figure 23: Hydrograph of model validation with Radar data (May 2007 to December 2007) (49)

Figure 24: Accumulated Precipitation measurement by Radar and Average gauges (accumulated and calculated at every six

hours. The inserted straight line indicates a perfect fit; points where the Gauges measurement equals measurement by

Radar.) (53)

Figure 25: Total Accumulated Precipitation measurements and DNS forecasts; accumulated and calculated at every six

hours. (The inserted straight line indicates a perfect measurement; i.e., points where the DNS forecasts exact precipitation

measured by the Radar) (55)

Figure 26: Total Accumulated Precipitation measurements and DNS forecasts; accumulated and calculated at every six

hours. (The inserted straight line indicates a perfect measurement; i.e., points where the DNS forecasts exact precipitation

measured by the Radar) (56)

Figure 27a: Precipitation forecasts by DNS and 10 SNS with Radar Measurements (Hydrological Event 1; from 2300hrs

17th January 2007, to 1900hr 18th January 2007) (59)

Figure 27b: Precipitation forecasts by DNS and 10 SNS with Radar Measurements (Hydrological Event 1; from 2300hrs

17th January 2007, to 1900hr 18th January 2007) (60)

Figure 28: Normalized Bias of DNS and 10 SNS over 6 hrs forecasts lead time in 13 time series for hydrological Event 1;

from 2300hrs 17th January 2007, to 1900hr 18th January 2007 (61)

Figure 29: Normalized Error of DNS and 10 SNS over 6 hrs forecasts lead time in 13 time series for hydrological Event 1;

from 2300hrs 17th January 2007, to 1900hr 18th January 2007 (62)

Figure 30a: Precipitation forecast by DNS and 10 SNS with Radar Measurements (Event 2; 27th May 2007, from 0500 to

2300hrs) (63)

Figure 30b: Precipitation forecast by DNS and 10 SNS with Radar Measurements (Event 2; 27th May 2007, from 0500 to

2300hrs (64)


27th May 2007, from 0500 to 2300hrs (65)


27th May 2007, from 0500 to 2300hrs (65)

Figure 33a: Precipitation forecast by DNS and 10 SNS with Radar Measurements (Event 4; 20th July 2007) (67)

Figure 33b: Precipitation forecast by DNS and 10 SNS with Radar Measurements (Event 4; 20th July 2007) (68)


20th July 2007, from 0300 to 1600hrs (69)


ix


27th May 2007, from 0500 to 2300hrs (69)

Figure 36a: Hydrographs of flow simulation for Event 1; 2300hrs 17th January 2007 to 1900hr 18th January 2007 (73)

Figure 36b: Hydrographs of flow simulation for Event 1; 2300hrs 17th January 2007 to 1900hr 18th January 2007

(74)

Figure 37: NSE of Simulated flows by DNS and 10 SNS for hydrological event 1; 2300hrs 17th January 2007, to 1900hr

18th January 2007 (Inserted line indicating level of acceptance) (75)

Figure 38: Bias of Simulated flows by DNS and 10 SNS for hydrological event 1; 2300hrs 17th January 2007, to 1900hr

18th January 2007 (76)

Figure 39: Relative Bias of Simulated flows by DNS and 10 SNS for hydrological event 1; 2300hrs 17th January 2007, to

1900hr 18th January 2007 (Inserted line indicating level of significance) (76)

Figure 40: Hydrographs of flow simulation for event 2; 27th May 2007, from 0500 to 0900hrs (78)

Figure 41: Hydrograph of Calibration and Validation time series of Event 2; 27th of May 2007 (79)

Figure 42a: Hydrographs of flow simulation for Event 4; 0300hrs to 1600hrs 20th of July 2007 (80)

Figure 42b: Hydrographs of flow simulation for Event 4; 0300hrs to 1600hrs 20th of July 2007 (81)

Figure 43: Radar measurements and Nowcasting forecast (e10) Scans over the Brue catchment; (inserted catchment

boundary- within Northing 100 to 150, Easting 350 to 400Km): 20/07/2007, 11:30 (82)


boundary- within Northing 100 to 150Km, Easting 350 to 400Km): 20/07/2007, 12:30 (83)


boundary- within Northing 100 to 150, Easting 350 to 400): 20/07/2007, 13:30 (84)

Figure 46: NSE of Simulated flows by DNS and 10 SNS for hydrological event 4; 0300hrs to 1600hrs 20th of July 2007

(Inserted line indicating level of acceptance) (85)

Figure 47: Bias of Simulated flows by DNS and 10 SNS for hydrological event 4 (86)

Figure 48: Relative Bias of Simulated flows by DNS and 10 SNS for hydrological event 1; 2300hrs 17th January 2007, to

1900hr 18th January 2007 (86)


1

CHAPTER ONE

1.0 INTRODUCTION

1.1 Background of the Study

Flooding is the most common of all natural hazards and impacts on the greatest number of

people across the world. It is an inevitable natural phenomenon occurring from time to time

along river plains and natural drainage systems (Ramkumar et al., 2015). A meticulous

compilation of natural disasters data that spans from 1980 to 2008, indicates that from the

2,887 flooding events recorded over this period, 2,809,481,489 people were affected with an

addition of 195,843 deaths, and an approximated economic damage of (US $ X 1,000)

397,333,885 (EM-DAT, 2009). The reason behind this huge impact simply lies in the

attraction of the widely distributed floodplains and low-lying coasts to human settlement

worldwide. Three out of every five persons in the world presently lives within 60km of an

ocean or major rivers and it has been estimated that by 2010, 80% of the world's population

will inhabit a coastal strip hundred kilometres wide; the same area which already holds eight

of the world's ten most populated cities (Small and Nicholls, 2003).

Furthermore, floods caused by sea-level rise are expected to affect millions of additional

people every year by the end of this century, with small islands and the crowded delta regions

around large Asian rivers (such as the Ganges-Brahmaputra) facing the highest risk; and

regions of low lying areas of North America, Latin America, Africa and populous coastal

cities of Europe, also facing flood risk from both large rivers and ocean storms (IPCC, 2007).

The society may still continue to doubt the possibilities of this predicted disaster and the

reality of Climate change, but the nightmare of November 2009 where over 1,000 homes

were flooded in the town of Cocker -mouth in the UK city of Cumbria, left nobody in doubt


2

that flooding is the number one threat facing the UK. The society must adapt to deal with the

climate change induced increasing flooding risk, but it seems highly unlikely that any feasible

engineered adaptation mechanism will completely reduce the threat. Therefore, the provision

of warnings with sufficient lead time to enable society to mitigate losses will be very

important in reducing impacts.

1.2 Justification of the Study

Floods that cause large number of fatalities and costly damages have primarily been

associated with developing countries (Wisner et al., 2004) however, even the most developed

nations are significantly affected by flash flooding, fluvial and pluvial flooding. For example,

the 2002 floods in Europe killed roughly 100 people, affected 450,000 people and left $20

billion worth of damages (Bogardi, 2004). The data of European catastrophic flash flooding

since 1950 has been documented (Gaume et al., 2009) and detailed examination of this data

revealed that flash floods occured in all the hydro-climatic region of Europe. Building flood

defences (Barriers) has been the most popular approach in mitigating flood risks.

However, the magnitude of the present flood risk zones, with the possibilities of future

increase in flood risk zones, has made the provision of effective flood defences not only

unrealistic but also economically unaffordable. Moreover, the best form of natural disaster

defence is not to work against nature (by challenging flood with mechanical barriers) but by

working with nature. Therefore, an integrated flood management system that is based on

Hydrological forecasting is the most effective method of flood mitigation.

The availability of flood forecasting and warning system ensures timely evacuation and

relocation of valuables, alerts rescue workers, enables the possibility of installing flood

resilience measures (e.g. Sand Bags and Property barriers), prevent secondary disaster like


3

electrocution and provide the opportunity for effective planning to reduce aftermath impacts.

However, at the heart of a flood warning system is hydrological forecasting; a process that

uses precipitation and stream flow data in rainfall-runoff and stream flow routing models to

forecast flow rates and water levels for periods ranging from few hours to days ahead. The

accuracy of forecasted rainfall data, and effective calibration and adoption of the proper flow

routing models are therefore the essentials of flood forecasting.

This work therefore attempt to explore the concept of probabilistic hydrological forecasting,

by incorporating radar measured rainfall data with that of rain gauges measurement, and

using one of the UK-Environmental Agency preferred Model; the Probability Distributed

Hydrological Model (PDM), to simulate flows for the Brue catchment in the South west of

England. Presently, around 5 million people in 2 million properties live in areas at risk from

flooding in England and Wales, with some of these areas along the flood plain of Brue River

in Somerset, South-East of England (Defra, 2009). An effective flood forecasting system is

therefore the only hope for saving the flood prone areas in poor developing countries that are

practically without any defence, as well as for the people in developed country like the UK

who are still awaiting a flood defence.

1.3 Research questions

This research attempts to answer the following questions:

How effective are precipitation forecasts by a Deterministic nowcasting1 system

(DNS) in forecasting Radar-measured precipitation?

Is there any significant difference in precipitation forecasts by ensembles of a

stochastic nowcasting system (SNS) and a DNS?

1 Nowcasting- ‘A technique for very short-range forecasting that maps the current weather, then uses an estimate of its speed and

direction of movement to forecast the weather a short period ahead — assuming the weather will move without significant changes’ (Met-Office, 2010).


4

In terms of forecasting flows for the Brue catchment using the PDM; are precipitation

forecasts from DNS better than the ensemble forecasts from SNS?

What are the important hydrological parameters for calibrating the PDM for Brue

catchment?

How effective is the PDM in forecasting flows for the Brue catchment by

incorporating forecast generated from radar data with precipitation data measured by

raingauges?

Does a SNS really provide an excellent opportunity for quantifying uncertainties in

flow forecasting through the ensemble quantitative precipitation forecasts it

generates?

1.4 Aims and objectives

The broad aim of this research is to develop a framework for probabilistic flood forecasting

system for the Brue catchment with the PDM model, using integrated precipitation data from

the raingauges, the deterministic nowcasts and the stochastic nowcasts.

The objectives of this research are:

To evaluate the efficiencies of various precipitation measurements and forecasts

methods.

To understand the principles of Hydrological forecasting with the PDM model

To evaluate the concepts of probabilistic hydrological forecasting

To investigate the importance and effects of model parameters in the calibration stage.

To test different auto calibration methods for parameter estimation

To investigate the importance of the calibration and validation time series

To Build an initial PDM to simulate flows for Brue Catchment

And to investigate the ability of the PDM to forecast runoff and analyse the limits of

predictability.


5

CHAPTER TWO

2.0 LITRATURE REVIEW

2.1 Flood: types, causes and importance

Of all natural disasters, floods impact on the greatest number of people across the world

(Moore et al., 2005). A flood is simply an overflow of an expanse of water that submerges

land. The EU Flood directives further defines flood as the temporary covering by water of

land not normally covered by water (EU, 2007). There are diverse sources or causes of

floods. The EU flood directives identifies these to include floods from rivers, mountain

torrents, Mediterranean ephemeral water courses, and floods from the sea in coastal areas, but

may exclude floods from sewerage systems (EU, 2007). Moreover, flooding can be separated

into three main categories: flash flooding, river flooding, and coastal flooding (French and

Holt, 1989). Flash flooding is defined as a flood that rises and falls quite rapidly, usually as a

result of intense rainfall over a small area, in a short amount of time, usually under 6 hours;

river flooding is defined as the rise of a river to an elevation such that the river overflows its

natural banks causing or threatening damage; and coastal flooding pertains to flooding which

occurs from storms where water is driven onto land from an adjacent body of water (Ashley

and Ashley, 2008).

Floods are naturally occurring inevitable events that are dependent not only on rainfall

amounts and rates, but also on the topography of the area, land use of the region, soil type of

the watershed, and antecedent moisture conditions (Funk, 2006). Floods that significantly

disrupt or incapacitate a society by causing a large number of fatalities and costly damage

have primarily been associated with developing countries, for example, Bangladesh floods

(Wisner et al., 2004). However, even the most advanced nations are affected: the 2002 floods


6

in Europe killed roughly 100 people, affected 450,000 people and left $20 billion in damages;

the US, which suffered 50 deaths and $50 billion in damage in the Mississippi River flood of

1993, has averaged 25 flood deaths annually since the 1980s (Bogardi, 2004).

A meticulous compilation of natural disasters data that spans from 1980 to 2008, indicates

that from the 2,887 flooding events recorded over this period, 2,809,481,489 people were

affected with an addition of 195,843 deaths, and an approximated economic damage of (US

$ X 1,000) 397,333,885 (EM-DAT, 2009). The reason behind this huge impact simply lies in

the attraction of the widely distributed floodplains and low-lying coasts to human settlement

all around the world. Since water supply has been a decisive factor in the search for adequate

settlement locations throughout history, river banks and lakesides have become preferred

living spaces. Most of the cities in the World are located in the valleys and flood plains or on

coasts (WMO/GWP, 2008). It has been predicted that pressure to live and work in flood-

prone areas, which typically feature attractive rich soils, abundant water supplies and ease of

transport, will increase as the world’s population continues spiralling upward. The United

Nations University Institute for Environment and Human Security (UNU-EHS) therefore

warns that unless mitigating efforts are stepped up, the number of people vulnerable to flood

disasters worldwide is expected to mushroom to two billion by 2050 as a result of climate

change, deforestation, rising sea levels and population growth in flood-prone lands (Bogardi,

2004).

2.2 Principles of Integrated Flood Management

Flood management process has been traditionally problem driven. This usually basically

involves the implementation of projects like emergency evacuation, provision of relief

materials and compensation for losses. Moreover, inappropriate flood-management strategies


7

pursued over the years have been largely reactive in response to flood threats rather than

being proactive (Vijai, 2006).

For example, around 5.2 million properties in England - or one in six properties - are

currently at risk of flooding from surface water, rivers and the sea (Defra, 2009). In the recent

past, constructing defences has been the main way of dealing with the risks of flooding and

coastal erosion. Although physical defences remain a vitally important part of flood

management approach, it is however very costly to build and maintain and may not always be

the most sustainable option. Latest predictions are that in order to maintain the same level of

protection against flooding from rivers and the sea, funding will need to at least double again

by 2035 (Defra, 2009).

However, the Plan of Implementation of the World Summit on Sustainable Development

(WSSD), held in Johannesburg in August/September 2002, highlights the need to “... mitigate

the effects of drought and floods through such measures as improved use of climate and

weather information and forecasts, early warning systems, land and natural resource

management, agricultural practices and ecosystem conservation in order to reverse current

trends and minimize degradation of land and water resources …” (APFM, 2004).

Integrated Flood Management is therefore a process promoting an integrated – rather than

fragmented approach to flood management. It integrates land and water resources

development in a river basin, within the context of IWRM, and aims at maximizing the net

benefits from flood plains and minimizing loss to life from flooding (APFM, 2004). It

comprises a combination of management methods like Source control to reduce runoff (e.g.

permeable pavements, afforestation); Storing runoff (e.g. detention basins, wetlands,

reservoirs); Increasing the capacity of the river (e.g. bypass channels, channel deepening or

widening); Separating the river and the population (e.g. land use control, dikes, flood-

http://www.defra.gov.uk/environment/flooding/funding/index.htm

http://www.defra.gov.uk/environment/flooding/funding/index.htm


8

proofing, house raising); Emergency management during the flood (e.g. flood warnings,

emergency works to raise or strengthen dikes, flood-proofing, evacuation); and Flood

recovery (counselling, compensation or insurance) (APFM, 2004).

2.3 Principles of flood forecasting

It is a matter of fact that good policy and planning can reduce the exposure to flooding

through control of land management and housing development, and well-designed flood

defence schemes will alleviate the impact of flooding. However, complete protection from

flooding is rarely a viable goal (Moore et al., 2005). There is therefore a need for flood

forecasting system that is efficient in issuing warning of imminent flooding to allow timely

human evacuation and relocation of valuables.

Flood forecasting is the use of real-time precipitation and stream flow data in rainfall-runoff

and stream flow routing models to forecast flow rates and water levels for periods ranging

from a few hours to days ahead, depending on the size of the watershed or river basin (AMS,

2010). It is a technique which uses the known characteristics of a river basin to predict the

timing, discharge, and height of flood peaks resulting from a measured rainfall, usually with

the objective of warning populations who may be endangered by the flood (Allaby, 2004). An

integrated forecasting system ‘chain’ with rainfall measurement sources, rainfall displays that

provides first-alert and flood-preparedness information, rainfall processing that provides

inputs to flood forecasting and modelling systems, and decision-support facilities that trigger

dissemination of flood warnings to communities informed on how to respond (Moore et al.,

2005) is presented in Figure 1.

http://amsglossary.allenpress.com/glossary/search?id=streamflow-routing1

http://amsglossary.allenpress.com/glossary/search?id=watershed1

http://amsglossary.allenpress.com/glossary/search?id=river-basin1


9

Figure 1: A framework for an integrated flood warning system (Moore et al., 2005)

Moreover, a flood forecast system must provide sufficient lead time for communities to

respond. Increasing lead time increases the potential to lower the level of damages and loss of

life. Equally, forecasts must be sufficiently accurate to promote confidence so that

communities will respond when warned because if forecasts are inaccurate, the credibility of

the programme will be questioned and no response actions will occur (UN, 2002).

2.4 Historical trends of Hydrological Modelling

Historically, the Rational Method proposed by the Irish Engineer, Thomas James Mulvaney,

(Mulvany, 1850) has been widely recognized as the beginning of hydrological modelling

(Beven, 2002). The Mulvaney’s Rational Method concepts provided a clear exposition of the

concept of time of concentration and its relation to maximum runoff; it estimates peak flow

but not floods volume and is physically meaningful only in small impervious catchments in

which flow is effectively a purely kinematic process (Todini, 2007).

The Mulvaney’s model is described by a simple mathematical equation:

Qp = CAR. (1)


10

The equation does not attempt to predict the whole hydrograph but only the hydrograph peak

Qp, with input variable, A, the catchment area, R, the maximum average rainfall intensity and

C, an empirical coefficient (Beven, 2002). This model was applied to the design of sewers

around the 19th

century (Kuichling, 1889, Lloyd-Davies, 1906).

Furthermore, (Sherman, 1932) introduced the concept of the unit hydrograph (UH). This was

based on the principle of superposition of effects, allowing the complete flood hydrograph to

be predicted from rainfall sampled at constant interval (Todini, 2007). After the introduction

of the system theory, the unit hydrograph was later interpreted as the response of a linear,

causative, dynamic stationary system into two forms of hydrograph units; the instantaneous

unit hydrograph (IUH) and the finite period unit hydrograph (TUH) (O’Donnell, 1966) as

described by Todini, 2007). In other to achieve a better physical interpretation of catchment

response, the 1960s saw the development of models in which individual components in the

hydrological cycle were represented by interconnected conceptual elements each of which

represented a particular subsystem (Todini, 2007). Some of these models were described in

(Dawdy and O’Donnell, 1965), and (Crowford and Linsley, 1996).

Moreover, a new type of lumped model was introduced at the end of the 1970s. These were

based on the concept that the rainfall runoff process is mainly dominated by the dynamics of

saturated areas which can be related to the soil moisture storage, based on the Dunne

assumption that all precipitation enters the soil and that surface runoffs originates by

saturation of the upper soil layer (Todini, 2007). Examples of these models are the

Xinanjiang soil moisture distributed model (Zhao, 1977) and the Probability Distribution

Model (PDM) (Moore and Clarke, 1981). (Beven and Kirkby, 1979) developed a better

distribution function model called the TOPMODEL, based on the assumption that

accumulation of soil moisture can be approximated by successive steady states of the water

table originating in the upper soil layer (Todini, 2007).


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Conclusively, the advances in remote sensing technology that provides detailed variety of

information like soil types and land use, and especially the availability of weather radar

technology, have recently led to the development of hydrological models that are used in real

time probabilistic hydrological forecasting.

2.5 Basic Classification of Hydrological Models

There are different ways of classifying the numerous hydrological models. However,

hydrological models can basically be classified into two broad classes, but of four types.

These are the Lumped or Distributed Hydrological Models, and the Deterministic Models or

the Stochastic Models.

The lumped models treat the catchment as a single unit, with state variables that represent

averages over the catchment area, as average storage in the saturated zone (Beven, 2002).

The GR2M model (Makhlouf and Michel, 1994) and the Probability distributed hydrological

model (PDM) More (Moore, 2007) are examples of lumped model. This model is capable of

simulating monthly discharge using estimations of average rainfall in a basin. It provides a

simplified representation of the rainfall–discharge process and is characterised by a small

number of parameters which do not correspond to specific physical attributes (Niel et al.,

2003). On the other hand, Distributed hydrological models make prediction that are

distributed in space, by discretizing the catchment into a large numbers of elements or grids

squares and solving the equations for the state variables associated with every element grid

square (Beven, 2002). Distributed model sometimes have a routing component of the main

river(s) within a catchment which however requires detailed information of cross-sectioning

in the river(s).


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The HRCDHM model (Hydrology Research Canter Distributed Hydrologic Model) is an

example of a distributed model. The HRCDHM is a sub catchment based model which uses

the Sacramento model for runoff generation within each sub catchment (Carpenter and

Georgakakos, 2006). It is a ‘data hungry’ model with potential difficulties in providing

enough data to ensure optimum model functioning. It also includes components for temporal

distribution of runoff at the sub catchment outlet and kinematic channel routing between sub

catchments and to the watershed outlet (Carpenter et al., 2001, Carpenter and Georgakakos,

2004).

Moreover, Deterministic models are models in which the processes are modelled based on

definite physical laws and no uncertainties in prediction are admitted (Seth, 2009).

Deterministic models permits only one outcome from a simulation with one set of inputs and

parameters values (Beven, 2002). The water and environmental consultants — catchment

(WEC-C) model is an example of a distributed, deterministic model of numerical form, that is

capable of simulating both water and solute movement within a catchment (Croton and Bari,

2001). Other examples include the SHE (Système Hydrologique Européen) Model (Abbott et

al., 1986, Jain et al., 1992), the TOPOG (Terrain Analysis Hydrologic Model)(O’Loughlin,

1986, Vertessy et al., 1993) and IHDM (Institute of Hydrology Distributed Mode)(Calver

and Wood, 1995).

In contrast to the Deterministic hydrological models, the stochastic models allow for some

randomness or uncertainty in the possible outcomes, due to uncertainty in input variables,

boundary conditions or model parameters (Beven, 2002). The Autoregressive moving

average (ARMA) model has been the stochastic model of choice to generate synthetic

sequences, however, recent advances in the understanding of the inter-annual and multi-

decadal variability in hydrological time series caused by the nonlinear climate dynamics

recent research has advocated for more complex stochastic models (Thyer et al., 2006).


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The lag-one autoregressive (AR(1)) model (Grayson et al., 1996) and the two-state hidden

Markov model (HMM) are examples of complex stochastic models (Thyer et al., 2006).

2.6 Rainfall-runoff models in the UK

The Environmental Agency (EA) in the UK adopts a range of both locally and internationally

developed models for flood forecasting. They range in type from transfer function (empirical

black box), through lumped conceptual to more physically-based distributed models (Moore

and Bell, 2001) Some of the models used by the EA include the Thames Catchment Model

(TCM), Midlands Catchment Runoff Model (MCRM), Probability Distributed Moisture

model (PDM), Isolated Event Model (IEM), US National Weather Service (Sacramento)

model (NWS), Transfer Function model (TF), Physically Realisable Transfer Function model

(PRTF) and the Grid Model (Developed by IH for the NRA) (Moore and Bell, 2001). All

these models are capable of transforming rainfall and evaporation time series of total

catchment flow. The Thames Catchment Model (TCM), the Midlands Catchment Runoff

Model (MCRM), the Probability Distributed Moisture model (PDM), and the US National

Weather Service Sacramento model (NWS) are all lumped conceptual models with

continuous water accounting procedures, and each model is associated with an updating

procedure whereby recent measurements of flow are incorporated into the model so as to

improve forecast performance in real-time (Moore and Bell, 2001).

The result of a comprehensive comparison of these models suggests that no model

consistently out-performs all others across a number of catchments. The TCM was identified

as one of the best performing models when judged using the R2 statistics whilst the PDM was

more successful while judged according to the Threshold CSI criterion (relevant to the

issuing of flood alerts) and in forecasting flood peaks (Moore and Bell, 2001).


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The results of the 2001 Model comparison also indicates that Operationally, the TCM, PDM

and IEM models appear to be the most appropriate flood forecasting models to use, of those

assessed, the choice depending on the complexity of catchment response whilst all models

have value in the right situation (Moore and Bell, 2001).

2.7 The Probability Moisture Distributed Model (PDM)

(i) Principles

The hydrological Probability Distributed Moisture (PDM) model; developed at the Centre for

Ecology and Hydrology is a fairly conceptual rainfall-runoff model which uses a distribution

of soil moisture storage capacities for soil moisture accounting (Moore, 1985, Moore, 1999,

Moore, 2007) production of runoff along the gradient of a catchment is mainly controlled by

the soils water absorption capacity which can be conceptualised as a simple store of a storage

capacity. Based on the principle that different points in a catchment have differing storage

capacities and that the spatial variation of a capacity can be described by a probability

distribution, the PDM was therefore developed to integrates the point runoffs to yield the

catchment surface runoff into surface storage (Moore and Bell, 2001). A schematic

representation of the PDM (Moore, 2007) and a conceptual description of the PDM (Cabus,

2008a) are presented in Fig. 2 and Fig. 3 respectively.

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