UBC Theses and Dissertations

UBC Theses Logo

UBC Theses and Dissertations

Flood advisor : an expert system for flood estimation Fayegh, A. David 1985

Your browser doesn't seem to have a PDF viewer, please download the PDF to view this item.

Item Metadata

Download

Media
831-UBC_1985_A7 F39.pdf [ 3.97MB ]
Metadata
JSON: 831-1.0062732.json
JSON-LD: 831-1.0062732-ld.json
RDF/XML (Pretty): 831-1.0062732-rdf.xml
RDF/JSON: 831-1.0062732-rdf.json
Turtle: 831-1.0062732-turtle.txt
N-Triples: 831-1.0062732-rdf-ntriples.txt
Original Record: 831-1.0062732-source.json
Full Text
831-1.0062732-fulltext.txt
Citation
831-1.0062732.ris

Full Text

FLOOD ADVISOR : AN EXPERT SYSTEM FOR FLOOD ESTIMATION by A. DAVID FAYEGH B.A.(Math), Queen's U n i v e r s i t y , K i n g s t o n , O n t a r i o , 1983 B.Sc(Eng)., Queen's U n i v e r s i t y , ' K i n g s t o n , O n t a r i o , 1983 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF OF THE REQUIREMENTS FOR THE DEGREE OF THE FACULTY OF GRADUATE STUDIES (Department of C i v i l E n g i n e e r i n g ) We accept t h i s t h e s i s as conforming to the r e q u i r e d standards THE UNIVERSITY OF BRITISH COLUMBIA October, 1985 (c) A. David Fayegh, 1985 Masters of A p p l i e d Science i n In presenting t h i s t h e s i s in p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s t h e s i s for scholary purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s for f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of C i v i l Engineering The U n i v e r s i t y of B r i t i s h Columbia 2075 Westbrook Place Vancouver, Canada V6T 1W5 Date : /^/ OrrToR&rxL / / 1 8 Jf i i ABSTRACT Expert computer programs have recently emerged from research on a r t i f i c i a l intelligence as a practical problem-solving tool. An expert system is a knowledge-based program that imitates the problem-solving behaviour of a human expert to solve complex real-world problems. While conventional programs organize knowledge on two levels: data and program, most expert programs organize knowledge on three levels: data, knowledge base, and control. Thus, what distinguishes such a system from conventional programs is that in most expert systems the problem solving model is treated as a separate entity rather than appearing only implicitly as part of the coding of the program. The purpose of this thesis is twofold. First, i t is intended to demonstrate how domain-specific problem-solving knowlege may be represented in computer memory by using the frame representation technique. Secondly, i t is intended to simulate a typical flood estimation situation, from the point-of-view of an expert engineer. A frame network was developed to represent, in data structures, the declarative, procedural, and heuristic knowledge necessary for solving a typical flow estimation problem. The control strategy of this computer-based consultant (FLOOD ADVISOR) relies on the concept that reasoning is dominated by a recognition process which is used to compare new instances of a given phenomena to the stereotyped conceptual framework used in understanding that phenomena. The primary purpose of the FLOOD ADVISOR is to provide interactive advice about the flow estimation technique most suitable to one of five generalized real-world situations. These generalizations are based primarily on the type and quantity of the data and resources available to the engineer. They are used to demonstrate how problem solving knowledge may be used to interactively assist the engineer in making d i f f i c u l t decisions. The expertise represented in this prototype system is far from complete and the recommended solution procedures for each generalized case are in their infancy. However, modifications may be easily implemented as the domain-specific expert knowledge becomes available. It is concluded that over the long term, this type of approach for building problem-solving models of the real world are computationally cheaper and easier to develop and maintain than conventional computer programs. TABLE OP CONTENT ABSTRACT i i TABLE OF CONTENTS iv LIST OF FIGURES v LIST OF SYMBOLS vi ACKNOWLEDGEMENT v i i CHAPTER 1: INTRODUCTION 1 CHAPTER 2: EXPERT SYSTEMS 4 2.1 : Background 4 2.2 : Expert Systems 6 2.2.1 : Knowledge 9 2.2.2 : Knowledge Representation Methodologies 10 2.3 : Knowledge Representation Using Frames 13 2.3.1 : Perspective 13 2.3.2 : Frames 14 2.3.3 : Reasoning With Frames 15 2.4 : Synopsis 16 2.5 : The Problem Solving Model For Flow Estimation..18 CHAPTER 3: FLOW ESTIMATION PROCEDURES 22 3.1 : Overview 22 3.2 : Probability, Statistics, And Hydrologic Data — 23 3.2.1 : Return period and reccurence interval 24 3.3 : A Prototype Hydrological Knowledge Base 28 3.3.1 : A Bayesian Approach For Flood Estimation.... 31 3.3.2 : Typical Flood estimation problems 32 3.3.2.1 : Case 1 32 3.3.2.2 : Case 2 33 3.3.2.3 : Case 3 37 3.3.2.4 : Case 4 38 3.3.2.5 : Case 5 39 CHAPTER 4: CONTROL STRATEGY AND SEARCH 41 4.1 : Introduction 41 4.2 : Stereotype And Instance 42 4.2.1 : Search 43 4.2.2 : Frame Hierarchies 48 4.2.3 : Recognition 51 4.2.4 : Expectation, Matching, and Completion 52 4.3 : Encoding The Knowledge Base 53 4.4 : Using The Flood Advisor 56 CHAPTER 5: DISCUSSION AND SUMMARY OF RESULTS 57 5.1 : Suggestions For Future Research 60 BIBLIOGRAPHY 62 APPENDIX : An interactive Session With FLOOD ADVISOR 64 V LIST OF FIGURES Figure 2.1 : Illustration of the NEW-PROBLEM frame 19 Figure 3.1 : Return period as a function of design life...29 Figure 3.2 : Solution Script for Case 1 34 Figure 4.1 : Illustration of the PROBLEM-AT-HAND frame....44 Figure 4.2 : Illustration of the FLOW-ESTIMATION frame. 46 Figure 4.3 : Illustration of composition hierarchies 49 vi LIST OF SYMBOLS A .... basin drainage area a .... a constant b .... a constant p(k;p,n) .... Binomial probability mass function k .... number of success (exceedences) n .... number of Bernoulli t r i a l s (years) p .... probability of exceeding QT in one year Q .... variable representing peak annual flow QI .... the index flood QT .... magnitude of the T-year event QT* .... any event with magnitude greater than QT T .... the return period of a T-year event v i i ACKNOWLEDGEMENTS I am greatful to Dr. S. 0. Russell for providing valuable guidence, encouragement, and supervision during the course of this research. Thanks are also due to my colleagues and friends for many enlightening discussions and suggestions. In particular I would like to thank Peter Cahoon for his assistance in setting up the control program on the C i v i l Engineering Vax. 1 CHAPTER ]_ j_ INTRODUCTION A water resource engineer is often faced with the task of making flood estimates which are most suitable to the particular design problem at hand. Like most hydrological calculations, flow estimates are prone to error which increase as the degree of approximation increases or when the estimation procedure is applied beyond the range of conditions for which i t was intended. The problem is that of heuristic optimization. A procedure which may be appropriate in one location, may produce poor estimates in another location. It is a d i f f i c u l t task to determine which procedure is most suitable and under what circumstances. In most situations there is no.single "best" method and the engineer must determine whether the cost, scope, or importance of a particular project justifies the additional cost of more elaborate methods or procedures. Conventional computer programs (such as PDRFFA, EPFFM, FLOODS, etc.) are extensively used in hydrology as a tool for solving well-defined flow estimation problems. Although these programs provide valuable summaries of computations and consequently assist the engineer in making d i f f i c u l t design decisions, they are expensive to develop and must often be modified (or completely re-written) to incorporate new procedures or rules of practice. In addition very few of these programs are capable of interpreting the summaries that they produce in the context of the problem at hand. Expert systems have recently emerged from Al research as a practical problem solving tool in certain domains of 2 application. This study will examine the suitability of these systems for solving design-oriented engineering problems. The design and implementation of domain-specific expert systems are largely dependant on the domain of application and on the choice of the knowledge representation scheme. In engineering design, i n i t i a l problem formulation is usually followed by numerical analysis. Such analysis includes manipulation of observed or experimental data based on some underlying problem solving model. At some stage of the problem solving process, numeric summaries of computations (produced by some well-defined procedure) are required for making decisions about the most appropriate method of solution. Consequently, for an Al expert program to be useful in this type of application, i t must be able to invoke procedures for performing complex numerical computations and provide information on how to manipulate the results of such analysis. It was found that the frame knowledge representation technique is the most suitable for design flow estimation. This technique allows procedures necessary for carrying out specific calculations to be attached to the general problem solving model for directing the reasoning behaviour of the system. This thesis describes the FLOOD ADVISOR, a computer-based consultant whose goal is to provide interactive advice about flow estimation under five generalized situations. The FLOOD ADVISOR is an example of a knowledge-based expert system in which a superior level of task performance is acheived by representing, in data structures, useful 3 specialized knowledge obtained from expert engineers. In presenting this prototype model, this thesis takes the following form: Chapter 2 discusses the frame representation technique used to represent declarative, procedural and heuristic knowledge in the FLOOD ADVISOR. The proper design of structures such as reservoirs, bridges, culverts, levees, highways waterworks, sewage disposal plants, storm sewers, etc is dependant on the type, quality and quantity of hydrologic data and on the economic cost and importance of the structure. Chapter 3 describes five generalized real-world situations as a characterization of a typical flood estimation problem. Procedures used in dealing with each situation are then reviewed. Chapter 4 outlines the recognition-based reasoning .mechanism . used to manipulate this prototype knowledge based system and illustrates how to encode the knowledge base so that i t can be processed by the control program. Chapter 5 discusses the advantages and disadvantages of the FLOOD ADVISOR and presents a number of suggestions for future research. 4 CHAPTER 2 j_ EXPERT SYSTEMS 2. 1 j_ Background The origins of A r t i f i c i a l Intelligence (Al) may be traced back to Allan Turing (1912 - 1953). In a famous paper entitled: "Computing, Machinery, and Intelligence" , Turing proposed that computational mechanisms could be constructed to behave in a manner that resembles human intelligence (Hofsdeter, 1979). In his paper, Turing outlines the rules of the "imitation game" (now known as the Turing test) that could be played with a machine to determine whether i t posesses 'intelligence 1. Since then, there have been numerous philosophical and moral debates regarding whether machines can (or should) posess human-like intelligence. The scientific community has not yet reached a concensus on what 'intelligence' really means mainly because an accurate model of human mind and intelligence is not available. Intelligent behaviour in human beings is associated with understanding language, learning, recognition of faces and objects, reasoning, solving problems, writing technical reports, composing music, design of computer systems, and so on. In order for a computer system to exhibit intelligence, i t must be able to a r t i f i c i a l l y simulate these types of mental ac t i v i t i e s . The design of such computer systems has been the subject of Al research in the past 30 years and has lead to the development of some useful experimental programs that (after Barr and Fiegenbaum, 1982): 1- Solve complex problems in chemistry, geology, and medicine at expert levels of performance, 5 2- manipulate robotic devices which perform repetitive "sensory-motor" tasks, and 3- understand questions posed in simple dialects of some desired language and translate text from one language to another. Whether or not these experimental Al systems posess human-like intelligence, they have emerged as practical tools for solving domain-specific real-world problems. Al methodologies are rooted in mathematical logic and the theory of computations. The logical systems of Russell, Whitehead, and others (developed in 1930s and 1940s) demonstrated that reasoning may be formalized in "consistent" (although "incomplete" (Godel, 1930s) "formal systems". The mathematical formalization of logical reasoning implies an abstract connection between reasoning and intelligence. Theories of computations were later developed by Church and Turing. These techniques demonstrate that the process of mathematical deduction can be mechanized by reducing the problem into two subproblems. First , the axioms, theorems, facts, and lemmas within any given formal system are expressed in symbolic logic and second, a set of rules or operators are developed to mechanically manipulate the syntactic form of the encoded facts. In this light, computations may be viewed as some type of symbolic  processing and numbers alone (without a symbolic context) are an "inessential aspect of computation" (used for the interpretation of the internal state of the machine). These key ideas were used for the development a simple "non-6 numerical model of computation" (Barr and Fiegenbaum, 1982). The mathematical formalization of logic and the theories on the nature of symbolic computation final l y emerged as Al after the development of the computing machines themselves (pioneered by Babage, Turing, and others). Soon after the f i r s t computers were built, the f i r s t Al programs were written to play chess, solve puzzles, translate text from one language to another, understand spoken language, etc. Al concepts emerged as a results of ideas about control systems, memories and processors, computing languages, and operating systems. The complexity of the computer as a man-made device has encouraged the emergence of a new science for describing complex processes in terms of data structures and procedures involving a large number of steps. In summary, Al research deals with creating programs that mimick human mental ac t i v i t i e s associated with intelligence. Thus algorithms are developed which incorporate domain-specific knowledge of the world in a system which can assist humans in solving practical real-world problems. 2.2 j_ Expert Systems Expert systems have recently emerged as a practical problem-solving tool from Al research. Typically, expert systems are used as intermediaries between human experts (who interact with the system in "knowledge acquisition mode"), and human users (who interact with the system in "consultation mode"). Like most Al systems, expert 7 consulting systems display a rigid separation between the standard computational components of data, operations, and control. At the appropriate level of abstraction, one may identify a "global database" that is operated upon by certain well-defined "operators" a l l under the control of some "global control strategy" (Nillson, 1980). The global database may be composed of a variety of data structures including arrays, sets of predicate logic expressions, l i s t s , frame networks, and semantic networks. The purpose of these data structures are to define the context and the final and intermediate goals that the system is trying to achieve. For example, in systems designed for proving mathematical theorems, the problem solving context consists of sets of definitions, theorems, axioms and lemmas. The goals are statements of other facts and theorems to be verified or proved. In data retreival systems, the context of the situation consists of a set of facts and the goal is the question to be answered. In robotic control systems, the context is a visual model of the world which consists of statements describing the physical surrondings of the robot and the goal is the recognition of a specified description (scene) as a result of a sequence of robot actions (Barr and Fiegenbaum, 1982) The operators are that component of the problem solving model which may be used to manipulate the contents of the global database. For example, in proving theorems of a given formal system, the operators are the rules of mathematical logic such as "modus ponens" and "resolution" (Barr and 8 Fiegenbaum, 1982). In symbolic integration, the operators are the rules which must be used to simplify a given expression into i t s component parts which are known to be easier to integrate (for example integration by parts or trigonometric substitution). The main component of an Al expert program is a control strategy that decides when and where information is to be processed. For example, i t is the responsibility of the control program to determine what operators to apply and when and where to apply them. In some systems the control is highly centralized while in others, as in FLOOD ADVISOR, the control is distributed among the operators themselves. The choice of a control strategy affects the contents and the organization of the global database. In most programs, the objective is to find an appropriate sequence of operators which may be applied to the current situation for making inferences and conclusions. Each sequence of operators in turn modifies the context of the current situation in some way. It is noteworthy that the control strategy assumes that a global database containing the declarative, procedural, and heuristic knowledge already exists. In other words, a l l the concepts that the computer 'understands', every pattern that it recognizes, and a l l the methods that are used to manipulate the database have been programmed into i t in complete detai1 . Detailed surveys of expert systems and other Al topics may be found in many reputable text books (see Bibliography). The following sections discuss knowledge 9 in general and knowledge representation methodologies commonly used in Al expert programs. 2.2.1 Knowledge A staggering amount of knowledge about the world is available to human beings individually and collectively. For example, an individual is able to understand and interpret another person's actions simply because the other individual is also a human being with similar needs who lives in a society which has certain standard methods for f u l f i l l i n g those needs (Schank and Abelson, 1977). The knowledge in a given area of expertise f a l l s into two broad categories: the factual (or static) knowledge of the domain which is the commonly shared knowledge found in text books and journals [these are the symbolic descriptions or metaphors that charecterize the definitional and empirical relationships of the domain (Hayes,1984)]; and the heuristic knowledge which constitutes the rules of plausible reasoning and good practice, [the heuristic knowledge may be thought of as procedures for manipulating the factual knowledge of the domain]. Thus a human expert must intelligently outline procedures for solving new problems by using the factual knowledge of the domain in conjunction with common sense and practical rules of thumb. In contrast to the factual knowledge of a domain, the judgemental rules of practice are rarely found in text books or journals. Expertise is transmitted in PhD programs, internships and through relevant experience. In summary, expert knowledge is 10 a combination of heuristic knowledge and the facts of the discipline (Fiegenbaum, 1983). 2.2.2 j_ Knowledge Representation Methodologies The knowledge representation technique used to represent domain-specific expertise is largely dependent on the control algorithm and vice versa. Some representation techniques are better suited to a given domain than other methods. Consequently, the system designer must develop specific knowledge representation schemes which allow specific and powerful reasoning mechenisms to be used for manipulating the available knowledge in the domain of interest. Knowledge in a given domain should be represented i°n such a way as to posess the following properties : (after Rich, 1983): 1- be able to represent a sufficient amount of problem-solving knowledge pertinent to the domain of interest, 2- be able to modify the data structures to incorporate new knowledge inferred from the old, 3- be able to use heuristic rules to guide the search in the most promising direction, and 4- be able to acquire knowledge from human experts. (the simplest case is direct insertion into the f i l e containing the knowledge as in FLOOD ADVISOR) Several knowledge representation techniques have been advocted for accomplishing some of the above objectives. These techniques may be classifie d into two broad 11 categories: "declarative" methods and "procedural" methods (Rich, 1983). In declarative methods, such as predicate logic, knowledge is represented as a static set of facts. In procedural representation, knowledge about the world is embedded in procedures which are applicable to well-defined situations. The main disadvantage with this technique is that the underlying knowledge is not explicit and as a result they are d i f f i c u l t to modify. Most Al systems use a procedural representation at some level of their operation and there are no fine lines between these two methodologies. For example, in declarative methods, the specified set of facts are usually accompanied by a set of general-purpose procedures which are used to manipulate them. In other words, a combination of both techniques must be used in Al expert programs since the control program manipulates the knowledge base by using operators which are themselves procedures coded in some programming language. (See Winograd, 1975 for a discussion of the so-called declarative/procedural controversy.) The following section summarizes some common knowledge structures u t i l i z e d in expert systems. Reference should be made to Nilsson (1980), Winston (1984 and 1985), and Barr and Fiegenbaum (1982) for a more detailed treatment of these methodologies. (A)- Predicate logic - Simple declarative facts are represented as "instantiated predicates" and are operated upon by a set of rules (known as the "rules of inference" in logic) to derive other facts that are also true. Using this 12 representation scheme, derivation of new facts from known facts is mechanized. This feature is the reason for the popularity of this method. It should be noted that these methods may be shown to be complete and consistent (within the given formal system), however, when the number of facts become large, there is a combinotorial explosion in the possibilities of which rules to apply to which facts at each step of the reasoning process and knowlege about which facts are relevant to what situations is needed to guide the search. (B) - semantic nets - In this method, an explicit psychological model of human associative memory is implemented using a net which consists of nodes representing concepts, events, objects, and situations, and links connecting the nodes. The links represent the functional and relational properties of the nodes relative to one another. This allows important associations to be made explicitly. Relevant facts about a concept, event or situation can be inferred from the nodes to which they are directly linked, without a search through a large database. The is-a (is-composed-of) and subset (or is-part-of) links in semantic nets are particularly important since they establish a property inheritance hierarchy in the net (note that the "is-a" and "is-part-of" relationships are common in different types of knowledge structures (including frames) and will be fully discussed in chapter 4) (C) - State-Space Representation : Using this technique the problem is structured in terms of alternative variables at 13 each possible stage of the problem. The main idea is that from a given state of the problem, the set of a l l possible states following that state are determined by the application of a set of operators (see Nilsson, 1971 and 1980 for further details on search techniques applicable to this representation.) (D)- production systems : In this representational scheme, the global database consists of rules (called product ions ) in the form of condition-action pairs (for example, if more than 20 years of annual peak streamflow data is available, then use conventional frequency analysis to determine the flood with the desired return period). Production systems are useful mechenisms for controlling the interaction between the declarative and procedural knowledge of the domain. Current research in production systems involves the development of efficient control strategies and the ab i l i t y to develop self-modifying systems, (see Nilsson (1980) for complete details) (F)- frames and Scripts : these techniques which are used for representing hydrologic knowledge in FLOOD ADVISOR are discussed in complete detail in the following sections. 2.3 j_ Knowledge Representation Using Frame Structures  2.3.1 j_ Perspective There is abundant evidence that human experts employ a well-coordinated body of knowledge obtained from previous experience to interpret their everyday professional environment. When faced with a new problem-solving 14 situation, the expert looks for a similar and relevant "pattern" that best matches the situation at hand. In other words, an expert has "expectations" (based on similar experience) about what he/she will find in the new problem-solving situation. In addition, the expert has knowledge about the sequence of actions which must be taken in order to solve a particular problem. To simulate this kind of expert behaviour on a computer, one must i n i t i a l l y find a method for representing expert knowledge in a form which may be processed by a computer program. 2.3.2 ± Frames Domain-specific knowledge about an object, situation or event may be conveniently represented in computer memory by using the frame representation scheme i n i t i a l l y proposed by M. Minsky in 1975. Minsky defines the frame concept as: "computational instantiation of a context" (Minsky, 1975). Mental representation of concepts [including objects, events, actions, situations, and sequences of events, actions, and situations (Havens, 1978)] are easily facilitated by frames nested within each other. The theory of representing knowledge in frames relies on the idea that the world consists of "quasi closed subsystems", each of which can serve as a context, that can be organized in such a way so as to fac i l i t a t e recall (Hayes, 1984). Note that the same general approach for representing knowledge in computer memory has been advocated as scripts by Schank and Abelson (1977), units by Bobrow and Winograd (1977), and 1 5 schemata by Bartlett (1932) and Havens(1978). In computer memory, a frame consists of a set of relations (or slots), each containing a name, pointers to other frames and an expectation about the type of information that can be used to transfer control of processing to other frames and procedures. Representing knowledge using frames allows interpretation of new information about a situation by reference to previous experiences. Thus, similar to human experts, a new situation is analyzed by evoking an appropriate knowledge structure from memory and then f i l l i n g i t in with details of the current situation. This type of approach to problem solving is at the heart of the frame representation technique. 2.3.3 ± Reasoning with Frames The main feature of the frame representation technique is that they make i t relatively easy to infer (as yet unobserved) facts about the concept, object, or situation at hand. This type of inference mechanism is facilitated in several ways (after Rich, 1983). 1- Information about many important aspects of the problem solving situation may be easily accessed at any time during a consultation session. The information embedded within this type of knowledge structure may be utilized as though i t had been explicitly observed. 2- Attributes which are known to be true of some stereotyped situation may be easily embedded in the frame and used to f i l l the individual slots. This type of nested structure 16 allows the construction of specialized problem solving models from their highly modularized component parts. Useful information associated with the attributes (slots) may be used to heuristically guide the search (for example by providing advice on what to do next and how to do i t ) . 3- Frames may be used to describe multiple instances of the concepts, events or situations that they represent. Once a particular instance of a frame has been created, i t is compared (or matched) to the generic frame for the discovery of departures. Such departures may correspond to significant aspects of the current situation and are consequently used for making inferences and conclusions (see chapte 4 for more details of these mechanisms). 2 .4 : Synopsis As mentioned previously, the choice of the knowledge representation scheme is largely dependent on the domain of application. In engineering design, i n i t i a l problem formulation is usually followed by numerical analysis. Such analysis includes manipulation of observed or experimental data based on some underlying conceptual problem solving model. Numeric summaries (produced by some well-defined algorithmic procedure) must be produced and eventually used by the engineer as an aid for making a choice between available options at some stage of the problem solving process. Thus, for an Al expert program to be useful, i t must be able to evoke procedures for performing complex numerical computations and provide information on how to 1 7 manipulate the results of such analysis. For example, in the context of design flow estimation, i t may be necessary to perform conventional frequency analysis on annual peak flow records for some desired stream. An expert system for flood estimation should be able to perform the following tasks (after i t has been established that the need for frequency analysis exists): 1- inform the user about the assumptions made on the nature of the data and evoke procedures for verifying these assumptions (see chapter 3). 2- i f i t has been established that the data series meets the assumptions made, a procedure should be available for performing conventional frequency analysis. If the data series indicates a significant trend or jump, then the most suitable procedure for handelling the current situation should be recommended and evoked upon request. Note that instructions on how to use the available procedures (programs) must also be provided upon request by the user. 3- after a frequency analysis on the peak annual flows has been made, the expert program should provide information on how to manipulate the numeric summaries of the analysis made in the previous step in the context of the particular problem at hand. The frame representation technique is believed to be be the most suitable for engineering applications. Using the frame representation, procedures necessary for performing numeric computations may be easily incorporated in the problem solving model to drive the reasoning and problem solving 18 behaviour of the system. 2.3.3 j_ The problem Solving Model for Flow Estimation Using a modified version of KRL (Knowledge Representation Language) i n i t i a l l y proposed by Bobrow and Winograd (1977), the generic NEW-PROBLEM concept in the context of flood estimation may be represented as shown in figure 2.1. (after Barr and Fiegenbaum, 1982) This generic frame is a conceptual model of a typical flood estimation problem and has places (or slots) for related concepts and facts such as the location of the site, the cost of the project, types of available data, consequences of failure, etc. The 'Specialization-of i_ Design-flow-estimation' slot is used to establish a property-inheritance hierarchy among frames '(see chapter 4 ) . This allows information about the parent frame to be inherited by its children. Each slot may have a complex frame-like structure i t s e l f . For example, the 'Types ;' slot of this generic frame has sub-slots (sub-frames) of i t s own. The contents of the 'range:' sub-slot of this slot are prespecified expectations about the types of possible flood estimation scenarios one may find in practice. The 'if-needed' sub-slot contains an "attached procedure" that directs the reasoning mechanism. These procedures are used to determine the slot's value i f this value must be known. The 'default' sub-slot specifies a value in the 'range' to be used if there is no contradictory evidence. Once a frame has been copied to create an instance 19 FIGURE 2.1 : I l l u s t r a t i o n of the NEW-PROBLEM frame Generic NEW-PROBLEM frame .Specialization-of j_ Design flow estimation • Types 1 ...range : (explain, case 1, case 2, case 3, case 4, case 5) ...default : explain . . . i f-needed: IF a long period of record i s av a i l a b l e on the stream of i n t e r e s t and the recording station i s in the near v i c i n i t y of the location of int e r e s t , THEN easel. IF a long period of record i s av a i l a b l e on the stream of i n t e r e s t but the recording station i s not in the same basin as the basin of in t e r e s t , THEN case2. IF a short streamflow i s avai l a b l e on the stream of ...... inte r e s t and the recording station i s in the near v i c i n i t y of the location of in t e r e s t , THEN case3. IF no streamflow records are avai l a b l e on the stream of inter e s t but records are a v a i l a b l e for other other nearby streams in the region of i n t e r e s t , THEN case 4. IF no streamflow data i s available relevant to the s i t e or region of interest but r a i n f a l l records for the area are a v a i l a b l e , THEN case 5. OTHERWISE explain .Design-structure j_ ...range : ( r e s e r v o i r , bridge, culvert, levee, highway, waterwork, sewage disposal plants, storm sewers) ...if-needed:(determine size and s t r u c t u r a l hydraulic capacity) .Avai lable-data }_ ... range :(streamflow, r a i n f a l l , observables, explain) ...default : explain ... if-needed:(Collect a l l a v i l a b l e data- inspect the s i t e ) .Physical-character i s t i c s : ...range:(area, slope, vegetative cover, moisture conditions) ...land-use-type: range: (urban, rural) .Cost: .. .range:(construction, structure, design, f a i l u r e ) ...if-needed: (optimize objective function) .Locat ion ...range : (an address, geographical location) ...if-needed : (Look at the regional map) .Solution-method : ....range:(Frequency analysis, Bayesian, Regional a n a l y s i s , 20 Deterministic models, stochastic models, explain) ....default : explain .Event sequence j_ Begin-solution-script 21 of the concept that i t represents, the default assignments play the following roles (Havens, 1977): 1- They provide generic knowledge about that instance of the context. [Generic knowledge is that knowledge that is generally representative of the concept.] 2- They specify expectations about the type of data which is necessary to replace the default values of that instance. The concepts of instance and stereotype are discussed in chapter 4. The 'Event Sequence : Begin-solution-script' slot specifies the script that the engineer may typically encounter in solving a new problem. A script is similar to a frame. Schank and Abelson (1977 p. 41) define a script as "a predetermined, stereotyped sequence of actions that defines a well known situations". Scripts may be used to handle stylized situations, but, they are not capable of dealing with totally novel situations. Underlying the declarative structure of frames and scripts (that i s , the manner in which knowledge is organized), is the dynamic or procedural aspect of frame-based systems. Procedures are attached to slots to drive the reasoning or the problem-solving behaviour of the system. In the NEW-PROBLEM frame of figure 2.1 these are the ' i f -needed' procedures that are activated to determine the value of the slot. 22 CHAPTER 3 i FLOW ESTIMATION PROCEDURES  3.1 j _ Overview A water resource engineer is often faced with the task of making flood estimates which are most suitable to the particular design problem at hand. Like most hydrological calculations, flow estimates are prone to error which increase as the degree of approximation increases or when the estimation procedure is applied beyond the range of conditions for which i t was intended. As mentioned previously a procedure which may be appropriate in one location, may produce poor estimates in another location. It is a d i f f i c u l t task to determine which procedure is most suitable and under what circumstances. In most situations there is no single "best" method and the engineer must determine whether the cost, scope, or importance of a particular project j u s t i f i e s the additional cost of more elaborate methods or procedures. In this light, a computer-based consultant would be extremely useful in selecting the appropriate procedure. The proper design of structures such as reservoirs, bridges, culverts, levees, highways waterworks, sewage disposal plants, storm sewers, etc is dependent on the type, quality and quantity of hydrologic data and on the economic cost and importance of the structure. This chapter describes five generalized real-world situations as a characterization of a typical flood estimation problem. Procedures used in dealing with each situation are then reviewed. These generalizations are based primarily on the type and quantity 23 of the data and resources available to the engineer. They are used to demonstrate how problem solving knowledge may be used to interactively assist the engineer in making d i f f i c u l t decisions. The expertise represented in FLOOD ADVISOR is far from complete and the procedures recommended as a solution method for each generalized case are s t i l l in the process of being developed. The following sections review basic flood estimation concepts and techniques to set the context for further discussion. The sequence of actions which are assumed to be the most appropriate for the solution under each condition are then discussed. 3.2 j_ Probability, Statistics And Hydrologic Data Hydraulic structures must be designed on the basis of hydrologic , economic, and other relevant data. The value of any type of data must be measured in terms of i t s ultimate use. Quantitative scientific data may be classified into two kinds: experimental data and historic data (Chow, 1954). The experimental data are measurements obtained from experiments and may be obtained repeatedly. The historical data on the other hand, are collected from natural phenomena that can be observed only once and will not occur again. Most hydrological data are historical data which are observed from natural hydrologic phenomena. Statistics are necessary to deal with computations performed on historic data while probability deals with the measure of chance or likelihood based on observed data (Chow, 1964). A major type of hydrologic data is streamflow records 24 which has two major uses: to provide a general regional description of the streamflow regimes in the region; and to assist in project operation and design (Dalrymple, 1960). The maximum observed streamflow (the peak flow) on any stream over a period of one year varies from year to year in an apparently random fashion. This randomness has led to the use of probability and statis t i c s in selecting the hydraulic capacity of storm water f a c i l i t i e s . The following is a generalized treatment of hydrologic frequency analysis. Reference should be made to Chow for a more detailed treatment of this topic. 3.2.1 j_ Return Period and Recurrence Interval In many occasions, terms such as the 50-year flood or the 50-year r a i n f a l l are used rather too loosely and the implications associated with these terms are often misunderstood. It is a d i f f i c u l t task to estimate the magnitude of the flow associated with these terms and the corresponding uncertainty or variability associated with these estimates. This section outlines generalized methods for making such estimates under typical situations. In order to provide a framework for further discussion, a breif summary of some common terminology is presented below. 1- A "T-year event" (QT) represents an event with a return period of T years (the term "return period" is defined below). In other words, a T-year event is defined as an 25 event such t h a t , over a long p e r i o d of record (much l a r g e r than T y e a r s ) , the average time between events having a magnitude equal to or greater than the T-year event i s T years. Thus the expected number of such exceedences over nT years i s n (where n i s any P o s i t i v e i n t e g e r ) . 2- The "return p e r i o d " of a T-year event as o u t l i n e d above i s T years. The a c t u a l time between the occurence of a T-year f l o o d i s often c a l l e d the "recurrence i n t e r v a l " . From the above d i s c u s s i o n one may conclude t h a t , in the long-run (or on the average), the recurrence i n t e r v a l equals the return p e r i o d . Since the average time between the occurrences of a T-year event i s T years, the p r o b a b i l i t y of a T-year event i n any given year i s 1/T. In other words, one expects the T-year f l o o d to be exceeded , on the average, once every T years. ( i . e . PT = 1/T where T i s the return p e r i o d a s s o c i a t e d with an event QT in any given year. So f a r i n the d i s c u s s i o n of return p e r i o d , the f o l l o w i n g assumptions have been made about the the peak annual f l o o d s e r i e s and the v a r i a b l e Q: 1- Independent Random Sample - T h i s means that the peak annual flows are independent from one year to the next. 2- S t a t i o n a r i t y - The s t a t i o n a r i t y assumption implies that the s t a t i s t i c a l p r o p e r t i e s of the data are not changing with time. This assumption may be i n t e r p r e t e d to mean that there 26 are no significant changes within the watershed which may result in changes of the flow regime that is characteristic of the watershed. Under the above assumptions, the probability of occurence of a T-year event (QT) being equalled or exceeded in any given year is a constant from year to year and the successive years represent independent Bernoulli t r i a l s (Benjamin and Cornell, 1970). [ note : Pr [ Q >= QT ] = p = 1/T ] QT ] = p = 1/T ,on the average, in any given year] A magnitude greater than QT (denoted by QT*) is refered to as a success . Since QT* (any values exceeding QT) is a Bernoulli random variable, the probability of k occurrence of QT* in n years may be computed by using the Binomial distribution. In other words, the probability of k exceedences of QT in n years is p(k,p,n) = {n!/((n-k)!*K!)]*(p**k)((1-p))**(n-k) For example, the probability of k=5 exceedences of the 10-year flood (Q10) in n=25 years i s : p(5,1/10,25) = 251/(25-5)!*5! * (1/I 0**5)*(9/10**20) = 6.5% In other words , over a large number of 25-year records (say 1000 25-year records), 6.5% of the records will have exactly five observed peaks that exceed Q10. Similarly, the 27 probability of zero exceedences in n years may be calculated. In this case the above formula simplifies to: Pr[QT being exceeded exactly zero times in n years]=(1-p)**n where p=l/T. Thus the probability of at least one (i.e. One or more) exceedences in an n year period is the complement of the above equation: Pr[QT being exceeded at least once in n years]=1-(1-p)**n If n is set equal to T in the above equation, i t may be shown that as T approaches infinity, the probability of at least one exceedence of the T-year flood in T years approaches a constant 0.632. This means that i f a hydraulic structure having a design l i f e of T years is designed on the basis of the T-year flood, then the probability of exceeding the design capacity (QT) is approximately 63% (Benjamin and Cornell, 1970). Additional estimates of probabilities of exceedences in a finite number of years are often needed and may be easily computed. Design of a project begins with the selection of a design period (the intended l i f e of the structure). Having fixed the design period, the engineer must enquire about the probability of occurrence of damaging floods during the intended l i f e of the project. The conventional frequency curves are not equipped for answering such an enquiry but may be modified to incorporate this information. One approach is to specify an acceptable 28 probability of exceeding the design capacity of the structure during the design period. For example, to be 95% certain of not exceeding the design capacity of the structure during its intended lifetime of n=lO years; one needs to estimate the 196-year event (.05=1 -(1-1/T)**10 = 196).) Calculations like the above may be carried out for various design periods, return period and acceptable risks and plotted as shown in figure 3.1. Another approach to solving the above problem is to accept a design rule. For example, the design rule that the structure should be designed to survive 3 times the largest observed flood. Thus if QL is the largest flood observed during the last n years, then the design flood is QT=3*QL. However using this procedure without any specialized knowledge of the watershed of interest often leads to a design choice which is economically infeasible. Many governmental organizations have regulations governing the design return period to be used. These return periods are usually based on the size of the structure and the consequences of the structural hydraulic capacity being exceeded. For example, in British Columbia, in rural areas road culverts may be based on 10 to 50-year return period . Minor structures in urban areas may be based on the 25 to 200-year event. 3.3 j_ A Prototype Hydrological Knowledge Base In order to assign a flood magnitude to a given return period, one must have knowlege of the flood flow regime 29 F i g u r e 3«1 R e t u r n p e r i o d a s a f u n c t i o n o f d e s i g n l i f e 30 governing the area of interest. As mentioned previously, the approach taken in the determination of a design flow value depends primarily on the type, quantity, and quality of hydrologic data that is available and on the cost and importance of the hydraulic structure. In order to incorporate hydrological expertise in FLOOD ADVISOR , five generalized cases were used to characterize a typical design situation or pattern which are recognized by the system. CASE 1 : A long period of streamflow record is available at or in the vicinity of the location of interest. CASE 2 : A long period of record is available on the stream of interest, however, the recording station is located some distance upstream or downstream of the location of interest. CASE 3 : A short streamflow record is available on the stream of interest. CASE 4 : No records are available on the stream of interest but records are available for nearby streams in the region of interest. CASE 5 : No streamflow records are available for the region. The following sections outline the procedures recommended by the FLOOD ADVISOR in dealing with each case. A Bayesian framework for combining different types of 31 information is i n i t i a l l y discussed since it plays an important role in the suggested procedures. 3.3.1 j_ A Bayesian Approach to Flood Probability Estimation When adequate streamflow data are available, i t is a simple task to perform a conventional frequency analysis and derive the flood with the specified return period. However,, when observed data are insufficient or expensive to obtain, the engineer must use his/her subjective judgement to weigh the available information. Usually an inspection of the project site reveals a surprising amount of information. For example, a bridge or culvert of known hydraulic capacity that has not been exceeded since the time i t was constructed, reveals useful information. Unfortunately, this type of information can not be directly used in frequency analysis but may be incorporated in the estimate by using Bayes' criterion. A computer program (FLOODS) has been developed by Russell (1982)' for estimating design floods using a Bayesian framework. The program uses a compound distribution which is a weighted average of a number of individual distributions. I n i t i a l parameter values and weights of the component distributions are assigned on the basis of subjective estimates of the mean and standard deviation of the flood peaks. The weights of the component distributions are updated by the application of Bayes rule in the light of additional information such as recorded floods, the largest observed flood in a given number of years or a flow which has not been exceeded in a number of 32 y e a r s ( R u s s e l l , 1 9 8 2 ) . The FLOODS program i s used by the FLOOD ADVISOR w i t h o u t any change i n the c o d i n g of t h i s program and i s a t the h e a r t of some the recommended p r o c e d u r e s . Note t h a t the FLOOD ADVISOR s e t s the c o n t e x t f o r u s i n g the FLOODS program. 3 . 3 . 2 j_ T y p i c a l F l o o d E s t i m a t i o n Problems  3 . 3 . 2 . 1 j _ case J_ When a r e a s o n a b l y l o n g p e r i o d of stream f l o w r e c o r d s are a v a i l a b l e on the stream of i n t e r e s t and the r e c o r d i n g s t a t i o n i s i n the v i c i n i t y of the a r e a of i n t e r e s t , the procedure most o f t e n used i s f l o o d f r e q u e n c y a n a l y s i s . The purpose of fr e q u e n c y a n a l y s i s i s the p r e d i c t i o n of f u t u r e events from p a s t r e c o r d s . When past data a r e used t o p r e d i c t the f u t u r e , i t must be assumed t h a t t h e r e i s no s i g n i f i c a n t change i n the f l o o d p r o d u c i n g c h a r a c t e r i s t i c s of the watershed of i n t e r e s t over t i m e . In o t h e r words the a v a i l a b l e r e c o r d s may be thought of as a sample from some s t a t i s t i c a l p o p u l a t i o n which c o n s i s t s of a l l the p a s t and f u t u r e r e c o r d s w i t h no s i g n i f i c a n t t r e n d o r jump i n the da t a s e i e s . S t a t i s t i c a l a n a l y s i s of the sample d a t a r e q u i r e s the d e t e r m i n a t i o n of parameters which a re d e s c r i p t i v e of the the pa r e n t p o p u l a t i o n . The t r u e v a l u e s of such p o p u l a t i o n parameters a r e never known i n f l o o d f r e q u e n c y a n a l y s i s and are e s t i m a t e d from the sample d a t a . The method of a n a l y s i s i s t o s e l e c t a p r o b a b i l i t y d e n s i t y f u n c t i o n t o d e s c r i b e the d a t a , e x t r a c t c e r t a i n s t a t i s t i c s from the d a t a , and e s t i m a t e 33 the f l o o d with the d e s i r e d r e t u r n p e r i o d . Some of the assumptions made i n the Case 1 s i t u a t i o n are as f o l l o w s and must be v e r i f i e d before t h i s method can produce r e l i a b l e e s t i m a t e s . (a) -The data are s u f f i c i e n t i n q u a l i t y and q u a n t i t y to produce r e l i a b l e estimates f o r the parameters of the p r o b a b i l i t y d i s t r i b u t i o n s e l e c t e d . (b) -The flow c h a r e c t e r i s t i c s of the stream have not been ch a i n g i n g over time ( s t a t i o n a r y data s e r i e s ) (c) -The peak annual flow o b s e r v a t i o n s are s t a t i s t i c a l l y independent from year to year. (d) -The data are r e p r e s e n t a t i v e of the flow behaviour expected during the design l i f e of the p r o j e c t under i n v e s t i g a t i o n . (e) - The flow i s n a t u r a l flow (unregulated) S e v e r a l a l g o r i t h m i c programs are a v a i l a b l e that perform c o n v e n t i o n a l frequency a n a l y s i s . One such program i s PDRFFA which i s used by the FLOOD ADVISOR. The user may request i n s t r u c t i o n s on where to c o l l e c t data, how to input data to the program, and on how to obt a i n a hardcopy of the output generated by t h i s program. A d d i t i o n a l i n f o r m a t i o n i s o f f e r e d r e g a r d i n g the i n t e r p r e t a t i o n of output. F i g u r e 3 . 2 summarizes recommended event sequence f o r s o l v i n g the case 1 problem. 3 . 3 . 2 . 2 j_ Case 2 When streamflow data i s a v a i l a b l e on the r i v e r of 34 FIGURE 3.2 j_ SOLUTION SCRIPT FOR CASE J_ SOLUTION-SCRIPT1 : Props : (stream flow data, rainfall data, FLOWFREQ program, FLOODS program, EPPFM, design structure, design flow, design l i f e , consequence of failure, basin, river) Roles : (consultant, clients, end-users) Point-of-view : consultant Time-of-occurence : (time of project construction) Place-of-occurence: (basin or watershed of interest) EVENT SEQUENCE : ...First: Start-Solution Script ...then : Collect streamflow data ...then : Check assumption Script ...then : IF assumptions are valid then : Input streamflow record then : Run-PDRFFA then : Choose-best-fit then : Determine-design-life-of-the-structure then : Determine-acceptable-risk then : Determine-return-period then : Estimate-flow-from-chosen-distribution then : Determine-cost-and-consequence-of-failure then : Determine-increase-in-cost-for-decreased-risk then : Consult-appropriate-agencies-for-guidelines then : Make-final-estimate then : Submit-final-estimate then : End-solution 35 interest but at a location some distance either upstream or downstream of the point of interest, there are several procedures that can be used to estimate the flood frequency relationship at the point of interest. These procedures largely depend on the type of data available. The following is a summary of these techniques. 1- Perform conventional frequency analysis on the available data at the nearby location (see figure 3.2) 2- Adjust flow records from the location upstream or downstream of the point of interest as follows. (a) - If the flow record includes an entire hydrograph, then this hydrograph may be routed to the point of interest making proper adjustment for local inflows and outflows along the routing reach (Haan, 1977). (b) - If data on the stream are available at 2 locations, correlate annual flood peaks to the basin area and use this correlation to adjust the flow rate accordingly. The T-year flood magnitude (QT) is commonly related to the basin area (A) by the following equation (Haan, 1977): QT = a * (A ** b) The constants a and b for a given return period (say the 10 year flood) are estimated as follows: 36 1- Run PDRFFA for both locations. 2- Obtain estimates for the desired return period. 3- The equations to be solved are: (I) : QT(1) = a * (Al ** b) for basin 1 and (II) : QT(2) = a * (A2 ** b) for basin 2 Note that b generally ranges between 0.5 and 1.0 and is a function of the return period. 4- Estimate the T-year flood for the basin of interest using the estimates of a and b obtained in the above step. (c)- If data on the stream are available at only one location, then assume a value for b and compute a and QT as outlined above. The approaches have been suggested by Hann and are recommended when the basic flood producing characteristics of a l l the basins are similar. The above procedure is not applicable when a mix of drastically different land uses exists among the basins. If the watershed characteristics are changing along the stream, then the above procedure may be carried out as an aid in estimating QT but should not be used to produce final estimates. Unfortunately, the above methods require more data than is usually available and may be quite costly and time consuming. If the particular design does not justify such costly efforts, one may use the FLOODS program to obtain an 37 estimate of the design flood for the desired return period. 3.3.2.3 j_ Case 3 Commonly only a short stream flow record at the location of interest is available. This may be due to the fact that the land use on the basin has recently changed or that the gaging program was only recently initiated. A short streamflow record is one of less than 10 years in length (Haan, 1977). A record of this length contains a great deal of information, but is not suitable for a conventional frequency analysis. If a record of the r a i n f a l l that produced the recorded runoff is available (or can be estimated from nearby raingages), then these records may be used together to estimate the empirical coefficients in an approximate model. Under these circumstances, a continuous simulation, an event or hydrograph model, or a model for estimating peak flows may be used to make an estimate. Once a model has been chosen and the model parameters have been estimated, a long-term r a i n f a l l record may be processed to simulate a long-term streamflow record. The generated record may then be subjected to a conventional frequency analysis. If no long-term r a i n f a l l records are available at or in the vicinity of the site of interest, then long-term records from nearby raingages may be used for simulation. In the absence of any applicable long-term ra i n f a l l records, the FLOODS program may be used to compute a preliminary estimate of the event of interest, or a stochastic r a i n f a l l generation model may be used to produce 38 a synthetic rainfall record to be used in the runoff model. If other streamflow gaging stations are available in the region, then regional frequency analysis may be used as outlined in case 4. 3.3.2.4 j_ Case 4 If no streamflow record (or a short record) is available for the site of interest but streamflow records are available at several nearby locations; then the engineer must resort to regional frequency analysis. Regional frequency analysis has been discussed in great detail by several authors (see Bibliography). The f i r s t step in the regional approach is the selection of several of the the nearby stations that have "hydrologically similar " watershed charecteristics as that of the basin of interest. At each of these locations a Case 1 flood frequency analysis is carried out. An "index flood" , such as the 2-year flood, is then defined. At each station, the ratio of the magnitude of the T-year event to the index flood is computed for different values of the return period. These ratios are finally plotted against T and a "smooth" curve is drawn to f i t the points. Once a regional flood frequency curve has been constructed, the area of the watershed along with other geomorphic, physical and possibly meteorological factors are related to the index flood by means of regression analysis. If QI is used to denote the index flood (the dependent variable) and i f X1,X2,....,Xm represent factors (the 39 independent variables) then a regression equation of the form: QI = a0+a1.X1+a2.X2+ ... +am.Xm may be obtained to estimate the index flood for the location of interest. [Note that he index flood for the site may be estimated by using any available streamflow records.] Once an estimate of the index flood has been made, the regional frequency curve may be used to estimate the T-year event. In its present form, the FLOOD ADVISOR does not incorporate a conventional program which performs regional analysis. However, the system provides the user with advice on how to handle this situation. 3.3.2.5 j_ Case 5 The engineer is often faced with situations where no streamflow records are available on the stream of interest or on nearby streams. Under these circumstances, deterministic models must be used to determine the magnitude of runoff events of desired frequency. Deterministic models, such as the Clark model, again depend on the type of data that is available to the engineer, the purpose of the modelling effort,the time and money available for the modelling scheme, and the importance of the accuracy of the estimates. An event- based model (such as the unit hydrograph approach) is used to analyse the most sever rainfalls for the year and produce the streamflow data which 40 can be subjected to frequency analysis at a later stage. The FLOOD ADVISOR incorporates EPFFM , an interactive program written in .FORTRAN, for this particular case. The Rational formula may also be used to estimate the T- year event. However, i t must be assumed that the frequency of the estimated flow peak is the same as the frequency of the rai n f a l l used in the equation. This, however, is not necessarily true because of the effect of such factors as the antecedent s o i l water content. It is only over the long-run that the expected or average return period of the runoff equals the return period of r a i n f a l l . This is the reason for the popularity and extensive use of this method in the past and at the present. 41 CHAPTER 4 J_ CONTROL STRATEGY AND SEARCH  4 .1 j_ Introduction The numerical algorithms for flood estimation and other data base manipulaters presented in the main body of this thesis must be organized to allow easy access to the individual components of the 'recognition process'. To make such a scheme possible, the control of the processing must be distributed through various levels. The control of a searching and matching algorithm is central to the idea of computers in general. The central processing unit (C.P.U), is a typical application of a global control that decides 'when' and 'where' information is to be processed. The control strategy proposed for this, type of pattern-matching must be simple and flexible. The requirement of simplicity is adequately met by using frames and scripts to represent declarative, procedural, and heuristic knowledge which is available in the FLOOD ADVISOR. The control structure of this system supervises processing by organizing knowledge around well-defined sets of conceptual entities, each with an associated description and procedure. The knowledge represented in FLOOD ADVISOR f a l l s into three different categories (after Havens, 1978). 1- Each frame contains factual knowledge about the concept being represented by the frame. Factual knowlege is in turn represented as follows: ..A- Declaratively, as predefined functions. For example, the 42 probability density functions used in the FLOODS program. ..B- Procedurally, as computations. For example, the determination of the outflow hydrograph based on a synthetic unit hydrograph. ..C- Data-driven and procedurally. This means that certain parameters w i l l be estimated on the basis of observed data. For example, the estimation of s t a t i s t i c a l parameters from maximum annual flow records. This allows reasoning based on the results of numeric computations. 2- Each frame also implements procedural heuristic knowlege to guide the search process needed to satisfy the expectations called for by the slots. For example, is there enough evidence to indicate that a different method of analysis should be used for proper flow estimation?. 3- Frames form relationships with each other and create networks which hierarchically distribute and supervise the control of processing. This allows complex concepts to be represented by frames nested within each other and allow an encyclopedic retrieval mechanism. 4.2 ; Stereotype and Instance Central to the frame representation scheme is the notion of a stereotype and instance. A stereotype frame may be copied to form multiple instances of a context (Havens, 1978). Once a frame has been copied to create an instance of the concept or stereotype that i t represents, default assignments are used to provide generic knowledge about that instance of the stereotype frame (or context). In addition, 43 they are used to specify expectation about the type of data required to change the default value of that instance(Havens, 1978). To further illustrate the above concepts, consider the PROBLEM-AT-HAND frame shown in figure 4.1. This frame has the same slots as the generic NEW-PROBLEM frame (see figure 2.1), however, the contents of these slots are more fully specified. The PROBLEM-AT-HAND frame is an instance of the generic NEW-PROBLEM frame summarizing a l l that is known about this particular stereotype. As mentioned previously, the process of instantiating a context is computationally equivalent to a search for a certain embedded instance of the concept that satisfy the frame's expectation. In order to illustrate some of the fundamental ideas used in this procedural recognition model, consider the FLOW-ESTIMATION frame shown in figure 4.2. The notation employed is slightly different from that introduced in chapter 2 and has been adapted after Havens. The mnemonics TD and BU stand for top down and bottom up searches. A top-down search is a hypothesis driven search for a pattern or goal. It works both procedurally and numerically to try and satisfy the frame's expectations and radiates downward in a hierarchy and has "is-composed-of" relation with the data. A bottom-up search is data-driven and may be has "is-part-of" relationship with the data and a procedure. These mechenisms are discussed in length in the following sections. 4.2.1 : Search 44 FIGURE 4.1 : I l l u s t r a t i o n of the PROBLEM-AT-HAND-FRAME PROBLEM-AT-HAND frame .Specialization-of j_ Design flow estimation .Types j_ ...range : (explain, case 1, case 2, case 3, case 4, case 5) ...default : explain ... if-needed: IF a long period of record i s a v a i l a b l e on the stream of int e r e s t and the recording st a t i o n i s in the near v i c i n i t y of the loca t i o n of i n t e r e s t , THEN easel . IF a long period of record i s av a i l a b l e on the stream of interest but the recording st a t i o n i s not in the same basin as the basin of in t e r e s t , THEN case2. IF a short streamflow i s available on the stream of interest and the recording station i s in the near v i c i n i t y of the lo c a t i o n of i n t e r e s t , THEN case3. IF no streamflow records are a v a i l a b l e on the stream of interest but records are avai l a b l e for other other nearby streams in the region of i n t e r e s t , .THEN case 4. IF no streamflow data i s available relevant to the si t e or region of interest but r a i n f a l l records for the area are a v a i l a b l e , THEN case 5. OTHERWISE explain (easel specified) .Design-structure j_ ...range :(reservoir, bridge, culvert, levee, highway, waterworks, sewage disposal plant, storm sewers) ... (culvert specified) ...if-needed:(determine size and s t r u c t u r a l hydraulic capacity) .Available-data }_ ... range :(streamflow, r a i n f a l l , observables, explain) ...default : explain ... if-needed:(Collect a l l a v i l a b l e data- inspect the s i t e ) ... (streamflow specif ied) .Physical-character i s t i e s : ...range:(area, slope, vegetative cover, moisture conditions) ...land-use-type: range: (urban, rural) ... (was not specified) .Cost: ...range:(construction, structure, design, f a i l u r e ) ...if-needed: (optimize objective function) ... (was not speci fied) .Location : ...range : (an address, geographical position) . ..if-needed : (Look at the regional map) ... (was not specified) . Solut ion-method ' . ... .range:(Frequency analysis, Bayesian, Regional analysis, ....Deterministic models, stochastic models, explain) ....default : explain ... (frequency analysis) .Event sequence ^ Begin-solution-script1 46 Figure 4.2 : ILLUSTRATION OF THE FLOW ESTIMATION frame NAME : (FLOW-ESTIMATION) frame DATA : (TYPE-OF DATA = RANGE (streamflow, r a i n f a l l ) (TD-method f i n d data-type) (BU-method found data-type) STRUCTURE : (TYPE-OF STRUCTURE = RANGE ( c u l v e r t , bridge, )) (TD-method f i n d structure-type) (BU-method found structure-type) COST : (TYPE-OF COST = RANGE(const'n, design, f a i l u r e , s t r u c t u r e ) (TD-method f i n d cost) (BU-method found cost) PHYSICAL-CHARECTERISTICS : (TYPE = RANGE ( l o c a t i o n , landuse)) (TD-method f i n d l o c a t i o n and landuse) (BU-method found l o c a t i o n and land use) SOLUTION-METHOD : (AN ACTIVITY-CONNECT TO DATA,STRUCTURE,COST,PHYS-CHAR) TYPE-OF SOLUTION METHOD = (1,2,3,4) ...... (TD-method f i n d a s o l u t i o n method) (BU-method found a s o l u t i o n method) ISA : A PROBLEM SOLVING CONCEPT INSTANCES : NIL 47 Most Al systems may be charecterized by a search task which is directed by domain specific heuristic knowledge. The development of a computer system that imitates the problem-solving model used by human experts involves the development of a powerful search mechanism for a given representation in addition to powerful heuristics in the area of expertise. A number of search techniques have been advocated for frame networks. The following is a summary of the methods which may be used in FLOOD ADVISOR. (after Havens (1978) and Bobrow (1977)) (I) - Top-down or hypothesis-driven search : Using this technique, heuristic knowledge is embedded in each stereotype frame to guide the search process, (see the discussion of compositional hierarchies presented below). In addition, the default expectations may be thought of as hypotheses about the type of input required to f i l l the slots of that instance. In summary, top-down methods are designed to search for information which can satisfy the expectations called for by the slots. (II) - Bottom-up or observation-driven search : Discoveries from observation can be compared against domain specific knowledge to constrain the set of a l l possible interpretations of a given situation. Since no hypotheses need to be postulated, no back tracking is necessary. In summary bottom-up methods are designed to continue the recognition process motivated by the satisfaction of their associated expectations. 48 4.2.2 2. Frame Hierarchies Frames form hierarchical networks in two ways. First complex concepts may be represented by frames which are in turn a composition of other concepts represented by sub-frames. The hierarchical structure which results is often called a composition hierarchy (Rich, 1983). This is a static data structure which represents the composition of a l l possible instances of that class. Figure 4.3 illustrates the composition hierarchy for the FLOW-ESTIMATION frame of figure 4.2. This figure may be interpreted as follows: A typical flood estimation problem situation is composed of several other generic concepts. Examples of these are type of structure, type of available data, etc. Each of these related generic concepts is in turn composed of i t s own class of concepts represented by a stereotype sub-frame. Each of these sub-frames is also composed of its own generic concepts represented in a sub-sub-frame. Thus the generic FLOW-ESTIMATION frame represents the class of a l l flood estimation problems. Each instance of the FLOW-ESTIMATION frame is composed of a l l the components of this generic frame. An "inverse composition relation" between frames has also been shown in figure 4.3. Each stereotype frame forms composition relationships with one or more sub-frame. The sub-frames in turn form an inverse- composition relation with the parent frame. This relation is known as "part-of" relationship and is the primary mechanism by which bottom-up search may be conducted over the frame network (Havens, 1978). Frames form hierarchies in another way. Each frame 49 FIGURE 4.3 : I l l u s t r a t i o n of Composition Hierarchies (is—composed—of) DESIGN FLOW ESTIMATION ' W (is-part-of) SOLUTION METHOD tn sewer Frequency [regional]' Bayesian jdeterministic stochastic 50 represents a stereotypical concept that may have many partially specified instances. These instances may themselves serve as stereotype frames each having a number of more fully specified instances of the same generic concept. In this fashion frames may be used to set up instance hierarchies. At the f i r s t level of an instance hierarchy is a frame which represents an un-instantiated generic concept. Each sub-frame of this frame (level 2) may represent partially specified instances of that same concept. Each of the descendants of these instances in turn represent more fully specified instances of the concept. Eventually at the bottom of the tree structure, completely  specified instances of the generic concept are finally represented. The instance hierarchies are similar to the the "is-a" link used in semantic net representation techniques (Barr and Fiegenbaum, 1982). In the FLOW-ESTIMATION frame of figure 4.2 , the last two slots of the frame establish an instance hierarchy. Flood estimation may be thought of as an instance of the more general concept of problem solving . Hence the is-a relationship asserts that this frame is an instance of another stereotype. As indicated by the 'INSTANCE : NIL' slot, the generic FLOW-ESTIMATION frame does not have any of its own. The generic FLOW-ESTIMATION frame of figure 4.2 illustrates a number of features of the recognition-based reasoning mechanism employed in this model. The slots in this frame represent the composition knowledge about flood 51 estimation problems. A flood estimation problem consists of a set of related concepts and topics. Examples of these are popular concepts that are necessary for the appropriate selection of an estimation procedure. For perception, these composition relationships must define the structural and functional aspects of the concept being represented by the frame and its slots. (Havens, 1978). This knowledge is used to recognize stereotype instances of that particular concept. In other words, the problem which is currently under investigation is recognized by the discovery of its component parts (rather than the whole). 4.2.3 j_ Recognition Perception may be thought of as a recognition task that composes a description of a perceived concept from a sequence of external observations (Havens, 1978) which in this case is obtained by requesting for information from the engineer through an interactive dialogue. In the recognition model utilized in this system, each frame may be viewed as an "active recognizer" of the general concept that i t represents. Thus every frame must contain active heuristic knowledge in order to guide the recognition process (search). Such active heuristic knowledge is called a "method" (Bobrow and Winograd, 1977) and may be thought of as procedured designed to recognize the concept being represented by the frame i t s e l f . These procedures allow the development of domain-specific search techniques. For example, the query about the type of available data will aid 52 in the recognition of the applicable method of solution. In contrast to blind search methods, where a particular hierarchical instance remains active until satisfied, these procedures (or methods) are data driven (in this case via standard input) and their task is to choose a particular instance of the generic frame upon the discovery of some evidence (input) that matches a particular expectation. As will be discussed in section 4.3, a series of algorithms have been developed in the 'C programmming language which perform simple types of dynamic recognition using a pre-specified data base over which to conduct a search. 4.2.4 ; Expectation, Matching, and Completion The underlying recognition model which must be utilized in the development of the heuristic search procedures consists of three phases : expectation, matching, and completion. Expectations in the context of this problem solving stereotype are in the form of queries about the type of information available to the engineer. At any point in the process of recognition, the frames' expectations are linked with a method which is designed to continue the process of recognition, based on satisfying the requirements of that same expectation, (for example, for a given answer to some question, what are the next questions which will narrow down the search?) The process of trying to satisfy a given expectation is abandoned when the method f a i l s to satisfy the assigned expectations after a number of pre-53 conceived external observations. In this light, the recognition process is a matter of "differentiating a specific instance", rather than a "specific selection" (Havens, 1978). The second phase involved in the process of recognition is the matching phase which forms an iterative recognition "cycle" with the expectation phase. The methods may be designed to calculate a new set of expectations from previous observations during the expectation driven search. At this time the recognition process is suspended until new information is input which satisfies the newly cmputed expectations. In summary, the matching process involves a clue driven search over the frame network that relies on the syntactic matching of the expectations contained in the stereotype frame against the observations. Completion occures when a l l of the expectations of a particular insance have been satisfied. The completely matched instance is then returned to a higher level (parent schema- see instance hierarchies) for which the completed instance is a component part. Thus, the recognition of a FLOW-ESTIMATION instance (or situation) proceeds through several cycles of creating expectations, suspending the methods attached to those expectations upon completion and then moving on to match simplers clues. When a l l of the expectations called for by the FLOW-ESTIMATION frame have been satisfied, the completion phase begins and the completed frame becomes a clue for a higher level instance. Using the information contained in this completed instance, 54 the expectation-matching cycle is initiated on the next level up. If a match is found at this level, a higher level is attempted, until the top most level is satisfied. In summary, the completion phase is a limiting condition which depends on the types of information that are available to the engineer solving a particular flow estimation problem. 4.3 j_ Encoding The Knowledge Base The matching algorithm .for the FLOOD ADVISOR was implemented by Oberski and Z i t t i n i in the C language and best operates in conjunction with the Unix (c) operating system. The program is set up to search through an explicitly specified solution space using both top-down and bottom-up search techniques. The solution space is specified in a f i l e containing the declarative, procedural, and heuristic knowledge of the domain. This f i l e is then read and processed by the control program. If the format of the f i l e containing the encoded knowledge are not organized appropriately, an error message is displayed and the user is back in the Unix environment. Once the knowledge-base has been encoded appropriately, the user must input his choice from some kind of option menue. The choice of the menue layout and i t s details are totally up to the encoder. The system then produce its domain-specific solution space by setting up a frame network somewhat similar to a tree structure. To further ill u s t r a t e , consider the following example of a hypothetical knowledge base: start "!main-proc" > node1.1 node 1.2 node 1.3 explain < node 1.1 "!procedure 1.1" > nodel.1.1 node 1.1.2 < 55 node 1.1.1 "!procedure 1.1.1" > < node1.1.2 "!procedure 1.1.2" > < e x p l a i n l . 1 "!procedure-e1.1" > < node1.2 "!procedure 1.2" > node1.2.1 explain1.2 < node 1.2.1 "!procedure 1.2.1" > < explain1.2 "!procedure-e1.2" >.< Each l i n e i n the above s t r u c t u r e represents a frame (or s l o t ) c o n s i s t i n g of upto one hundred s l o t s . For example, the f i r s t l i n e represents the parent frame and has been named s t a r t i n the above example. The s l o t s a s s o c i a t e d with t h i s frame have been named node1.1, node 1.2 and node 1.3 f o r convenience. The expression which appears in double quotes, i s the attached procedure. The s t r i n g i n s i d e the qoutes may be e i t h e r a Unix command (or a sequence of unix commands), or a simple s t r i n g of maximum 64 c h a r a c t e r s i n length, (note that the exclamation mark need not be used i f a short message i s to be d i s p l a y e d ) . The program s t a r t s execution by reading from the knowledge base and sets up the knowledge t r e e as f o l l o w s : 1 - The i n i t i a l f i e l d in the f i r s t l i n e ( f i e l d s i n each l i n e are separated by blanks) i s a s s o c i a t e d with the s t a r t node. 2 - The standard s l o t s for each frame are then read from the knowledge base and p o i n t e r s are set up to connect the parent node (frame) to i t s successor nodes ( t h i s i s done in a d e p t h - f i r s t fashion) , Once the knowledge tree has been set up, the program waits f o r standard input. When a s t r i n g of input i s entered by the user (that i s , when a s l o t i s f i l l e d ) , the search f o r the s p e c i f i e d s t r i n g w i l l proceed s t a r t i n g with the immediate successors of the current node. If a match i s not 56 found, the c u r r e n t l e v e l i s then searched. I f the s t r i n g can not be found a t t h a t l e v e l , the program moves a window back up one l e v e l and searches t h a t l e v e l f o r a match. T h i s p r o c e s s i s c o n t i n u e d u n t i l a match i s found a t which time the program causes the e x e c u t i o n of the procedure a t t a c h e d t o the s l o t b e i n g f i l l e d . I f the s t r i n g can not be matched i n t h i s way, the window comes to r e s t a t top of the t r e e by d e f a u l t and the c o r r e s p o n d i n g sequence of a c t i o n s w i l l be executed. 4.4 j _ U s i n g the FLOOD ADVISQR The p r o c e s s of u s i n g FLOOD ADVISOR c o n s i s t s of the f o l l o w i n g s t e p s : (a) - The user i s i n s t r u c t e d t o en t e r known f a c t s about the f l o o d e s t i m a t i o n problem i n t o the c o n t e x t . (b) - The c o n t r o l program i s then invoked t o match the inp u t s t r i n g w i t h the s l o t s r e p r e s e n t a t i v e of the g e n e r i c frame. Once a match has been found, the c o n t r o l program causes-the e x e c u t i o n of the procedure a t t a c h e d t o t h a t s l o t . (c) - The r e s u l t of the above st e p i s t o add t o or modify c e r t a i n a s p e c t s of the c o n t e x t b e i n g m o d e l l e d . Once the c o n t e x t has been m o d i f i e d , new s l o t s become c a n d i d a t e t o be f i l l e d by the us e r . T h i s process i s c o n t i n u e d u n t i l a g o a l s t a t e has been reached. 57 CHAPTER 5 tDISCUSSION AND SUMMARY OF RESULTS A problem s o l v i n g model was developed f o r d e a l i n g w i t h f i v e g e n e r a l i z e d s i t u a t i o n s as a c h a r a c t e r i z a t i o n of a t y p i c a l f l o o d e s t i m a t i o n problem. S e v e r a l s o l u t i o n p rocedures were recommended i n each c a s e , based p r i m a r i l y on the t y p e , q u a n t i t y , and q u a l i t y of the a v a i l a b l e d a t a . The e x p e r t i s e r e p r e s e n t e d i n FLOOD ADVISOR i s not complete and the procedures recommended as a s o l u t i o n procedure i n each g e n e r a l i z e d case a re p r e s e n t l y being c o n t i n u a l l y improved. T h i s p r o t o t y p e system was used t o demonstrate how s p e c i a l i z e d problem s o l v i n g knowledge may be used t o i n t e r a c t i v e l y a s s i s t the engineer i n making expert d e c i s i o n s . In a d d i t i o n , i t i l l u s t r a t e s how ex p e r t knowledge used f o r d e a l i n g w i t h t y p i c a l flow e s t i m a t i o n s i t u a t i o n s can be r e p r e s e n t e d i n computer memory u s i n g the frames r e p r e s e n t a t i o n t e c h n i q u e . Expert systems are powerful t o o l s o n l y when a l a r g e amount of e x p e r t knowledge i s r e p r e s e n t e d i n e a s i l y a c c e s s i b l e d a t a s t r u c t u r e s . Condensing the l a r g e amount of a v a i l a b l e h y d r o l o g i c knowledge i n t o a r e l a t i v e l y w e l l -d e f i n e d s e t of f a c t s and procedures would r e q u i r e a c o n s i d e r a b l e amount of e f f o r t e s t i m a t e d a t two to t h r e e man-y e a r s of c o - o p e r a t i v e r e s e a r c h among e x p e r t water r e s o u r c e and knowledge e n g i n e e r s . In the case of the FLOOD ADVISOR, some of the b u i l d i n g b l o c k s a l r e a d y e x i s t e d . For example, the FLOODS program which i s at the h e a r t of some of the recommended s o l u t i o n procedures, was a l r e a d y a v a i l a b l e . As mentioned e a r l i e r , the e x p e r t i s e r e p r e s e n t e d i n the FLOOD 58 ADVISOR i s i n c o m p l e t e and t h e recommended s o l u t i o n p r o c e d u r e s a r e i n t h e i r i n f a n c y . The p u r p o s e o f t h i s " t o y " s y s t e m was t o d e m o n s t r a t e t h e p o t e n t i a l a p p l i c a t i o n s o f e x p e r t s y s t e m s i n w a t e r r e s o u r c e e n g i n e e r i n g . I n i t s p r e s e n t f o r m , t h e k n o w l e d g e a c q u i s i t i o n mode i n FLOOD ADVISOR i s by means o f d i r e c t i n s e r t i o n s i n t o t h e k n o w l e d g e b a s e . An i n t e r a c t i v e g r a p h i c p r o c e d u r e may be d e v e l o p e d t o a s s i s t t h e e x p e r t e n g i n e e r i n e n c o d i n g h i s / h e r h i g h l y s p e c i a l i z e d k n o w l e d g e . The k n o w l e d g e a c q u i s i t i o n s e g m e n t o f t h e FLOOD ADVISOR may a l s o be i m p l e m e n t e d by u s i n g t h e f r a m e t e c h n i q u e . I n o t h e r w o r d s , t h e g e n e r i c KNEW-PROBLEM f r a m e ( s i m i l a r t o t h e g e n e r i c NEW-PROBLEM f r a m e o f f i g u r e 2 . 1 ) w o u l d c o n s i s t o f a s e t o f s t a n d a r d s l o t s t h a t d e s c r i b e t h e c o n c e p t s r e l a t e d t o K n o w l e d g e a c q u i s i t i o n p r o b l e m s . ( t h a t i s , s p e c i a l i z a t i o n o f j_ K n o w l e d g e A c q u i s i t i o n ) T h i s f r a m e , a n d t h e NEW-PROBLEM f r ame ( f i g u r e 2 . 1 ) may be u s e d c o n c u r e n t l y i n t h e c o n t e x t o f d e s i g n f l o w e s t i m a t i o n t o a l l o w a d i r e c t i n t e r f a c e b e t w e e n t h e c o m p u t e r a n d t h e human e x p e r t s . The d e v e l o p m e n t o f t h i s i n t e r f a c e w i l l be t h e s u b j e c t o f f u t u r e r e s e a r c h by t h e a u t h o r ( s e e s e c t i o n 5 . 1 ) s . I n e n g i n e e r i n g d e s i g n , i t i s o f t e n r e q u i r e d t o p e r f o r m n u m e r i c a n a l y s i s on t h e d a t a b e f o r e a d e c i s i o n c a n be made a b o u t t h e m e t h o d o f a n a l y s i s . I n o t h e r w o r d s , r e s u l t o f c o m p u t a t i o n s a t e a c h s t a g e may d e t e r m i n e t h e r a n g e o f a p p l i c a b l e r u l e s o r p r o c e d u r e s . A l t h o u g h t h e FLOOD ADVISOR c a n n o t d i r e c t l y i n c o r p o r a t e t h e r e s u l t s o f n u m e r i c a n a l y s i s i n t o i t s l i n e o f r e a s o n i n g , i t was s e t up t o p r o v i d e 59 instructions on how to use existing conventional programs for performing the desired calculations (and invokes such programs upon request). The heuristic knowledge used for the interpretation of the generated output is then used to provide advice on how to interpret the data. The FLOOD ADVISOR sets the context for using three conventional computer programs, namely, EPFFM, FLOODS, and PDRFFA, as a tool for solving well-defined flow estimation problems. These programs provide valuable summaries of computations and are consequently used by the FLOOD ADVISOR to assist the engineer in making decisions. The knowledge in FLOOD ADVISOR was represented using the frame representation technique. This technique was chosen over other techniques because of the following features : (a) a sufficient amount of knowledge pertinent to the domain of interest may be easily represented in computer memory, (b) the data structures are easy to modify and new knowledge inferred from the old may be readily incorporated into the problem solving model, and (c) procedural heuristic knowledge may be used to guide the reasoning (search) behaviour of the system. In conclusion, expert system architecture allows the development of practical problem-solving models of the real world that offer not only the ability to perform standard engineering calculations but also access to specialized knowledge that is otherwise only available to experts in the fie l d . 60 5.1 Suggestions For Future Research The following section is an outline of the three main phases of the research proposed for improving the FLOOD ADVISOR. As pointed out previously, an expert system for engineering applications must be capable of performing numerical analysis in addition to mechanical manupulation of specialized data structures containing the factual knowledge of the domain. For this reason, it would be necessary to incorporate existing computer models within a larger problem solving context in order to be able to deal with a large number of typical problem solving situations often encountered by expert water resource engineers. The gathering of the available flow estimation procedures and their implementation within an otherwise declarative data structure is at the heart of this proposed system. At the outset of the research however, is the implementation of an interactive graphic program designed for acquiring knowledge from expert water resource engineers. The realization of this component of the expert system would provide an efficient method for modularizing and encoding the expert knowledge. This phase of the research is presently under development. The final phase of the research involves the development of a comprehensive framework for representing problem-solving knowledge in terms of conditional probabilities of events. As in the FLOODS program, the Bayes' rule may then be applied to combine information from a variety of sources to compute probabilities of occurrence of events, given that certain other events have already 61 occurred. The time required for each phase of this research is estimated at approximately 6 to 12 month of cooperative research. 62 BIBLIOGRAPHY BARR A. & FIEGENBAUM E.A. (1982) The Handbook Of A r t i f i c i a l  Intelligence, vol. 1, pp. 3-43, 143-216. , Kaufman inc. BENJAMINE, J.R. & CORNELL, C.A. (1971) Probability,  Statistics, And Decision For C i v i l Engineers, McGraw H i l l Book co. BOBROW, D.G. & WINOGRAD, T. (1977) An Overview of KRL: A Knowledge Representation Language, Cognitive Science, vol. 1, #1, Jan. 1977, pp. 3-45. CHARNIAK, E. & MCDERMOTT, D. (1985) Introduction To A r t i f i c i a l Intelligence, Addison-Wesley publishing co., pp. 453-482. CHOW, V.T. (1964) Statistical And Probability Anaalysis Of Hydrologic Data, The Handbook Of Applied Hydrology, McGraw-Hill book co., ch.8, p. 1-96. DALRYMPLE, T. (i960) Flood frequency Analysis, Manual Of  Hydrology: part 3_, Flood-Flow Techniques, U.S. Gov. Printing office, pp.1-80. DUDA, R. & GASCHING, J.G. (1981) Knowledge-Based Expert Systems Come Of Age, Byte, vol. 6, #9, sept. 1981, pp. 238-279. DUDA, R. & SHORTLIFFE, E.H. (1983) Expert Systems Research, Science, vol. 220, April 1983, pp. 261-268. FENVES, S.J. ET AL (1984) Knowledge-Based Expert Systems In C i v i l Engineering, Computing In C i v i l Engineering ed. Hodge, C.S. Pp. 249-257. FIEGENBAUM, E.A. (1983) Knowledge Engineering : The Applied Side, Intelligent Systems eds. Hayes, J.E. & Michie, D., John Wiley & Sons Book co. HAAN, CT. & BARF I ELD, B.J. (1978) Hydrology And  Sedimentology Of Surface Mined Lands. Institute For Mining & Mineral Research (IMMR), University of Kentachy , U.S.A HAVENS, W.S. (1978) A procedural Recognition Model For  Machine Intelligence, PhD thesis, Dept. Of Computer Science, U.B.C pp. 5-74 HAYES, R.F., WATERMAN, D. & LENAT, D. (1984) Building Expert  Systems, Addison-Wesley co., ch. 129-167. MINSKY, M. (1975) A Framework For Representing Knowledge, The Psychology Of Computer Vision, ed. Winston, P.H., McGraw H i l l book co., pp. 211-280. 63 NILSSON, N.J. (1980) Principles Of A r t i f i c i a l Intelligence, Tioga publishing co., pp. 17-50 & 361-417. NILLSON, N.J. (1971) Problem-Solving Methods I_n A r t i f i c i a l  Intelligence, McGraw-Hill book co., pp. 17- 78. RICH, E. (1983) A r t i f i c i a l Intelligence,)-u McGraw-Hill book  co., pp. 201-292. RUSSELL, S.O. (1982) Flood Probability Estimation, Journal of the Hydraulics Division, Proc. Of ASCE, Vol. 108, #HY1, Jan., 1982, pp. 63-73. SCHANK, R.C. & ABLESON, R.P. (1977) Scripts, Plans, Goals  And Understanding, pubs., L. Erlbaum Associates, pp. 2-67. SCHANK R.C. & RIESBECK, C.K. (1981) Inside Computer  Understanding, pubs., L Erlbaum Associates, pp. 11-41. WINSTON, P.H. (1984) A r t i f i c i a l Intelligence, Addison-Welsley publishing co., pp. 163-290. aaanaaaaaaaaaaaaaaasaaaaaBaaaaaBBaaaaaaaaasaaaasaBaaaaaataaaataaaaaaaaaaaaaaaaaa 888 ojpfiij 888 anu3w uoi}do s n o u s j d a m 0} >j:pq }a6 oj^  -C£) 888 888888a88888888EBBBB888888888S8888BB8BBB88BBB88BB88B88BStBB8at8BB888B88B8BB888B8 888 eases n n a 3~iayOI~lddy SI S3SW0 3AC13y 3H1 dO 3N0N -C93 888 aaaaaansaaaaaaaaBBnaaaBaaaaaaaoaaaBaaaaaaaattaaaaaaanaanatiaaaataaaaaaaaaaaaaaaaaB 888 BBB -p3ij,s j3}em 3 ^ J O ; »|qBijBAB s i e*ep n e j u i t J '103 888 888 gases 8B8 'uoi63- i aqi J O J a] ] i P A B S J B s p j o s s j *o ] ju69j}8 o (v| -CSD 888 8888888a888a88B888Ba88838888888888883888B88888888888388at:888Bt8B8S888a88888888B8 888 808 '^'-"U! 1° p3l|Sj3}Bro tt88 888 BB8 9m u) •smeajjs fiqjBau J O J 3|qe|iPAB a . 'B s p j o s a j > j^ pg J J J J J J 888 f 9 8 6 3 BBB ' 1 S S J * l g ! >° wea-ns uo a|qe|ieAe S J C spjosau o^ j -f^} 888 88888888888888B8a88a88aa888aB83888B888S88B88883B88838888t8888t:888888833888888888 888 838 j s s j s i u i jo u i s e q a m se u i s e q awes au^ u i i s a j a ^ u i jo 888 888 £ases 888 " f 3 J l ! syi uo a i q e p B A e s i p j o s a j moijuieaj}S j j o q s y -C£~) 888 88B8888888B888888Sa888888888888888a888888888B88888888888:::8888t88a8888a88888B8B88 888 888 '}99j9ni] uo i jeso | a ^ U I B a J } s u m o p J C a c s ^ s d n BB8 888 888 pa^Booi s i U O I I B J S 6 u i p . i a s 3 J ai|^ ' y3A3M0H ' i s a j a j u i n It» 888 gases 888 i° meaj^s &m uo a i q e p e A B s i p j o s a j jc p o i j a d 6uo) y - 888 888S88388888B338aBBB338B88B8333888388888a888888888888883t8888t:88888883a883338888 888 888 jo B J I S a^j se u i s e q awes aqi u\ s i U O I J S J S 888 888 888 6uip-iosaj au.% Q|^y J S 3 J 3 J U 1 '^ o U I E S J J S a i|} uo 3|qej iPAB JJJJJJ 88B jases 888 s i p j o s a j (s J J S S gj u t ^ J 9 1 B 3 J 6 ) p o i j a d 6uo) y _ d } 888 888888888888888888888888888888888838888388888888888888881:88881:888888888888888388 888 a 3 1 N 3 888 N 0 I 1 d 0 888 888888888838888B88e88883888888888888aB888888888888B83Ba8t:8888t:888888888888a88S88 i QNyH-iy-usiaoad 3HI OI 3~iayims isow s i sssyo ONiMcmod 3HI do 3NQ HOIHM ,03SBS, ja^ua <}qncp ui j [ s jdasuos s i6o]o jpf iq i) i 1 m fiiiJBi|iiuej J B S n | aq unions sasBS 3 | q i s s o d v i s o^ auo i | S i | q e ? s a oj^  u o i s s a s s;t{] ^ o ^ x a } u o s a i| _L NOiiyaN3wwoo3a SNOiidwnssy sioyd NMON* 1X31N00 i0d=ai o jpli 14 | ne> ap a q | l ! m uaajss s i L) 1 <sapos uoi jdo aAo qe 3 4 } 3 d f i } s 1 ui noR ^ 1 : g/gj /vjNyy/v) ' • " ' - s j a ; j a | 3syo d3M01 3 s n 1SPW n o f i 888888888888888888B8888B88888888888a888888888888t:8888t:8a88a88888883aa888 88 Z-~iaiO 888388888 u»BJ6CJd a<0 « J ) 11*3 O 88 U8 fieidsip 888888888 anuaui siu,deJ6 fieidsiQ CC 38 83 <M»M 888888883 u 0 1 •( B »> J c > u 1 |SJ9u9g CS 38 jttt ojpfiu, 888888888 uoi;e u ,)^sa m o u 88 88888B8B88888888888888888888888a88S88888B88B8888t8888}::aS88888aaa8888B88a 88 a 3 i N 3 888888838 N Q 1 1 d 0 88 8888838888888388888888888888888883888888888888881:83881:383383888883888888 30N3UI ONlMOHOd 3H1 UlQdd 301 OHO iinOA JI31N3 N0ISS3S SI HI aOd 1X31N00 3H1 13S 3S:y3-|d • s u o ) i f r i ] i 5 p a 2 ) \ e j a u a 6 3 s a i ) i jo auios i|} 1 m 6 u i i e s - p - I O J UJJd3 P u e SQOOld ' ydddJJQd 'fijameu >su)e-i60Jd u o i j e u n } s a «io | j JB|idod 99J>|) asri oj mOL| uo papiAOJd os |C aje suoi j a n j j ! u | ' j a a u i e u a ai!n ••iqe|ieAe s a s j n o s a j pue e}Bp s i 6 0 | 0 j p f i q ^ 0 fiji^uerib pue <fi; i ierib <9df l aqi uo'ft|iJBuiiJd 3se<) aJB s u 0 1 \ B 2 1 1 B J au 36 3 S 3 4 J L •suoi^en}is pj jom_|B3J p32l|BJaua6 S A I ) ^ 0 3uo o^  ajqe^iris j s 0 UJ anbiuijsa^ uoi ) I ? D I ) S S M 0 1 > SM5 ^noqB asiApe 3Ai^SBJa^ui BpiAOJd o; p3U6isap' jusi |nsuo3 p9S)>q.J3jrd«o 5 e s i dOS I AOy OODId : 3 s 0 d a n d ************************ T-0 N 0 i s d 3 A a o s i A a y a o o i d 01 3 u o o q q | n i U 1 I J H HOSIACW aOOl^I ^l^TM uotssas 8A-cq.OBa9q.u1 uy : XIa^EdciV 179 65 easel m = F 0 i i CONTEXT : Flsod estimation C c a 6 e l specified) KNOWN FACTS : More than 15 years of record is available on the stream of interest and the recording station is in the same basin as the s i t * of interest. To perform conventional frequency analysis on the record The data series satisfies assumptions Type 'e.xpll ' if you need explanation GOAL ASSUMPTIONS RECOMMENDATION PLEASE ENTER YOUR OPTION FROM THE FOLLOWING MENUE ooooooo888888888883880030oooo8888888880000000088B8oooooooooo88880088888floooooooo OOO O P T I O N 88888880011 E N T E R 8808088 80008880888080008838880:108000888088888000000008088008888880000000000000000000080 800 C D - Explain assumptions made in case 1 8000000000 expll 0800000 00000000008888800030000308800008888800008880000000000000000080888000000000888888 008 C2D- Edit data f i l e containing Peak flows 8088888000 edit 0008888 88000000088888800838880300000888880000088088888888000000000880000888888000880000 880 C33- Explain how to verify assumptions 0000000008 ver 0000000 00888888888888800030880300000000080000088800000888888880800000000000000008800008 000 (4)- To get back to the previous menue 0888888888 hydro 8800008 80888888888888000030000300808888888888888888888888888888888888888880088800088008 exp 1 1 THE FOLLOWING ASSUMPTIONS HAVE BEEN MADE AND MUST BE VERIFIED CSEE CHOW. VEN TE. HANDBOOK OF APPLIED HYDRAULICS, CHAPTER 8 5 C D - The data are sufficient in quality and quantity to produce r e l i a b l e estimates for the parameters of the probability d i s t r i b u t i o i selected. C2) - The flow charecterist ics of the stream have not been chainging over time Cthat i s . STATIONARY data series with no TREND or JUMP} C3) _ The peak annual flow observations are s t a t i s t i c a l l y independent from year to year. C4D— The data are representative of the flow behaviour expected during the design l i f e of the project under i nve s t i gat i on C53- The flow is NATURAL Cand thus RANDOM). CUNREGULATED) 080888888800000888388083888888800088888888888880888888888888 08888 O P T I O N 8888 ENTER 8888 088888888800000000300003888888888888880000008800088888888880 00088 C D - to enter your data in a f i l e 8008 edit 0000 000888888888888800300003000000000000000000000000888888888888 00008 C2)~ to get back to the previous menue 8000 easel 0000 000000000000000000300003008888000000000888800000000000000000 ed i t 66 TO EDIT A DATA FILE NECESSARY AS AN INPUT FILE TO PDRFFA PROGRAM. YOU MUST KNOW SOMETHING ABOUT THE VMS EDITOR. IF YOU ARE NOT FAMILIAR WITH THE EDITOR, CONSULT WITH THE APPROPRIATE MANUAL OR A FRIEND. IF YOU ARE FAMILIAR WITH THE VMS EDITOR, THEN ENTER THE ' e d i t ' OPTION. ONCE YOU HAVE ENTERED ' e d i t ' , THE SCREEN WILL BLANK AND YOU WILL BE IN THE VMS EDITOR. YOU MUST THEN SIMPLY TYPE OVER THE LINES WITH YOUR DATA. THE FIRST LINE IN THIS FILE CONTAINS SIX ONES STARTING IN COLUMN 4 TO 9. THEY MUST BE LEFT UNCHANGED. THE SECOND LINE CONTAINS THE NUMBER 30 FOLLOWED BY FOUR ZEROS, THE IDENTIFICATION CODE OF THE GAGING STATION, FOLLOWED BY AN OPTIONAL RIVER NAME AND HEADING. 123456789012345678:3012345678901234567890123456789012345678901234567890123 1 1 1111 30 0000 08NE001 INCOMAPPLEUX RIVER, TO 1979, PEAK ANNUAL FLOW. 1915 244. 1915 197. 1952 263. 1953 538. THE NUMBER 30 IS THE NUMBER OF YEARS OF RECORD AND MUST BE KNOWN IN ADVANCE. THE FOUR ZEROS ARE THE AREA OF THE BASIN OF INTEREST IN SQ KM OR SQ MI. THIS VALUE WILL NOT EFFECT THE CALCULATIONS AND IS THUS OPTIONAL. AFTER YOU HAVE FINISHED TYPING OVER THE FILE WITH YOUR DATA. THE FOLLOWING SEQUENCE MUST BE ENTERED TO SAVE YOUR DATA: 1- PF1 key, 2- E key. and 3- ENTER key Cnot RETURN) YOU HAVE THE FOLLOWING OPTIONS 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 8 8 3 8 8 8 8 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 O P T I 0 N S 8 8 8 ENTER 8 8 8 8 8 8 8 8 8 8 8 8 8 6 8 8 8 8 8 8 8 3 8 8 8 8 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 CD- E d i t data f i l e for PDRFFA 8 8 8 ed 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 8 8 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 C2)~ Run PDRFFA with example f i l e 8 8 8 run 8 8 8 8 8 8 , 8 . 8 8 8 8 8 8 8 8 8 8 8 8 8 8 3 8 8 8 8 3 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 C3)- Return to the previous menue 8 8 8 easel 8 8 8 _ 8 8 8 8 B B 8 8 8 B E 8 8 8 8 8 8 B 3 8 8 8 8 3 8 8 8 8 8 B B 8 8 8 8 8 8 8 8 8 8 8 B 8 8 8 8 8 B 8 8 8 8 8 8 8 f l ed i i 1111 0000 08NE001 INCOMAPPLEUX RIVER, TO 1979, DAILY DISCHARGE 1914 244. 1915 197. 1952 263. 1953 538. 1954 272. 1955 394. 1956 279. 1957 200. 1958 254. 1959 259. 1960 326. 1961 345. 1962 282. 1963 259. 1964 362. 1965 223. 1966 252. 1967 326. 1968 362. 1969 250. 1970 261. 1971 280. 1972 430. 1973 248. 1974 334. 1975 228. 1976 278. 1977 286. 1978 203. 1979 195. 08NE001 INCOr'flPPLEUX RIVER. TO 1979, PERK RNNURL FLOW LOG PERR50N TYPE I I I DISTRIBUTION FPRflMETERS ESTIMATED BY MAXIMUM LIKELIHOOD 10i tn LU CD Cr <x zz u CO 2. + t 1 i.d05 1.2S 2.0 5.0 10. 20. 50. 100.200. SOO. RECURRENCE INTERVAL IN YEARS PAUSE. . .H IT ANY KEY TO CONTINUE ON 08NE001 INCOKflPPLEUX RIVER. TO 1979. PERK RNNURL FLOW LOG PERRSON TYPE i n DISTRIBUTION 1 PRRftMETERS ESTIMATED BY MOMENTS + % 1 I.60S I. OS 1 .25 2 .0 S . 0 10. 20. 50 . 100.200. 500 . RECURRENCE INTERVAL IN YERRS PAUSE...HIT ANY KEY TO CONTINUF 00 08NE001 INCOffiPPLEUX RIVER. TO 1979. PERK RNNURL FLOW LO3-N0RMRL DISTRIBUTION 1.605 1 . 2 S 2 . 0 5 . 0 10. 2 0 . 50 . 1 0 0 . 2 0 0 . 500 . RECURRENCE INTERVAL IN YEARS PAUSE. . .H IT ANY KEY TD CONTINUE 08NE001 INCOKflPPLEUX RIVER. TO 1979. PERK RNNURL FLOW THREE PARAMETER LOG-NORMAL DISTRIBUTION 3. FRRRMETERS ESTIMATED BY MAXIMUM LIKELIHOOD 10. 1 1 1 1 1 1 1 1 1 1 9. 8. ti, cS 1 1 ' 1 1 1 1 1 1 1 WOOB I. OS 1 . 2 5 2 . 0 S O l O . 2 0 . 50 . 1 0 0 . 2 0 0 . 500 . RECURRENCE INTERVRL IN YEARS PAUSE...HIT ANY KEY TD CONTINUE O 08NE001 INCOKRPPLEUX RIVER. TO 1979, PERK RNNURL FLOW GUMBEL I DISTRIBUTION 005 1.05 1.25 2.0 5.0 10. 20. 50. 100. 200. 500. RECURRENCE INTERVAL IN YERRS PAUSE...HIT ANY KEY TO CONTINUE 72 JD=FOL)T. M CONTEXT KNOWN FACTS GOAL ASSUMPTIONS RECOMMENDATION of F l o o d e s t i m a t i o n u s i n 9 c o n v e n t i o n a l f r e q u e n c y a n a l y s i s More th-an 15 y e a r s o f ' r e c o r d i s a v a i l a b l e on the s t r e a m i n t e r e s t and the r e c o r d i n g s t a t i o n i s in the same b a s i n as the s i t e of i n t e r e s t . To p r o v i d e a s s i s t a n c e on how to i n t e r p r e t the d a t a The d a t a s e r i e s s a t i s f i e s a s s u m p t i o n s . C a r e f u l l y a n a l y z e the o u t p u t d a t a u s i n g one of the o p t i o n s shown b e 1 o w : P L E A S E ENTER YOUR OPTION FROM THE FOLLOWING MENUE 88888888888888888838888380888888088808800000888808888088888888888888888080088888 888 O P T I O N 8888888888 E N T E R 8888888 8888888888888888883888838888888888888888888888888 8888888888888888888888888888888 888 C D - P r i n t o u t p u t of PDRFFA CPRINTRONIXD 8888888888 p r i n t 8888888 8888888S88888888883888838888888 f l8888888888888888S88888888888B88888888B88888S8888 888 C 2 ) - D i s p l a y o u t p u t of PDRFFA on s c r e e n 8888888888 d i s p l 8888888 888888888888888888388883888 88888888888888888888888888888888888888888888888888888 888 C 3 ) - P r o v i d e g e n e r a l p r o b I e m - s o I v I n 9 a d v i c e 8888888888 a d v l 8888888 88888888888888888838888388888888888888888888888888888888888888888888888888888888 a d v l 1D=EXPN CONTEXT KNOWN F A C T S GOAL ASSUMPTIONS RECOMMENDATION F l o o d e s t i m a t i o n u s i n g c o n v e n t i o n a l f r e q u e n c y a n a l y s i s More t h a n 15 y e a r s of r e c o r d i s a v a i l a b l e on the s t r e a m of i n t e r e s t and the r e c o r d i n g s t a t i o n i s i n the same b a s i n as the s i t e of i n t e r e s t . To p r o v i d e a s s i s t a n c e on how to i n t e r p r e t the d a t a The d a t a s e r i e s s a t i s f i e s a s s u m p t i o n s -C o n s u l t w i t h CHOW/ 1964 , and HAAN, 1977 The two p a r a m e t e r LOGNORMAL d i s t r i b u t i o n and the t h r e e p a r a m e t e r LOG PEARSON TYPE III a r e e x t e n s i v e l y u s e d in p r a c t i c e and a r e a 3 o o d c h o i c e C 9 i v e n t h a t the a s s u m p t i o n s a r e s a t i s f i e d ) P L E A S E ENTER YOUR OPTION FROM THE FOLLOWING MENUE 88888888888888888838888388888888888888888888888888888888888888888888888888888888 888 O P T 1 O N 8888888888 E N T E R 8888888 88888888888888888838888388888888888888888888888888888888888888888888888888888888 888 C D - E x p l a i n a s s u m p t i o n s made in c a s e 1 8880888888 e x p l l 8888888 88888888888888888838888388888888888888888888888888888888888888888888888888888888 888 C2)~ To get back to the main menue 8888888888 h y d r o 8888888 88888888888888808838888388888888888888888888888888888888888888888888888888888888 d i s p l 73 M A X I M U M D A I L Y M E A N F L O W S 08NE001 INCOMAPPLEUX RIVER. TO 1979, DAILY DISCHARGE MAX I MUM RECURRENCE MAX I MUM DATE DAILY FLOW' RANK INTERVAL | DAILY FLOW | YEAR IN M3/S j ! IN YEARS IN M3/S ! 1914 244.0 [ | 1 ' 40.132 [ 538.0 j 1953 1915 197.0 j j 2 | 17. 330 ' 430.0 1972 1952 263.0 | | 3 | 11.051 j 394.0 't 1955 1953 533.0 4 8. 112 362. 0 1964 1954 272.0 ' | 5 | 6. 408 | 362.0 | 1968 1955 394.0 | [ 6 | 5.295 | 345.0 | 1961 1956 279.0 j 7 | 4.512 334. 0 1974 1957 200.0 | ! 8 ! 3. 930 326.0 | 1960 1958 254.0 j ! 9 ! 3. 482 | 326. 0 | 1967 1959 259.0 j ! 10 \ 3. 125 | 286.0 | 1977 1960 326.0 | i i I 2. 835 | 282.0 j 1962 1961 345.0 | ! 1 2 ! 2. 594 [ 280.0 | 1971 1962 282. 0 [ ! 1 3 ! 2. 390 [ 279.0 | 1956 1963 259.0 ' ! 14 | 2. 217 278. 0 1976 1964 362.0 ! 15 | 2. 066 272.0 | 1954 1965 223.0 ] ! 1 6 1. 935 ! 2 6 3 - 0 ! 1952 1966 252.0 17 1. 820 261. 0 1970 1967 326.0 't 18 1. 717 \ 259.0 1959 1968 362.0 j ! 19 [ 1. 626 | 259.0 | 1963 1969 250.0 2 0 ! 1. 544 ! 2 S 4 , 0 1958 1970 261.0 ' ! 21 | 1. 469 ! 2 5 2 - 0 ! 1966 1971 280.0 | ! 2 2 ! 1. 402 | 250.0 ' 1969 1972 430.0 ' ! 23 1. 340 ! 248.0 | 1973 1973 248.0 ' ! 24 [ 1. 284 244.0 1914 1974 334.0 | ', 2 5 ! 1. 232 [ 228.0 | 1975 1975 228.0 [ ! 2 6 ! 1. 184 ! 223.0 ' 1965 1976 278.0 j ! 27 | 1. 140 | 203.0 | 1978 1977 286.0 \ ' 28 [ 1. 099 ' 200.0 1957 1978 203.0 ' 29 | 1. 061 197.0 [ 1915 1979 195.0 j ! 3 0 ! 1.025 [ 195.0 | 1979 MEAN ANNUAL FLOOD: 287.7 M3/S DRAINAGE AREA: 0000 SQ KM 74 75.163 M3/S INCOMAPPLEUX RIVER, 75. 2 . 2374 MAX = STANDARD DEVIATION 0SNE001 SAMPLE STATISTICS MEAN = 288. 3.D. = SAMPLE STATISTICS CLOGS!) MEAN = 5.6330 3.D. = SAMPLE MIN = 195. SAMPLE PARAMETERS FOR GUMI3EL I A = .019169 U = 256. PARAMETERS FOR LOGNORMAL M = 5.6330 S » . 2374 PARAMETERS FOR THREE PARAMETER LOGNORMAL A = 152. M = 4.7765 S STATISTICS OF LOGCX-A3 MEAN = 4. 7765 S. D. = SAMPLE MIN = 195. SAMPLE PARAMETERS FOR GUMBEL I A = .019169 U PARAMETERS FOR LOGNORMAL M = 5. 6330 S •- . 2374 PARAMETERS FOR THREE PARAMETER LOGNORMAL 152. M = 4.7765 S = OF LOGCX-fO TO 1979. DAILY DISCHARGE C. S. = 1.5071 C. S. 538. . 7437 N = 30 C. K. = 6.4346 C.K. = 4.0767 . 5317 . 5317 MAX = 256. C. S. 538. - .0557 N = C. K. 3.3278 30 A = STATISTICS MEAN = PARAMETERS A = PARAMETERS A = DISTRIBUTION MEAN 5317 4.7765 FOR LOG 0883 FOR LOG 1048 STATISTICS 5.6330 S. D. = PEARSON III BY B = .7231e+01 PEARSON III BY B = .5140e+01 5317 C S. = - .0557 MOMENTS LOGCM) = 4.9946 MAXIMUM LIKELIHOOD LOGCM) = 5.0945 C. K. 3.3278 M = .1476e+03 M = . 163U+03 S. D. = .2375 C. S. . 8822 GUMBEL LOGNORMAL THREE PARAMETER LOG PEARSON I I I LOGNORMAL MAX LIKELIHOOD MOMENT RETURN ERR PERIOD X 1. 1. 1. 2. 5. 03 10. . 93 20. . 70 50. 20 100. . 00 200. . 10 500. . 90 005 050 250 000 000 000 000 000 000 000 000 FLOOD ESTM. 169. 198. 231. 275. 334. 373. 411. 459. 496. 532. 580. ST ERR 5. 14 5. 90 6. 56 7. 29 7. 76 8. 18 8. 65 FLOOD ESTM. 152. 189. 229. 280. 341. 379. 413. 455. 486. 515. 554. ST ERR 5. 04 5. 85 6. 65 7. 64 8. 34 9. 01 9. 83 FLOOD ESTM. 182. 201. 228. 271. 338. 386. 436. 506. 561. 619. 701. ST ERR 6. 22 8. 18 10. 50 13. 90 16. 50 19. 20 22. 70 FLOOD ESTM. 183. 202. 228. 270. 335. 384. 434. 505. 563. 627. ST ERR FLOOD % ESTM. 178. 200. 228. 272. 337. ST 6. 13 8. 14 10. 50 13. 90 16. 70 19. 60 6 7 10 15 719. 23.70 383. 431. 498. 551. 19 608. 23 690. 28 88888888888B8888888Ba888a8888888888888888Ba88888BBaB888at:aa8Bt:888B888:tB888B8B888 aaaaaaa s p ^ u aaaaaaaaaa »e j » 0 J >< saocnd 3m ,Jr,y cto aaa aaaaBaaBBaaaaaaBaaaBBaaaaaaaaaaaaaaaBaaaaaaaaaaaaaaaaaaacaBaataaaaaaaaaBaaaaaaaa B8B88BB BBBBBBBBBB u , B J 6 0 J d saDOld u ! « l « 3 C£} BBS 88888888888888888B888888888888888888888888B8888888888888t8888t8888888:}8888888888 8B888B8 ojpfiq 888B88BB88 anuauj s n o i A a J d *m 0 ) u jnj a j o x-C2} 888 8B88aa8888888a8a88888B88B888888888888BB8888B888B8B8BB388t:B888t:888888838888888888 8888888 SI<**a 8888888888 pom5"" u o i ; n | O S p s p u M . c s a j &m uie|dx3 CO 8B8 8888B888888BBB8888888a88888BB8888888888888a8a888888aaaa8t8888t8888888-4888a88B8B8 8888888 X 3 1 N 3 8888888888 NO I 1 d 0 888 88888888888888888888888888888888888888888888888888888888tB8B8t8888888:J8888888B88 30N3W ON I MDllOd 3H1 UOdd NO I IdO dflOA a3iM3 3Sy31d NOIiWaN3WW003d SNOiidwnssy iwoo uoi}8UE|dxs p a a u nofi j i i 21 d>: 3 t 3 d fi x ejpp no | p c s j j s p s p s ) |oo 9AEq pue s j is am papadsu] a A p u, r , 0 A •«o|) aq| aiPtuijsa 0} no q uo asiApe L| ^  A m nofi ap uo Jd oj_ •^saja^ui j o uoi|eoo| 3 M1 >° w B a J } s umop J O uipaj^sdri 1 p auios pa^eso] s i U O I J E J S 6uipjosaj am l n 1 ^sajajui ;o uipaj^s am uo aiqpi,ipAP si pjosaj jo sjpafi q\ uem 3 J 0 W : SiOyd NMONX Cpai;ioads J S S B J J uoiiBwi;sa pocij : 1X31N00 i0d=5T ft (u=ou ' f\ = s afi 5 2, n o fi 0} aiqBSi)ddE si g asBS *5'm uip^jas nofi ajy gasps 8888888aB8a888a8a88888888888888Ba88888888888a88888888888t:B888t8888888:t8888888a88 888 ojpfiq 888 anuaui uoi}do s n o i A a J d am oj >|SBq }a6 oj_ - C O 888 aBaaaaBaaaaaaBaaaaaBaaaaaaaaaBaaaaaaaaaaaaBBaaaaaasBaBaatBBaataaaaaaB^aaaasaaBBa 888 0asB3 888 31SyO HddW SI S3SyO 3 A C i a y 3H1 dO 3NDN -C9) BBB 88888888888888888888888888888888888888888888888888888888 t:8B88C888B888::t8888888B88 888 888 •pau.sjaiBm am J O ; 3|qe|i?Ae si e}ep I I B J U I B J • xna 888 888 gases 888 '"°16aJ am J O ; ajqeiiPAB aJB spjosaj mo|juiBaj;s 0(vj -CS) 888 88888aa88888888aaaaa888888888a88aa8a888a8B8888a8a88aaB8at88aat8888888 : t88888B88B8 888 888 ' I S ' J ' U ! i° paqsjajem JJJJJJ 888 888 3 L O u l 'suipaj^s fiqjpau J O J ajqeppAP aJB spjosaj <mg 888 888 i^ asps 888 ' isaja^ui jo wpaj^s am uo 9|qe|tBAB aJB spjosaj OIAJ -CtO 888 88888888888B888888888888BBB888888a88888888888888a8BBS888t:8B88t:8888888-.:t8888888888 888 888 }saja}ui ;o uispq am sp uiseq amps am u) }saja;ui ;o jjjjjt 888 £ases 888 uipaj^s am u o aiqepBAB si pjosaj » O | J « E S J I S ; J O L | S y - C O 888 888888888888888888888888888888888888888888888888888888881:88881:8888888388888888 88 JJ JJ Jt 888 "jsaja^ui j o u o i ^ B s o ) am i° m e a J^ s u m o p J C »B9Jisdn 888 888 888 paiBso] si U O I ; B ; S 6uipjosaj am <d3A3M0H ' 1 | 8 J ' 1 U ! 888 888 jases 888 1° lueaj^s am uo aiqpppAP si pjosaj ;c poijad 6uo| y _ eg) 8B8 888888888888888888888888888888888888888888888888888888881:88881:8888888:18888888888 888 888 •*saja%ui jo 9% i s am S B uispq auips au.1 ui si uoi}ei,s tt tt tt 888 8B8 6uipjosaj am QNy ^ s a j a ; u i ;o uieaJ^s am u 0 ajqBjiBAB 888 888 J9SB5 888 si p j o s a j jo (B J S S R g\ ja;paj6j poijad 6uo| y - C O 888 8aBBB8aBS8a8888BB88888888888888B88888888B8888a8888888BB8t:8888t:8888B88:t88888888B8 888 d 3 1 N 3 888 NO I 1 d 0 888 88 88888888888 8888 88888 8888888888888888888888888888 888 8 881:8 888 t8888888:J8888888888 L aNyH-iy-w3iaoad 3HI OI snayxins isow s i S3syo ON m o n a d 3HI do 3NO HOIHM ,0asps, J3}U9 'jqncp ul ;[ s^daouos si6o|Ojpft4 m ) m fi^i J B I | >u>e; jasp mo|aq umoi|S sases ajqissod xis \a auo 4Si |C|Bisa O_L uoissas s ) u) ;o jva^uos «'l|X uoiipuii^sa nc i j NOiiyaN3wwoo3a S N O i i d w n s s y nyoo sioyd NMONX 1X31N00 i0d=a? 0 jpft u, QL 76 e x p 12 W h e n s t r e a m f l o w d a t a i s a v a i l a b l e on t h e s t r e a m o f i n t e r e s t b u t a t a l o c a t i o n some d i s t a n c e u p s t r e a m o r d o w n s t r e a m o f t h e l o c a t i o n o t i n t e r e s t , t h e r e a r e s e v e r a l p r o c e d u r e s w h i c h may b e u s e d t o e s t i m a t e t h e f l o o d f r e q u e n c y r e l a t i o n s h i p a t t h e s i t e . S O L U T I O N S C R I P T F O R C A S E 2 P r o p s : C s t r e a m f l o w d a t a a t p o i n t B , P D R F F A p r o g r a m , d e s i g n f l o w , d e s i g n l i f e , c o s t , b a s i n A a n d b a s i n B ) R o l e s C C o n s u l t a n t , c l i e n t s , e n d - u s e r s ) P o i n t - O f - V i e w : c o n s u l t a n t P l a c e - Q f - Q c c u r r e n c e : C b a s i n A ) T t m e - Q f - O c c u r r e n c e •' C N o w ) R E C O M M E N D E D E V E N T S E Q U E N C E F i r s t : i f s t r e a m f l o w d a t a i s a v a i l a b l e a t t w o l o c a t i o n s on t h e s t r e a m t h e i c o r r e l a t e a n n u a l f l o o d p e a k s t o t h e b a s i n a r e a u s e d a n d u s e t h i s c o r r e l a t i o n t o a d j u s t t h e f l o w r a t e a c c o r d i n g l y , s l - p e r f o r m c o n v e n t i o n a l f r e q u e n c y a n a l y s i s f o r b o t h l o c a t i o n s s 2 - s e t Q T = a * CA * * b ) Q T = t h e T - y e a r f l o o d m a g n i t u d e A = b a s i n a r e a a a n d b a r e c o n s t a n t s s 3 - e s t i m a t e v a l u e s a a n d b u s i n g t h e Q T v a l u e s f r o m t h e P D R F F A p r o g r a m a n d a r e a s o f b a s i n B a n d b a s i n C C t w o e q u a t i o n s a n d t w o u n k n o w n s ) s 4 - e s t i m a t e t h e e v e n t w i t h t h e c h o s e n r e t u r n p e r i o d b y u s i n 9 t h e c o m p u t e d v a l u e s o f a a n d b i n Q T = a # C A A b ) w h e r e A A = A r e a o f b a s i n A C t h e p o i n t o f i n t e r e s t ) t h e n : i f r e c o r d s a r e a v a i l a b l e o n l y a t o n e p o i n t C s a y p o i n t B ) t h e n : r e p e a t e t h e s t e p s 1 t o 4 o u t l i n e d a b o v e u s i n 9 a n a s s u m e d v a l u e f o r b C ( 3 . 5 <= b <= 1 . 0 i s a g o o d r a n g e t o p i c k f r o m ) W A R N N I N Q Y o u m u s t c h e c k t h e f o l l o w i n g a s s u m p t i o n s b e f o r e a f r e q u e n c y a n a l y s i s . C a ) - S t a t i o n a r i t y C b ) - S t a t i s t i c a l I n d e p e n d e n c e C c ) — R a n d o m n e s s C d ) - R e p r e s e n t a t i v e n e s s C h y d r o 1 o g i c a 1 I y s i m i l a r b a s i n s C C e ) - N a t u r a l f l o w C u n r e g u 1 a t e d ) t h e n : i f f l o w r e c o r d i n c l u d e s a n e n t i r e h y d r o g r a p h , t h e n r o u t e t h i s h y d r o g r a p h t o p o i n t A m a k i n g proper a d j u s t m e n t s f o r l o c a l i n f l o w s a n d o u t f l o w s , t h e n • d e t e r m i n e c o s t a n d c o n s e q u e n c e o f f a i l u r e t h e n : d e t e r m i i e — i n c r e a s e — i n — c o s t a s a f u n c t i o n o f d e c r e a s e d r i s k t h e n : c o n s u l t a p p r o p r i a t e a g e n c i e s f o r r e c o m m e n d e d g u i d l i n e s t U n : m a U .a ( ! ,S I f \ n tn a e « i m a t o e x p f A B A Y E S I A N A P P R O A C H T O F L O W P R O B A B I L I T Y E S T I M A T I O N •X1 \^ >JS M/ W ^* W £^ \^ £^ ^ ^ W *j£ ^ ^ 1% }l£ £^ W ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ £^ ^ 0^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ oyl ^ ^ o^ o^ ^ ^ op ;p >^  ^ ^ ^ ^ ^ ^ Tfs ^ ?^  ^ ^ ^ ?p ^ ^ 7^  ^ ^ J|t jf* ^ 7p ^ ^ ^ ?^ 3^ ^ ^ ^ ^ ^ ^ ?^ ^ ^ ^ ^ o^ s ^ ^ W h e n a a d e q u a t e s t r e a m f l o w d a t a a r e a v a i l a b l e , i t i s a t r i v i a l t a s k t o e s t i m a t e t h e m a g n i t u d e o f t h e f l o o d w i t h t h e d e s i r e d r e t u r n p e r i o d . A c o n v e n t i o n a l f r e q u e n c y a n a l y s i s i s t h e b e s t m e t h o d o f s o l u t i o n g i v e n t h a t t h e n e c e s s a r y a s s u m p t i o n s a r e e a s i l y v e r i f i e d . C a c a s e 1 s i t u a t i o n ) H o w e v e r , w h e n o b s e r v e d d a t a a r e i n s u f f i c i e n t o r e x p e n s i v e t o o b t a i n , y o u , a s a n e n 9 i n e e , m u s t u s e y o u r S U B J E C T I V E J U D G E M E N T t o w e i g h t h e a v a i o l a b l e i n f o r m a t i o n . A c o m p u t e r p r o g r a m , F L O O D S , h a s b e e n d e v e l o p e d a t U . B . C . C R u s s e l l , 1 9 8 2 ) w h i c h u s e s a B a y e s i a n f r a m e w o r k f o r c o m b i n i n g i n f o r m a t i o n f r o m d i f f e r e n t s o u r c e s o f i n f o r m a t i o n . Y o u may u s e t h i s p r o g r a m v e r y e a s i l y b y e n t e r i n g f l o o d s ' . H o w e v e r , b e f o r e y o u d o s o , P H Y S I C A L L Y I N S P E C T T H E S I T E l o o k i n g f o r t h e f o l l o u i i i g t y p e s o f i n f o r m a t i o n : 1 - T r j 2 - T r y 3 -4 -i n T r y e x c T r y t h e c oe I out a n d 1 t h e s i y e a r s . a n d e a s o m e a n d e e e d e d a n d e ma 9 n i f f i c i e t o i n o c a t e t e w h a c u l v e r t o r i c h h a s n o t b < • i d g e i n t h e v i c i n i t y e x c e e d e d i n a n u m b e r s t i m a t e t h e m a g n i t u d e o f t h e g i v e n n u m b e r o f y e a r s , s t i m a t e a f l o w m a g n i t u d e w h i c h h a i n a n u m b e r o f y e a r s l a r g e s t f l o o d n o t b e e n u TS i u i *j c a i 9 s t i m a t e C s u b j e c t i v e I y , u s i n g y o u r r e a s o n s ) t u d e o f t h e m e a n a n n u a l p e a c k f l o w s C o r t h e n t o f v a r i a t i o n ) u s i n g h i g h , d i c a t e y o u r d e g r e e o f p r ob ab I e u n c e r t a i n t y . a n d I D = F E X P F C O N T E X T KNOWN F A C T S G O A L A S S U M P T I O N S F l o o d e s t i m a t i o n C c a s e 2 s p e c i f i e d ) S t r e a m f l o w r e c o r d s e x i s t o n t h e s t r e a m s o m e d i s t a n c e a w a y T o e s t i m a t e t h e f l o w w i t h a g i v e n r e t u r n p e r i o d Y o u h a v e i n s p e c t e d t h e s i t e a n d h a v e c o l l e c t e d a v a i l a b l e d a t a 77 PLEASE ENTER YOUR OPTION FROM THE FOLLOWING MENUE 8888800000t:B888888:18000:t8B880088888888088888B0B88B8B888888888808808B88B0B8888888 888 O P T I O N 8888808888 E N T E R 8880888 8B88888888C8880888488883880888888888888888000888888B888880888088808888B888888088 888 Cl) E x p l a i n the recommended s o l u t i o n method 8800888880 expl2 0888888 8000008888C8808888:J8888:J000008888008888888a08008880B8888888088808888008800888B88 088 C2)-To re turn to th * previous menue 0800888808 y 0800000 8888888888t888888838888:J88fl8800888808888888808088888808800080088008888080088888B 080 C3) Rur, the FLOODS P r o g r a m 0808808888 f l o o d s 0888888 

Cite

Citation Scheme:

        

Citations by CSL (citeproc-js)

Usage Statistics

Share

Embed

Customize your widget with the following options, then copy and paste the code below into the HTML of your page to embed this item in your website.
                        
                            <div id="ubcOpenCollectionsWidgetDisplay">
                            <script id="ubcOpenCollectionsWidget"
                            src="{[{embed.src}]}"
                            data-item="{[{embed.item}]}"
                            data-collection="{[{embed.collection}]}"
                            data-metadata="{[{embed.showMetadata}]}"
                            data-width="{[{embed.width}]}"
                            async >
                            </script>
                            </div>
                        
                    
IIIF logo Our image viewer uses the IIIF 2.0 standard. To load this item in other compatible viewers, use this url:
http://iiif.library.ubc.ca/presentation/dsp.831.1-0062732/manifest

Comment

Related Items