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Graduate Studies Legacy Theses
2001 Extreme rainfall in the greater Calgary area
Guthrie, James Harold
Guthrie, J. H. (2001). Extreme rainfall in the greater Calgary area (Unpublished master's thesis). University of Calgary, Calgary, AB. doi:10.11575/PRISM/18979 http://hdl.handle.net/1880/40796 master thesis
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Extreme Mallin the Greater Calgary Area
by
James Harold Guthrie
A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF MASTER OF SCIENCE
DEPARTMENT OF GEOGRAPHY
CALGARY, ALBERTA
APRIL, 2001 National Library BiIioth&quenationale 1+1 ofCanada du Canada Acquisitions and Acquisitions et Bibliographic Services services bibliagaphiques
396 Weilington ht 395. ma Wellington mwa ON KIA OW WONK1A ON4 Canada Canada
The author has granted a non- L'auteur a accord6 une licence non exclusive licence allowing the exclusive pennettant a la National Library of Canada to Bibliotheque nationale du Canada de reproduce, loan, dimlute or sell reproduke, prgter, distribuer ou copies of this thesis m microform, vendre des copies de cette these sous paper or electronic formats. la fonne de microfiche/fb, de reproduction sur papier ou sur format electronique.
The author retains ownersbxp of the L'auteur conserve la propriite du copyright in this thesis. Neither tfie droit d'autem qui protege cette these. thesis nor substantial extracts from it Ni la these ni des exsaits substantiels may be printed or othenvise de ceIle-ci ne doivent &re imprimes reproduced without the author's ou autrement reprodits sans son permission. autorisatioe Wemeraijdl events events maiysed in Calgcny, Alberta The stonns przniucing heavy raijall m Calgmy wemociizted with north travelling storms fiom Montana passing thghsouthern Alberta tkn veering wst tmak the mountaim. The qutial variability of mean andmaximum 24-hr rain$all events for 24 rain stations in Calgmy were analysed in relation to physical cmd anthropogenic characteristics throughour the city. With the aid of multiple regrmbn andysis, it ws possible to qu~nhfithe contribution of the physical and anttaopogenic vananables. The vanables that wre sign~fmntpredictors of mean amrual ntmrimum 24-hr rainfall were the distance fim storm entry and station elevation This stuhy also looked at the relationship betwen rhe spcltial pattern of mean admmrmmrmum 24-hT rabqiall and the 24-hr probable maximum precipitation (PUP) value. The puttems were similar. but not identical. These redsare important to the area of urban Rycilogy in Calgmy. and are a good starting point for the early stages offrood &sign and mitigation Therejbre, a design engineer can obtain fairly accurate estrstrmatesof mean annual maximum 24-hr rainfd and 2Chr probable marimum precipitation values for Calgary, Alberta ACKNOwLEDGEMErm
First and foremost, I would like to acknowledge my supervisor Dr. Lawrence C.
Nkemdirim. His guidance and support made it posmlle to complete my research. 1 would ahlike to acknowledge the City of Calgary Waste Water and Drainage division, especiaily Zennon Zahsky arad Eric Knudtson, for supplying valuable rainfan data for
Calgary. I wouId like to thank Dagmm Budikova fbr endless discussion aad for supptying me with her upper air database, as welt as Medina Hanson for graciously providing me with a DEM of Calgary- I would also like to thank Rick Smith at the
Univw of Calgary Weather Research Centre and all my Wy,friends. and kllow graduate students for providing outlets fbr discussion. Finally, I wodd like to recognise
Tiaa for believing in me and knowing that someday. I would hi& TABLE OF CONTENTS .. APPROVAL PAGE..-m...-...H.HH...H...-.t..M...-...... II ... ABSTRACT...... ~...~.-m"-~~.~..*..m~~..."..*n...n...~ IU
ACKNOWLEDGXMENTS ...... "...... -..- ....,...... iv
TABLE OF CONTENTS ...... ,.,., ...... ,...... v ... LIST OF TABLES ...... ,...... ,...... - ...... "...... "...... m
LIST OF FIGURES...... iX
LIST OF EQUATIONS ...... -* ...... xi
CHAPTER 1: INTRODUCTION ..,...... ,...... f
BACKGRO~MD...... 4
PROBLEM DEFIMTION ...... 5
RESEARCH OBJECINES...... 7
~PORTANCEOF TOP~C...... 7
CHAPTER 2:LITERATUR.E REVIEW ...... 9
2.1. V~~usrr~nOF WALL ...... 9
2.2. PROBA~LEM.AXBWM PRECIPITATION ...... 17 -. 2.2.1. Tradztronai Method...... 18
2.2.1.1. Moisture Maximisation...... 19 . . 2.2.12. Transposnwn ...... 21 2.2.1.3. Envelopment ...... -23
2.2.1.4. Summary ...... 24
. * 2.2.2. statrshcal Metho d...... 25
2.2.2.1. Hershfield Approach...... 2!j
2.2.22. NERC Approach...... 27
2.2.2.3. Summary ...... 28
CHAPTER 3:STUDY AREA ...... "...."...... 30
4.1. INTRODUCTION ...... 36
4.2. DAT.4 SELECTION...... 39
4.3. DATAESTIMATION ...... 40
4.3.I . Introduction...... 40
4.3.2. .&iethodolo gy...... 41
43.3. Reds...... -43
CIiAPTER 5: RAINFALL VARIABILITY...... 44
5.1. VARIASLESELECTION ...... 46
5.1. I . independent Physical Viuiables...... 46
5. I .2 . Independent Anthropogenic Vmirrbles ...... -47
5.1.3. Dependent Variable ...... -47
5.2. MODELCONSTRU~ON ...... 48 5.3. MODELVERIFICA~ON ...... 5 5
5.4. DISCUSSION...... 60
5.4.1. Distance fiom stonn entry...... 60
5.4.2. Elmation ...... 63
5.4.3. Rejected Vmiables...... 66
54.4. Summary ...... 67
CHAITER 6:STORM EVENTS ...... "...... *...... 68
6.1. ME~DOLOGY...... 71
6.2. SEPTEMBER12, 1985: ...... 73
6.3. AUGUST1 . 1988: ...... 76
6.4. JUNE1 3 AND 14, 1992: ...... 79
6.5. SUMMARY ...... 81
CHAFTER 7: PROBABLE MAXIMUM PRECIPITATION ...... " ..... 8s
7.1. SaEcnON OF A METHOD ...... 85
7.2. METHODOLWY...... 86
7.3. RESULTS ...... 89
7.4. COMPARISON ...... 92
7.5. K FACiüR AM) iïS DISïRiBUTION ...... 94
CEiAPTER 8: CONCLUSION GND RECOMMENDATIONS ...... 96 APPENDIX A: TABLES OF PRECIPITABLE WATER IN A SATURATED PSEUDO-ADIABATIC ATMO!SPHERE ...... 106
APPENDIX B: TABLES SHOWING THE VALUES USED AND THE CALCULATIONS OF THE b.RS, AND PMP VALUES...... 109
LIST OF TABLES
TABLE1.1 : SOMEEXAMPLES FO WA-IER-RE!SOURCE PROJECTS...... 3
TABLE1.2. U.S. hMY CORPOF ENGINEERSSAFEXY STANDARDS BASED ON SIZE ...... 3
TABLE3.1 : CALGARYCLIMATE NORMALS ...... 34
TABLE4.1 : GENERALINFORMA'IION FOR THE &WORT AND URBANRAIN STATIONS ...... 39
TABLE4.2. STATIONS USED FOR THE CALCULATlON OF MISSING DATA ...... , .. 43
TABLE4.3. OBSERVEDAND EST~MATEDANNUAL RAINFALL MAX~MUMS(MM) ...... 44
TABLE5.1 : DATAFOR THE URBANRALN STAnONS USED IN THE DETERMINATION OF
RAINFALL vtuum~~~n...... 49
TABLE5.2. [NFORMAT~ONUSED FOR IHE MODEL CONSTRUCTION ...... 54
T~LE5.3. MODELSUMMARY ...... 54
TABLE5.4: VALUESUSED IN THE CALCULATION OF THE T-TEST FOR EACH OF THE
VARIABLES IN EQUATION 5.1 ...... 56
TABLE5.5. CORRELATION MATRIX BETWEEN ELEVATION AND SLOPE ...... 66
TABLE6.1 :DATE OF OCCURRENCE OF EXTREME WUW ALL, EVENT AND STATIONS
EFFECTED ...... 68
TABLE7.1 : ~ZHOURPERSISTING DEW POINT FOR SEPTEMBER 12. 1985 (OC) ...... -88
TABLE72: MOISTURE ADNS-MENT RA'IIOS FOR THE: CALGARYRAIN STATIONS ...... 90 TABLE7.3 :PMP VALUES FOR 'IHE CALGARYRAIN STATIONS. IN ...... 91
LIST OF FIGURES
FIGURE3.1 :MAP OF STUDY AREA ...... 30
FIGURE 3 -2: SHADEDRELIEF MAP OF CALGARY AREA ...... 31
FIGURE3 -3: ELEVATIONCROSS-SECTION ...... 32
FIGURE 3.4. MAP SHOWING THE AVERAGE SLOPE OF THE CALGARYAREA ...... 33
FIGURE 3.5. NORMALMONTHLY RAINFALL FOR CALGARY,ALBERTA ...... 35
FIGURE 4.1 : CALGARYRAINFALL STATIONS ...... 38
FIGURE 5.1 :MEAN ANNUAL MAXIMUM 24-HR RAINFALL...... 48
FIGURE 5.2: SCATTERPLOT OF ELEVATlON VS .MEAN ANNUAL MAXIMUM 24-HR RAINFALL
...... SO
FICL~RE5.3. SCATTERPLOT OF SLOPE VS . MEAN ANNUAL MAXIblUM 24~~RAINFALL ...... 51
FIGURE 5.4. SCATTERPLOT OF ASPECT VS .MEAN ANNUAL MAXIMUM 24-1-i~RAINFALL .... 51
FIGURE 5.5: SCA~PLOT OF DISTANCE FROM STORM EWRY VS . MEAN ANNUAL
MAXIMUM 24~~RAINFALL...... 52
FIGURE 5.6: SCA'ITER PLOT OF BUILDWG DENSIlY VS. MEAN ANNUAL MAXIMUM 24-HR
RAINFALL ...... ,., ..... ,.,, ...... 53
FIGURE5.7. SCA~PLOT OF CALCULATED VS .OBSERVED p;m)...... 57
FIGURE5.8. SCATTWPLOT OF THE RESJDUALS AGAINST lHE PRESIClED VALUES ...... 59
FIGURE5.9. HISTOGRAMOF STANDARDBED RESIDUALS...... 59
FIGLIRE 5.10: SCATTERPLOTOF MEAN ANNUAL MAXIMUM 24HR RAINFALL AGAINST
DISTANCE FROM STORM EKIRY ...... ,...... 61 FIGURE 5.1 1: SCA~ PLAIT OF THE OBSERVED AND PROJECIED q;-)VALUES VS
DISTANCE FROM STORM ENTRY...... 62
RGuRE 5.12. ELEVATIONMAP OF CALGARY...... 63 l?lGURE 5.13: SCATIERPLOT OF MEAN ANNUAL MAXIMUM24~~ RAINFALL AGAINST
STATION ELEVATION ...... 64
FIGURE6.1 A: SEP~ER12, 1 985 RAINFALL DISTRIBUTION MAP ...... 69
FIGURE6.1 B: SEPTEMBER16, 1986 RAINFALL DISTRIBUTIONMAP ...... 69
FIGURE6.1~. AUGUST 1, 1988 RAINFALL DIS~RIBU~ONMAP ...... 69
FIGURE6 . I D: AUGUST17 . I990 RAINFALL DISTRIBUTION MAP ...... 69
FIGURF; 6.1 E: JUNE 13. 1992 RAINFALL DISTRIBUTION MAP ...... 70
FIGURE6.1 F: JUNE 14. 1992 RANFALL DISTRIBUTION MAP ...... 70
FIGURE6.1 G: JUNE 1 1. 1997 WALLDISTRIBUTION MAP ...... 70
FIGURE 6.2~.~EPIEMBER 12. 1985 05:OO 85 KPA MAP ...... 74
FIGURE6.2~ SEYEMBER 12, 1985 17:00 85 KPA MAP...... 74
FIGURE6.2~. SEPTEMBER 12. 1985 05:OO 50 KPAMAP...... ,...... 75
FIGURE 6.B.S-ER 12, 1985 17:W 50 KPA MAP ...... ,..,..,...... 75
FIGURE6.3~. AUGUST 1, I988 05:OO 85 KPA MAP ...... 77
FIGURE6.3~. AUGUST 1, 1988 17:W 85 KPA MAP ...... ,...... 77
FIGURE6.3~. AUGUST 1. 1988 05:OO 50 KPA MAP ...... ,., ...... 78
FIGURE 6.3D. AUGUST1, 1988 17:00 50 KPA MAP ...... 78
FIGURE6.4~. JUNE 13, 1992 0500 85 KPA MAP ...... 80
FIGURE 6.48. JUNE14, 1!992 17:OO 85 WAMAP ...... ,...... 80
FIGURE 6.4~.JUNE 13, 1992 17:00 50 KPAMAP ...... 81 FIGURE 6.5~.AVERAGE OF THE 85 KPA DATA FOR 'IHE 4 STORM EVENTS ...... 82
FIGURE 6.5~AVERAGE OF THE 50 KPA DATA FOR THE 4 STORM EVENTS ...... 82
FIGURE6.5~. AVERAGE TEMPERA= AND DEW POINT IEMERATUIES AT 85 KPA ...... 83
FIGURE 6.6: GENERALDIRECTON OF ENTRY & MOVEMENT OF HEAVY RAINFALL EVENTS. 84
FIGURE 7.1 :MAXIMUM RECORDED FERSISTING 12-HI€ DEW POINT TEMPERATURE FOR
CALGARY...... 87
FIGURE 7.2. PMP VALUES OVER THE CITYOF CALGARY...... 93
FIGURE 7.3: MAPS OF MEAN ANNUAL MAXIMUM 24-HR RAINFALL AND PMP VALUES FOR
CALGARY ...... ,., ...... 93
FIGURE7.4. MAP OF THE K VALUES FOR CALGARY...... 95
LIST OF EQUATIONS
EQUATION2.1 :FORMULA FOR CALCUlATNG PRECIPlTABLE WATER ...... 20
EQUATION2.2. MOISWMAXIMISATION RAnO ...... 21
EQUATION 2.3. MOISTURE MAXIMISATION RATIO FOR TRANSPOSED STORMS ...... 23
EQUATION 2.4. HERSHFIELD EQUATION 1 ...... -25
EQUATION 2.5. HERSHFELD EQUAIION 2 ...... 26
EQUATION 2.6. &, EQUATION...... 26
EQUATION 4.1 :Comno~ COEFFICIENT EQUATION ...... 41
EQUATION 4.2. Mu.11~~LlM3R REmSlONEQUATION ...... 41
EQUATION 5.1 : ~EWMNARYh4ULTIPL.E REGRESSION MODEL ...... 55
EQUATION 5.2. FINALMULTWLE REGREWON MODEL...... 57 Chapter 1: Introduction
Estimation of a design storm is needed for a broad spectrum of civil works.
Depemling on the size of a water resource project (Table I.1), three types of design storms are recognised They are chssified as the Frequency Based Storm (FBS), the
Standard Project Storm (SPS), or the Probable Maximum Precipitation (PMP). A FBS is based on the fkquency of recurrence for extreme storms using methods such as the
Gumbel distriiution. The FBS method calculates the exceedence W based on a desired return period or frequency. The SPS of a given duration is the most severe flood- producing rainstorm that has occurred in the region of the watershed. A SPS value can be obtained fiom a survey of past severe storms. The PMP is based on meteorological analysis and results in the theoretically greatest depth of precipitation that is physkdy possiile for a given duration at a particular geographic location.
The choice of a design storm for a water resource project and/or a drainage system
involves selecting the safety criteria and estimating tbe dorm that satisfies these criteria
The U.S. Army Corps of Engineers has classified the safety criteria, or hazard potential,
as low, significant, and high (Smgh, 1992). These hazard potentials can be used in the
selection of a design storm. The low classi6cation has no expected loss of life and
mh.imal economic loss. A signifcant hazard is categorid as one that carries
considerable economic loss, notably in agriculture, industry, or structures but with
mhhd loss of life and no damage in urban areas. The high hazard bas a cfasdication
of greater than a few for loss of lik and excessive economic loss, with extensive damage
to communities, industry, or agriculture- The safety criteria can be selected in either of two ways. The kit is consided a
"no riskn criterion. This criterion is when the Mure of the structure must be prevented at any cost. Faihrre of the structure is not acceptable if it would cause the loss of human life or would result m catastrophic economic and social consequenses. A typical situation is where a dam is located above a populated area.
The second approach is referred to as a "probability based" criterion. This approach is adopted because the society carmot atford to prevent aIl structures hm failure. Therefore, some probability of Mure must be tolerated (Singh, 1992). For example, storm sewers are designed to drain rahMevents of low intensity and that have a high probability of occurrence each year. Storm sewer systems can be designed to handle larger raiddl events, but the underground pipes would have to be wider than the streets they are buried under, making them extremely expensive and impractical.
Water resource projects are classified as small, intermediate, or large. No universal dety criteria have been established yet. However, the U.S. Army Corp of Engineers has recommended safety standards based on the project. These recommendations can be seen in Table 12.
Structures to retain water must be designed to pass extreme flood events withciut simcant damage or fkhe (Collier and Hardaker, 1995). It is recommended (Table
1.2) to use the PMP standard for any large water resource project, regardless of hazard.
The PMP is designed tbr a probability of ever occurriug that is dose to zero and,
therefore, is safe under extreme meteorological conditions (Auselmo et aL, 1996). Tabk 1.1: Some examples of water-mwcc projects (Sigh, 1992)
Size of Project E=P~-
Small Levees, drainage ditches, irrigation tanks, minor road bridges, urban storm drains, airport drainage systems, spillway appurtenances of small dams, detention storage reservoirs, etc.
Intermediate Hydropower plants, higation canals, medium-size dams and reservoirs, urban flood-control teservoirs, drainage systems, thermal power plants, dmybridges, etc.
Large Multipurpose water-resource projects, large dams, levees, spillways, major river bridges, major irrigation canals, nuclear power plants, large dams, big hydropower plants, etc.
Table 1.2: U.S. Army Corp of Engineen Safety Standards based oa size (Sbgb,1992) Hazard Size Safety Standard
LOW Small 50 to 100-yr flood
hermediate 100-yr flood to SPS
Large SPS to PMP
Significant Small 100-yr flood to SPS
Intermediate SPS to PMP
Large PMP
High Small SPS to PMP Intemedhte PMP
he PMP 1.1. Backpund
in Calgary, the normal summer flood season for the main rivers extends from
May 24 to July 15. The two largest rivers that flow through Calgary are the Bow River and Elbow River. Nine floods have exceeded the overbank flow on the Bow hrsince
1897, with all but one of them occurring before 1933. Overbank flow is initiated at a discharge of about 595 m3/s. The last major flood of the Bow River was 1518 m3/s m
1932. Twelve floods have exceeded overbank flow of 170 m3/s on the Elbow River since
1908. Seven of these, including the four largest, happened prior to 1933.
Tbe occurrence of floods on both rivers has declined over the years* This observation can be attniuted primarily to the construction of numerous dams upstream.
The existence of these dams does not mean that Calgary will not experience a river flood in the hture. only that the probability has decreased significantly.
In contrast, fiom 1979 to 1997 there were 63 recorded flood events m Calgary communities associated with rainfan (City of Calgary Waste Water and Drainage
Rainstorms Report Series). These rahfidl events all occurred in the months of May to
September. July and August had the greatest number of mididl flood events with 18 each, while June bad 16, September 6, and May 5. Of the 63 recorded rahM flood events. roum 80 percent of them occurred between the years of 1989 and 1997.
The City uses a collection of methods to control flooding due to raiddL These methods have changed and improved over the years. The primary method involves the use of storm sewers. In 1890, the first underground sewer pipes wmconstructed. These pipes served as a combmexi storm and sdtary sewer system. It was not Imtil the 1960's that the storm and sanitary sewer systems were completely separated. The storm sewer system in each drainage area is designed to handle low-iutensity rahfkk.
In most Canadian cities, the mdergrormd storm sewer pipes are designed to meet the North American standard of draining one-m-five-year storms. This is the case fbr most of the Calgary communities. All of the Calgary communities built m the 1990's have a system of underground pipes that can handle one-in-fie-year rainhll events
(www.gov.caigary.ab.ca). As we& a system of specially designed streets and storage ponds that store water tempor-, aiEow the newer communities to handle one-hone- hundred-year raiddl events and protect comm~esat lower elevations hm high- intensity raiafdl m upbill commmhies. in some of the older communities, however, the underground storm sewer pipes are designed for one-in-two-year rahfbl events.
Overland systems such as dry pond and wet ponds are becoming necessary since the underground storm sewers in some areas would have to be wider than the streets they are buried under. making them either extremely expensive or impractical. Due to physical constraints in developed communities, it is not always possible to design improvement projects that will increase the capacity of the storm sewer systems to handle one-in-one-hundred-year rahfall events. The systems can minimise flooding but it cannot eliminate all flooding.
Engineers designing urban flood mitigation devices can be hindered by the lack of reliable estimates of future extreme mi&X events. Urban storm drainage and sewer systems are usually designed based on historical caidkll records collected at airports or other nearby climatic stations (Changnon et aL, 1981). In most cases, the conditions and parameters experkxed at the recording station are not the sarxle for the entire area in which the estimates are used V&iIity of mhfX values may exis&due to any number of causes. Most of the muses, or variables, can be put iuto phydor anthrwpogenic categories. Understanding the variability of extreme has importaut aspects in mny areas of meteorology, hydrology, and hydrometeorology. It will aid urban flood design and understanding of weakand climate events in an urban setting.
An example of a physical dkcontmlIing cbteis topography (Singh, 1992).
The effects of topography on precipitation have been studied for many years. PossiiIe
topographical controls are slope, aspect, and eIevation. Elevation, orientation, and
steepness of slopes affect the amount of rain and where it is deposited (NRC. 1985).
Urbanisation is the most noticeable antbropogenic variable. Urban areas &kt
most forms of weather. The increase in urbanisation that began with the industrial
revolution bas led to microscale and mesoscale changes m the weather and climate in and
near urban areas in the mid-latitudes (Peterson, 1969; Landsberg, 1970; Ha1975;
Changnon et d., 1981). The identi6ation of urban rehted weather effects, as well as
attributing their causes. can be ~c~.This can be partially due to the avaiIabd3y of
information needed to identify urban related weather effects. Urban effects on wind,
temperature and vislhiky are the mast obvious and their changes wa be easiiy measured
(Changwn et aL, 1981). The urban idhence on mi&R and severe storms is tk most
complex of all urhweather effects. The causes ate uwdy ouly partiaCly understood,
as inadvertent precipitation changes are more difiicult to measure and expb(Changwn
et aL, 1981). 1.3. RCSCBIC~Objectives
The objectives of this research are separated into two parts. The primary objective is to evaluate the spatial variability of extreme rairhl events in the city of Calgary.
There are 26 stations m and around Calgary that record rahM. Each station has unique physicat and anthropogenic characteristics associated with it. These variables win be e&ed against annual maximum 24-hr raididl events to determine a connection between extreme rainhll and the characteristics of the city. A model will be presented to help explain the variability of raiddl in relation to the physical and anthropogenic characteristics of Calgary,
The secondary objective is to calculate the Probable Maximum Precipitation value, or PMP, for the Calgary region. PMP models are a common design practice for the construction of major flood devices and mitigation projects. The spatial pattern of the
PMP will then be compared to the results bm the 6rst objective. If the patterns are rehted, it would be safe to assume that the variables that affect the spatial pattern of annual maximum 24-Lu rainfall also affect the pattern of PMP values.
The results fiom these objectives may help to iden* high-risk areas and aid decisions regarding improvements to drainage and flood mitigation programs. It will also allow engineers to make assumptions on flood design projects for new co- which have no rainfaIl records, based on the area's physical and anthropogenic characteristics.
I.4. Inrporfance of Topic
The city of Calgary has identified storm sewer improvement projects designed to
reduce flooding hmhigh-intensity rahhlk. To construct all the ficikks that would have reduced tbe hooding caused by major rainstorms m tbe last 10 years, the City would have to spend abut 50 million dollars. tn addition to these projects, another 77 million dollars can be spent m older communities to upgrade their underground storm sewer systems (www.gov.calgary.ab.ca). Impkmentation of all of these projects would be impractical, both logidly and financiany. Chapter 2: Litemtrvt Review
This chapter contains background and technical information hm key articles relevant to this research. Section 21 reviews the variability of mhhll, while section 2.2 summarises popular calculation methods for the probable maximum precipitation (PMP) method.
2.1. Voriobili@of Rainfafll
Rainfall is normally the most variable hydrologic element over an area (Ram-
Iturbe. 1974a). Many scientists have studied the variability of raiddl over the years.
Early studies of rainfall variability looked at the kquency and spatial distriiution of different rahfidi intensities. and were generaIIy concerned with the relationship between rai&d and area (Horton and Marston, 1924; Court. 1961 ; Chow, 1964; Longley, 1974;
Rodriguez-Iturbe, 1974b: Dhar. 1977).
Horton and Marston (1924) discussed the distribution of intense minhll in the design of storm water drains m the United States. Horton and Marston presented an exponential equation that wodd estimate average raiddl for one day over an area, based on the highest measured precipitation and the area. They suggested that the precipitation depth would decrease as the radius, or distance, hmthe eye of the storm increases.
Horton and Marston (1924) stated that the quantity of rain precipitated by a storm m passing over a given area depended on two factors: (i) The rate at which rain is formed within the storm; and (3the rate of storm traveL However, they also concluded that the relation of meteorology of storm to mhfX depth was too complex and there should be firrther study on the consideration that the greater the distance hmthe eye of the storm the Iess the rate of precipitation. They believed that fiom an undtmtadng of these relations, an important advance m the determination of maximum rahW dowance wodd bave been attaaned fbr stom sewer design adother hydraulic works. Horton and
Marston contriied an interesting and valuable discussion on the early relation between depth, intensity of rainfilll, and areal coverage for storms of long duration.
The relationship between mhfdl and area was ahstudied in Canada Longley
(1974) perfond a spatial variation of precipitation over the Camdim prairies. Longley stated that previous analyses of precipitation trends over the Canadian prairies showed that the trends through the years were difhnt, for di&rent vdeys. This prompted his analysis of precipitation to discover Mer information on the spatial variations using correlation coefficients between individual stations. Correlations were made using the
monthly raidltotals hmApd to September (LongIey, 1974). The first thing Longley
found, using an exponential 6t, was that the correhtion coeflkient between stations
dropped as the distance beenthem increased. The second was that the correlation
also varied with direction. Here, the possibility of the storm path afkcting mididl
variability was introduced. When Longley examined the mean coefficients for a spec*
month and distance, it was discovered that the coefficients varied with direction. He
stated that tfx results could be interpreted to show the mean direction of storm tracks
over the prairies (Longfey9 1974).
Dhar (1977) attempted to use the same exponenthi rehionship suggested by
Horton and Marston (1924) to express a suitable rebtionship between rainfttll and the
awrage mxhm rain depth over dEmt areas m tndia Dbar stated that the
rehtioe obtained could be helpfur to a design engimer to obtain average maximum rain depths for a problem basin in India as long as some knowledge of the rrr;udrmrm point mididl was known. He perfbnned Depth-Area-Duration @AD) anafysis on rainstorms with durations of 1, 2, and 3 days. Average mxhmrain depths were then converted into percentages of rahfidl obtained at the centre of each rainstorm A mean percentage ratio was obtained for ~lketeorologicaldivisiom using the above statistics.
Dhar concluded that the average maximum rain depths, over cWerent areas exgressed as a percentage of central raiddl m a rainstorm for &rent durations, can be hted fairly accurately by using an exponential equation (Dhar, 1977).
More recently, Ben-Gai (1998) looked at the annual and monthly rainfgll totals in
Israel to reveal any long-term changes m the temporal and spatial distniution pattern,
The interest in the local and regional changing patterns of the kquency djstriiution of
raiddl stemmed from the ktthat the shape and dispersion of the frequency distribution
may provide a cIue as to how the probabilities of extremes will change if the mean
changes (Ben-Gai, 1998). The shape and scale parameters from the gamma distribution
were used to examine the spatial and temporal changes m the rainfaU They concluded
that a statisticd analysis of annual rainhIl distnition reveals some si@cant spatid
and temporal changes in the shape and scale parameter patterns of the lhed gamma
dhiLbution. The possibility that some of the cbaoges may reflect global changes m
middl patterns could not be ruled out (Ben-- 1998). It was suggested, however, that
the nature of the changes m Israel pointed towards the innuace of regional factors.
The relationship between rainGill variability and area has been well studkd
However, other variables that may have an on the variability of mididl
expzbced in a location have also been codered. One of the earlier studies that examined other variables was by Spceen (1947). He conducted an investigation to examine the effect of topography on precipitation in western Colorado. The paper described a graphical correlation tedmique for relating winter precipitation to the topographic parameters of elevation, maximum slope of the land, exposure, and orientation (Sjmen, 1947). This was accomplished by graphing values of precipitation as a mionof elevation for various slopes. The values were then related to orientation and exposure, creating a working set of charts. Spreen plotted the estimated values obtained fiom the charts with the actual dues to evaluate their agreement. A close estimate was obtained in most cases, accounthg for 88% of the original variance (Spreen, 1947).
While not easily transferable to other regions, this study provided usell information on the relationship between rainfaU and topography.
In 1973. the World Meteorological Organisation (WMO)investigated the increase
of raiddl with elevation more closeiy. An increase on windward slopes due to forced
lifting of air over mountains was observed When the study area was on the leeward side of the mountains, the reIief fiom the vdey floor to the ridge tops showed a .sin& effect.
Another feature of oropphic precipitation discussed by the WMO, indicated by theory
and supported by observations, was that foothili regions were the preferred location fbr
the initiation of showers and thundenhwers (WMO, 1973). This eff'ect dedhm
the stimulation of convective activity m unstable air masses by an initial and reIatively
small lift. This study by the WMO helped to characterise the effects of elevation on
precipitation that would allow these concepts to be tmsfemd to other locations.
The ekts of physical variables, such as topography, on rainfan variability have
not been the only causes studied in the literature. HufF (1975) investigated potential dem on the distninof heavy rainMs. The primary purpose of the study was to examine qumtihtkiy the effect of inadvertent weather modification on the frequency and mpitude of intense sborthration raia rates that were pertinent to urban and suburban sewer designs. Huff suggested that if urban areas htemify or moderate naturally occuniug heavy rainstorms, the fkqmcy and mapitude of flood-producing storms within the area will differ fiom the fhquency and magnitude experienced m nrral areas. This, in turn, would aftkt the design and engineering requirements for urban and suburban sewer systems. Comparison of urban-affected and rural (non-affected) rain ceUs was the primary tool in evaluating the urban eet. ?YE analysis concentrated on rain ceb associated with the production of heavy shortduration storms and on the distriiution of heavy rainstorms producing greater than 25 mm of rainfan. Analysis of
the rain cells indicated a substantialIy greater mi&iU voIume from the potentially urban-
affected cells. Huff (1975) suggests that m moderate to heavy rahfkh, which are
produced by natural atmospheric processes, the urban effect appears to increase.
AnaIysis of storm rahlids of greater than 25 mm showed an increase of these storms m
locations kquently downwind of the study area (Huff, 1975). HUE concluded that if
fiuther studies verify that rainfaU rate frequency distriiutions vary igniscantly between
urban, suburban, and rural areas m large urban-industrial regions, it may be necessary to
feevaluate sewer design storm parameters to prevent miemtimation of mff relations.
The most wen known study relating urbankition to middl is the Metromex report.
The Metromex project was a major natiod program designed and conducted by several
research groups to study inadvertent weather and climate modifidion by urban-
industrial eifkts and antlxropogenic changes of precipitation (Cbangnon et &, 1981). Inadvertent precipitation changes fiom wbauhhn ate bder to measure aad explain.
Prior to Metromg urban-related rain changes had ox@ limited study. Four general program goals were outlined in the Metromx report. Tbe kst was to study the e&cts of urban environments on hquency, amount, intensity, and duration of precipitation and related severe weather. The second was to identi@ the physical processes of the atmosphere that wefe responsible for producing the observed urban weather effects. The third goal was to isolate the ktors of the city complex that were the causative agents of the observed effects. The final goal of the Metromex project was to assess the hnpact of urban-induced inadvertent weather changes upon the wider issues of society (Changnon et d, 1981). In the 198 1 Metromex Project, urbanisation was qdedby looking at the development location of storms. The storm was considered a result of urbankition if
it developed over one of the urban locations in the study area. Based on obsemationaI
and theoretical evidence, an urban-induced increase in summer rainfaU thtmderstorms,
and idstorms over the study area and the region downwind fiom it was found. A
suggested causal agent for the weather effects was the warm and aerodynamidy rough
urban surfhces, which promote increased mixing and convection within the boundary
layer. It was concluded that urban enbaacement of thunderstorms and bailstom occurs
in an area extending from the downtown commercial district, while the urban
enbancement of total rahfhll over the city appears well established (Changnon et al,
1981). The study also looked at the physical variables that myhave aff'ected the raid-dl
klsin the study area of St Louis- It was concluded that topography probably did play
a role, but was not ttae major cause in determining their study area's raidid patterns.
They did notice that the area of St Louis near the Mississippi, Missouri, ad Illinois rivers had an above average amount of xahM. They attriithis to the above average dew point tempe!ratures and the obvious source of moisture fiom the rivers. Results of the Metromex studies generally showed that urban efkts on the cloud atxi precipitation processes were related to city size.
RainEiIl variability in Calgary has previously been studied Nkemdirirn (1981) explored the extra-urban and intra-urban mhiXl enhancement of warm season rainfall In
Calgary, a medium sized city. His study suggested that midill enhancement downwind of Calgary was not occurring and that Calgary had not received more warm season rainfaU as a result of urbanisation (Nkedirim, 198 1). It was suggested that the city had not grown either m size or m pollution status to influence the climate of the surrounding area. However, he did suggest that the results did not exclude the possl'bility of an internal distriiution of rakkall due to urban inawnces. Differences in stations and the distriiution of storm middl were found to be stathticaUy signi6cant (Nkemdirim, 1981).
This led to the conclusion that the variabie spatial distriiution of warm season minfdl within the city was real The mtra-urban distri'bution of available rahM suggested a very strong urban influence with the most important kors m promoting the pattern being atmospheric pollution, wind direction, and urban fabric (Nkemdkh, 1981).
Rainfall variability has also been studied m Israel because it experiences extreme cases of spatial and temporal variability of rainfan (Goldreich, 1994; WGai, 1998).
Goldreich (1994) mmmarkd research carried out on the spatial distriiution of mi&dl in
Israel and quantiiied the various climatological and topographical fictors causing the spatial whbiky- From this summary, five basic geographic factors were identified as explaining a major portion of the spatiaI mhbihy of nainfin m 1-L Four of the factors were unived, while the last was a characteristic of Israel's particular geography
(Goldreich, 1994). The five factors were: (1) proximity of the sea bmases rainfall; (2) raididl amount increases with ground (3) raiafan decreases m the lee of mountain ranges; (4) the raididl mcreases m urban areas, especial& downwind; and (5) rainfall increases northwards related to the trajectories of cydones though the area Gokh suggested that the orographic htor was the most prominent spatial feature in the distribution of annual minM in Israel, wide the spatial raiddl mern affected by the urbanisation had a discrete nature.
Rakhecha (1996) re-examhed the variability of raiddl in India using similar data as in the 1977 Dhar study, but he also included highest annual rahfialls and highest hourly values. The article stated that persistent mius throughout a season were associated with orographic litling of moisture laden winds, heavy rains for periods of days with cyclonic storms, and the short period heavy falls with intense thunderstorms. Rakhecha gave three causes of heavy rain in India. The 6rst was the formation and subsequent movement of cyclonic disturbances across the country. The second was orographic lifting of moist air as it rises dong the dope of a mountain barrier. The last cause was the breaks m the monsoon. The magnitude and kquencies of the heavy rains m India &r widely because of the variations of physiography and atmospheric features (Rakhecha,
1996). Rakhecha showed that heavy to very heavy raiddl for periods of days was associated with the movement of cyclonic distudmces Eom the Bay of BengaI and the
Arabian Sea, over India. The paper also pointed out that there was an element of randomess m the magnitudes of the highest one, two, and three day rahfSs even though observations were a&k for over 100 years. It was also concMed that cyclonic dktudmw caused wid- aud intense mhM in areas over which they travel and that most of the very high I-hour MIS had occurred m the coastal and mlmtaiwusateas.
2.2. hhbleMm-mum hc@itatiun
The WMO defined PMP as being the theomgreatest depth of precipitation for a given duration that is physically possiile over a particular drainage basin at a particular time of year (WMO, 1973). VaIues derived under the WMO definition are subject to change as knowledge of the physics of atmospheric processes increases.
Climatic trends can be ignored because they progress so slowly that their idwnces on
PMP are small compared to other uncertainties ia estimating these extreme values
(WMO. 1973). Ln 1982 the definition changed to the theoretically greatest depth of
precipitation for a given duration that is physically possible, over a given size storm area,
at a prtkuIar geographical location at a certain time each year (Hausen, 1987). Note the
italics portion emp hasising that precipitation is a fimction of storm size as opposed to the
earlier definition relating PMP to drainage area This change was made to correct the
false implication that the physicaI limits of precipitation are related to the size of specilk
drainage areas.
PMP estimates must exceed the envelope of the maximum observed values at the
site. Of the factors that have an iduence on the magitude of the PMP,the intensity and
duration of raiddl are the most important. Tbe deria-based PMP estimates are a
deterministic approach, as compared to h probabilistic approach that is based on
middls or flood speczed frequencies (NRC, 1985). It is important to mdk that the
PMP can be exceeded m firhae events and does not repnsnt the maximum possiile depth at the design site (Singh, 1992). It is a measure of the maximum probable precipitation that could be experienced based on meteorological variables.
To athate the PMP, two methods are currently used: the traditional approach and the statistical approach. The traditional approach requires the use of meteorological data, and consists essentially of moisture rnardmisaPion and transposition of abed storms.
The statistical approach solely analyses rahfM data and is probabilistic m nature. The latter approach may be used when dcient precipitation data is available; this method is particularty usefbl for making quick estimates, or where other meteorological data is lacking (WMO, 1973).
2.2.1. Traditional Method
Since 1967, the U.S. National Weather Senrice (NWS)has continued to refhe the deterministic approach of PMP estimation to increase the accuracy of reds. The magnitude of the PMP is partially a fimction of the amouut of detail and data available for a particular study. Accuracy, or reliability, of an estimate depends on the amount and quality of data available for applying various estimating procedures. In addition, the amount and quality of data availabIe determine if the traditional method can be used.
The NWS has made refinements to the traditional method available maiaJy through
their hydrometeorological report (HMR) series. They have provided PMP estimates for
various regions in the United States (NWS, 1984).
In this approach, major rainstorms are studied to determine maximum areal
rahfidk and ascertain, as best as possii, the theteorological factors important to the
raddL The HMR series spans many years and bas calculated gendd PMP
estimates fbr msiny parts of the U.S., where they boked at diflkmt durations and basin h. Mapshavealsobeenproddtoaid~dtoiogistsm~PMP~m certain areas. For the traditional method, PMP over a watershed is the depth of raididl that approaches the upper lid of what the atmosphere can produce. Which stom aad what level of muhisation are important to the resubg estimate of the upper limit. To develop the PMP using the tdithaal method, the foIlowing operations are performed on selected major-recorded storm rainfkk: a) moisture maxhisation; b) transposition; and c) envelopment.
2.2. I. 1. Moisture Maimisation
Moisture maximkition involves increasing storm rainhll depths in the storm location for higher atmospheric moisture than was available during the actual stom The purpose of storm maximktion is to determine the amount of increase in rainfizll of a storm due to physically possible alterations in the meteorological factors producing the storm (Singh, 1992). It is assumed that the PMP is derived from a hypothetical meteorological fiont in which maximum humidity and maximum dynamic efficiency converge (Anselrno et aL, 1996). Physical factors that can be distinguished are the mechanisms causing atmospheric moisture to precipitate and the moisture content of the air mass responsible for the storm (Singh, 1992).
It is difficult to manipulate physical mechanisms for increased precipitation or to increase mechanical efkiency of a stom The mecmproducing intense raiafdl can be assumed to be hi& e5cient and may ti close to the maximum etliciency. . . Therefore, storms are tmmmd for moisture content of the air miss.
Atmospheric moisture content can be expressed as precipitabfe water. Precipitable water is the amount of liquid water that wouid ocm in an air column of unit cross- section if all of its water vapour were condensed. This is a term, used mostly by hydrometeorologists, to express the total ~lyassof water vapour in a vertical cohnrm of the atmosphere. The vapom content is available in varying amounts in atmospheric hyers close to the earth's surf8ce. The tnrlk of the vapour content is present in the lower hyers of the atmosphere. For practicaI pqosgit is &sfkctory to consider the vapour coutent up to the 300 mb level in the atmosphere (S&h 1992).
To calculate the amount of precipitable water, W,an air column extending up hm the earth's .surfkce is condensed (Smgh, 1992). The metric version of the equation is expressed as (Smgh, 1992):
Where W is in gm/cm2,g is the acceleration due to gravity, p is the total pressure of moist air in milIii, and e is the partid pressure of the water vapour. Since the density of precipitable water is 1 g/c~3,W is the depth of precipitable water m centimetres. If the atmospheric pressure and vapour pressure are known, the depth of precipitable water can be calculated hmthe above equation.
Moisture maximidon of a storm requires identification of two saturation adiabats
(WMO, 1973). One typifies the dcal temperature distri'bution m the storm to be nmximkd, and the other is the warmest saturation adiabat to be expected at the same place and time of year as the stom Sbxe presstm and temperature are related, the moisture content is aIso related to temperature. The moisture content can be calculated hm t- consideratioas. Past tests have shown that storm and extreme vaiues of precipitable water may be approximated by surf& dew point values, when stmation and pseudo-adiabatic conditions are assumed (WMO,1973). When the air is cooled at a constant atmospheric pressure, the temperature at which the air becomes saturated is the dew point temperature. For an atmospheric column, the dew point is ufllany known at the ground dice. It can be assumed that tbe dew point in the cohmm varies with altitude and has a pseudo-adiabatic lapse rate. W& this assumption, the precipitabIe water can be computed for an atmospheric cob(Singb 1992). Shcedew pints representative of the moisture inflow into the storm identifjl the storm saturation adiabat.
The moist adiabat of the highest recorded dew point fbr the location or the dew point for some specific return period. 100 years, is considered sdliciently close to the probable warmest saturation adiabat. The WMO bas produced tables that calculate precipitabk water from the relevant dew points. A copy of these tabies and the characteristics associated with them are in Appendix A.
Moisture maximktion of storms in place consists of multiplying the observed storm rainfsll amounts by the ratio (RM)of the maximum precipitable water (WM) indicated for the storm location to the precipitable water ( Ws)estimated for the storm, or:
2.2.1.2. Trunsposition
Transposition invohes relocating storm precipitalion within a region that is
homogenous relative to pertinent t& and meteoroIogiw[ features. This step occurs
for the tmjor storms within a topographicaIly and IlleteomIoghQ homogeneous region (NRC, 1985) and is mre common when tale PMP values for a large geographical area. Storm tramposition is an important tool in the standard methodology fbr defining the precipitation potential for a region (NWS, 1984) and involves ad- for elevation, moisture-inflow barriers, and distance brn the moisture source. According to
Singh (IW), storm transposition is used in watersheds that have inadequate &MI data or have experienced no severe storms.
Once the meteorological homogeneity has been established, the next step for storm
transposition is the selection and Wsis of major-recorded stom. In the literature, there are different way-s to select storms. In the Northwest United States (NWS, 1966),
selected storms were those having heavy precipitation for 2-3 days over a large area
Wbile for the Tennessee River Watershed (NWS, 1969), the criterion used for seIecting
summer storms that produced Iarge voiwnes of midill was the number of stations that.
simultaneously, recorded maxjmum 24-hr rains.
When transposing storms some considerations should be taken into account. Storm
transposition is not recommended for mountainous areas where necessary adjustmnts for
topography cannot be made sati&tody, Areal limits for transposition must be dehd
for each individual stom because a storm does not necessarily have the same probability
of occurrence over all parts of the region. Other considerations are that storm
transposition over large changes in Iatitude should be avoided and that the axis of
isohyetal pattern with respect to haxis of the watershed should be taken into accom.
These could impose a $@ant change in storm air-mass characteristics (Siagh, 1992).
Transposition procedures involve the meteorological adysis of stom that will be
transposed, the determioation of the iimits of transposability, adthe applicafion of the proper adjustmmts required by the change in location WO,1973). There are four steps in the procedure outlined by the WMO m their PMP manual The first step is to
identi@ when and where the heaviest rainfalI occurred and the approximate causes m
terms of synoptic meteorology. The second step is to delineate the region in which the
meteorological storm type id- m the first step is both common and important as a
precipitation producer. The third step is to debate topographical limitations on
transposability. The fjnaI step is the appMon of adjutmmts for elevation, moisture,
and barrier adjustments. . . Moisture rmummh'on in transposing storms is somewhat more complicated. The
moisture adjustment is merely the multiplication of the observed storm raiddl amounts
by the ratio of the precipitiible water (Wz)for the enveloping dew point at the transposed
location over the precipitabte water (Wr)for the representative stom dew point (WMO,
1973; Smgh, 1992) or:
Where RI is the observed storm mSU for a particular duration and size of area,
and R2 is the stom rainfall adjusted tbr transposition. This equation incorporates both a
moisture maximidon and a transposition ad..
2.2.1.3. Envelopment
The fhai step of envelopment is exphined fblly m the 1973 WMO guidebook for
PMP estimation. Envelopment is a process for sekchg the largest value hmany set of
data To consider only two or three stoms or storm sequences, no matter how sophisticated the adjustments might be, gives no assurance that the. PMP level has been obtained (WMO,1973). The question of adequacy of a storm sampIe for estimating PMP . . is a ditFcuh one. However, an envelope of rainfall values IIlaxrmtsed and transposed to a basin is likely to yield vaIues characteristic of the PMP izlagnitude. In estimating PMP, the muimked and transposed rainfan data are piotted on graph paper against the duration of the event. A smooth curve is then drawn through the largest values which is the envelope curve for the area m question.
2.2.1.4 Summary
If storm transposition were unlimited and if maximum values of winds, moisture, and other variables of storms were combined. the results wouId be unr&c (NWS,
1966). To avoid this, judgements are based on record storms. In addition, guidelines can come kom results of other PMP studies and statistical analysis of extremes in observed variables. These are some procedures used in the estimation of PMP values by the traditionai method. This method has been used extensively for many years, but is limited by the expertise required to utilise it properly and the amount of meteorological data required to make any type of accurate estimation.
Several studies using this approach have ended with very divergent results for the same area. The ktthat studies disagree in their results points out that deficiencies stiU exkt in the traditional method (HersMeld, 1965). 2.2.2. Statistical Method
The use of storm models to estimate PMP has steadily Men in recent years m
hour of statistical methods (Collier and Hardaker, 1995). Conventional methods of
rainstorm ady& are time consuming and require detailed analysis of past rainfau
events. The statistical approach allows a design engineer to obtain average mxhm
rai&U estimates for an area if some knowledge of the probable maximum point rainfall
is kwwn for that area. The statisticai approach requires considerably less time to apply
than does the traditional, or meteorological, approach and one does not necessarily have
to be a meteorologist to use it (WMO,1973). There are two common approaches m the
literature for statistically calculating PMP estimates.
2.2.2. I. Hersweld Approach
The WMO dmia procedure, first proposed by Hershfield in the 19603, that is
wideIy accepted and is used prhnarily for making quick estimates for watersheds of no
more than about 1000 km2. It yields only point values of PMP and, thus. requires area-
reduction curves for adjusting the point values to various magnhdes of area. According
to Hershfield (1961), Yen T. Chow demonstrated that the only difference between the
various distriiutions which lend themselves to the an- of extreme-values hydrologic
data is the common statistical variable, & or standardised variate m equation 2.4.
In which xr is the rainfan for return period T, m years and the terms 2~and m are
the mean and standard deviation for a series of N anmlnt maxima Subthing the rnaxhum observed rabfbll X. for XT and & for K in equation 2.4 gives Hershfield's
PMP mdeL
Whm q,) is the &um observed raiW imd & is the number of stlmdard deviations that must be added to the mean to obtain 4, ). The variate, Kr,is found by rearranging equation 2.5.
It is important to note that when determining Em this way, the tnaximutn observed values are not included in the computation of the average and standard deviation ofx. K, reveals how rate a amhum event at one station is compared to the other stations. it can also tell how rare the raididl is at a station asslrming it follows a dishiiution,
For K, to be valid, assumptions of independence and randomness must be satisfied
(Hershfieid, 1961). A second characteristic of Kr is that it is uniquely related to the probability of occurrence of an event at a station, if a theoretical distri'bution is assumed.
With the kwwn Km value of a station, the PMP can be calculated using the mean and standard deviation of the ~naximmraiddl series Hershkld stated that the use of the mean and standard deviation as estimates hr PMP provide the amount of accuracy required to exploit the data There seenrs to be no qskrdc relatioe between tainfkn magdude and location, but that it occurs m a domf8sbion (Hershfield, 1961).
It is interest& to note that HdeId's & &is was based m Iowa, an area tbat is
not inhemd locally by bodies of water or orography.
It was first thought that K, was independent of mhhU magnitude, but it was later
found to vary inversely with rainfaU (WMO, 1973). There is a greater chance of getting a
larger extreme value as the length of record increases. Extrapolation of point mididl
vahres becomes more unreliable as size of area increases, generally over 1000 km2, so
estimates for large areas are not recommended.
HMR 49 (NWS, 1977) states that arid regions have higher values of K, than the
world average. It also recommends that direct application of Hershfield's equation
should be avoided since there is no completely objective method for detenaining 1..
(NPr5. 1977). Hershfield's study is based on the assumption that valuable information is
buried in each station's sample of extremes and that this sample can provide estimators
which can be used in conjunction with enveloping statistics to estimate PMP.
2-2.2.2. NERC Approach
The Natural Environment Research Council (NERC)of London presented a more
systematic method in 1975. In this approach, statistical and physical studies of middl
depth-duration-return period are made for point and areal rahfkl everywhere in the study
area, which in this case was the British Isles. Geographical distriin of estimated
maximum 2-hr and 24--hr precipitation is determined using a storm efficiency factor and
an an- of maximum dew points. Maximum are also estimated hmthe statistical
adysk of point rahfall relying on an envelope of alI the data on the diagram of growth
curves burxi m their flood sensenereport (NERC, 1975). The results are in general aggtwith those obtained using the storm eflkiency fktor. Relations are then found between areal rainfan over hed catchment ateas of many different sizes and the point raiddl with the same duration and return period.
These relations spec@ an areal reduction factor which when multiplied by point raiddl gives the corresponding areal rakM. The areal reduction factor increases with increasing rainEd duration and decreases with size of area, but the variation with geographical location is apparently not very significant.
A later report (Bell, 1976) states that good generid agreement was found with the flood studies values at moderate return periods, but a tendency to overestimate slightly at long return periods was found. Bell also concludes that evidence for location diff-es in areal reduction fktors was inconclusive, and he assumed that areal reduction fkctors were independent of the return period. However, Bell also states that areal reduction fictors decrease with an increase m the return periods.
Inaccuracies were expected due to the relatively brief records, but estimates of the sampling errors m areal reduction factor showed that these were wt excessive (Bell,
1976). There is no doubt that rainfdl frequency estimates corn brief records are less
accurate. This does not necessarily result m large sampling errors in areal reduction
hctors because of the high degree of positive correlation between point and areal rainfaa
2.2.2.3. Summary
Eliasson (1994) discussed the two statistical methods to estimate PMP values which
were described in this section. He stated that neither method offers any exphnation why
the PMP vahm can be calculated by the use of uabouaded mtkaical distdmions, but
both methods inchale the use of envelope curves that are not independent of the region. It is shown that when HersMeM or NERC mtbds are used, the limiting reduced variate is included m the PMP values and can be siprated hm regional parameters. The equation proposed by Hershfield is a way of approximating an answer when little is known about the estimated quanthy. It fgils to yield a precise answer because of the lack of universal transposability of any one value of K, (Verschuren and Wojtiw, 1980). It has been shown by the NWS that some statistical PMP estimates have been exceeded by record storm amounts from supplementary minM surveys. Since w recorded middl should exceed the PMP value, this raises the question of accuracy in the statistical approach- Chapter 3: Study Area
The study area is the city of CaIgary (51'03' N and 114O05' W) located in Alberta,
Cauada Calgary is located between the prairies to the east and the foothills of the Rocky
Mountains to the west (Figure 3.1).
Figurn 3.1: Map of Study Area (modi6ed 6wm Canadian Orford World Aths, 1992) 3.1. Topography
The topographical
features found in Calgary
are the product of
years of erosional and
depositional activities of
rive~rs, lakes, and glaciers.
The city is roughly 70
kilometres east of the hnt
ranges of the Rocky
Mountains and covers an
area just over 700 km2.
The city has rolling ridges
and hiIls aligned northwest
to southeast. parallel to the Figure 3.2: Shaded Relief Map of the Calgary Area Rocky Mountains.
The major topographic;ai features m Calgary are Nose Hill and Broadcast HiU m the
northwest. and the Bow Riv,er valley (Figure 3.2). The mean elevation is around 1100
meters above sea level. The range in elevation is from 604 meters at the lowest point to
1348 meters at the highest. Higher elevations are found m the northwest of Calgary and
the lower values are m the southeast (Figure 3.3). The cross-section shows a Iarge
decrease in elevation as one moves away corn the northwest portion of the city, which
becomes gentle southeast of I%e city centre. a; 0 smotmmlsmDnamzam3rmo2samcmm~ma, Dbr(mnc08bq (h.Cmu-Uh(rn) Fire 3.k Elwatiw cm~.olfron the mdw-estto tbr aoutbmt cwner of the city
Changes in elevation are visible in an average slope map of Calgary (Figure 3.4).
There are higher slopes in the northwest portion of Calgary with gentle, or no change, in slopes in the east and southeast. There is an exception to this in the southeast where higher slopes are bund as the Bow River exits the city.
3.2. Weather and CIWe
Geographical location determines the major htum of the local climate. The chtenonnals for Calgary, supplied by Meteorologd Services of Canada (MSC), can be seen in Table 3.1. The mean annual ddy temperature for Calgary is 3.gaC. The area experiences Iong and cold winters fbllowed by summers tfiat are usually short and COOL
The mean ternpermre through the months of May to September is around 13.3OC. Due to Calgary's relatively high elevation, the summer teqemms tend to be moderate. Figure 3.4: Map showing the average slope of the Calgary Area
Calgary has the lowest atmospheric humidity of all the major populated centres in the Prairies, The average mid-afternoon relative hllmidity is about 49%. with an average vapour pressure of 5.7 hPa. Lower relative humidity is found between the months of
May to September. In contrast these same months have the higher vapour pressure values. The avenge annual precipitation of Calgary is around 420 mrnlyear. with an annual potential evapotranspiration of around 528 mm (Mremdirim, 1998a). This classifies Calgary as a semi-arid region Tabk 3.1: Calgary Climate Nornrls (source: Environment Canada, www.cmc.ecgc.a/c~ate/normab) Month] Jan f Feb I Mar I Apr I May I Jun . Temperature
Daily Max (OC) -3 -6 -0.5 33 10.6 16.4 20.6 Daily M.u ("C) -15.7 -123 -8.4 -2.4 3 .O 7.4 Dady Mean ("C) -9.6 -6.3 -2.5 1 4.1 9.7 14.0 Precipitation 0.2 0.2 1.5 9.2 43 -9 76.7 , Rainla Snowfall (cm) 18 14.9 18.7 20.4 10.2 0.3 Month Jul Ang Sep Oct Nov Dec Tempemture Daily Max (OC) 23.2 1 22.7 17.4 12.6 2.9 -2.3 Daily Min (OC) 9.5 8.6 3.8 -1.2 -9.0 -14.4 Daily Mean ("C) 16.4 15.7 10.6 5.7 -3.0 -8.3 Precipitation RaintZlll (mm) 69.9 48.7 42.7 6.4 0.6 0.1 Snowfall (cm) 0.0 0.0 6.4 11.5 16.0 19.0 I
Of the 420 mm annual precipitation, snowfill accounts for roughly 32%. raidad
for 68%. The significant rahiidl starts m May and continues into September (Figure
3.5). The average warm season midlis 281.9 mm. June and July are the two rainiest
months receiving 76.7 mm and 69.9 mm, respectively. Most of the precipitation is of the
showay nature. However. July has the maximum amount of thunderstorm and hail
activity. The greatest oneday storm on record at the Calgary airport occurred on July 15,
1927 when 95.3 mm of rain fell m one day. On average, there are 5 1 rain days fiom May
through September. The average depth of midill per day is 5.8 mm. JmFsbMMI\prImU~~QdNw~ Moacb Figure 35: Norumi MoalbJy Raiint3ll lor Calpry, Albcrh Chapter 4: Data
4.1. I~troduction
The World Meteorological Organisation (WMO, 1973) stated that the accuracy, or
reliability, of aa estimated value depends on the amount and quaIity of data available for
applying various estimating procedures. In 1985 the National Research Council stated
that, " within meteorological similar areas observed minfU values could provide a better
general indication of maximum flood potentials than bod discharges fiom individual
watersheds." This has become accepted due to the large network of adable mididl
data Another important argument for the use of rahtU data is that it is an important
control on the intensity and duration of rainfU
The rainfii data used in this study were collected hrn two main sources. The first
source was the City of Calgary Waste Water and Drainage. They have been collecting
midill data since 1979. Most raidbll metering stations are located at fire halls. Early
readings were performed on a daily basis by individuals reading strip charts, As
technology increased, data loggers were used to record rainfdl dues at shorter durations
automatically. In 1997, 25 raidill metering stations were operated by Waste Water and
Drainage.
Waste Water and Drainage supplied various forms of data with different formats
ad levels of completeness. Their data covered the years hm1979 to 1997 fbr the
months of ApriI to October only. The city does not use heated rain gauges such that data
collected in April and October are uneven and unreliable due to the Iate and early snowfalls ercperieaoed m Calgary. For this mn, only data collected hmMay to
September, tbe wann season, are llsed in this study.
The earlier data (1979 to 1982 and 1986) were daily mididl totals, which were hand denon paper charts. The 1984 and 1985 data came in computer files of various types encompassing time periods of two weeks. There was either no data received or the data collected was too sparse for 1983 and 1987, so these years were wt included in this study. Data hrn 1988 to 1997 came as raw data logger mes. Using the software package RainPro, supplied by the City of CaIgary Waste Water and Drainage, fie- minute middl values were exmaed. Two databwm were created. One * contained the daily rainfsJl totaIs recorded for each city station The other contained the five-minute data
The second source of data was the Meteorological Service of Canada (MSC). The
MSC bas a station at the Calgary international Airport recording various weather and climate variables throughout the year- This station has been operating m a similar location since 1876. [n its lifetime, the station has moved four times, but never more than a kw minutes of latitude or longitude with no change in elevation. A database containing daily records brn 1885 to 1997 for the two main variables of temperature and precipitation, inchdig raidd, was obtained. The MSC airport station has excellent historical records for daily cahfhL While it was wt posslik to get any cahMl information at shorter durations, there is over 100 years of daily data.
The daily data fiom the City of Cdgary Waste Water and Drainage and MSC were combid. Figure 4.1 shows the location of the &I stations in Calgary activeIy recording data m 1997, while Table 4.1 shows the general hhrmation fbr each station. Figure 4.1: Calgary Rainfall Stations Tabk 4.1: Geneml information for the Airport md Urbm Rain Stations
Extreme rainhU amounts can be used as indicators of rumhum rates of convergence and vertical motion m the atmosphere (WMO, 1973). One c-n of emme rainfaIL is an event producing the most amount of rain received m an area for one year. Annual maximm raiuhll amounts fiom 1979 to 1997 at the stations in the city are
used to examine the variabihy of extreme mhlillevents in CaIgary. Twnty-six stations in Calgary recorded raiddl hm May to September.
Representative estimates can be obtahed hmrecords as short as 10 years (Ben-Gai et aL, 1998). Country Hills and McKemie Lake have only 3 years of data. Their records are too short and, therefore, are not included m the study. Coach H.Edgemont, and
Spy Hiil have data records shorter than 10 years but greater than 7 years. These stations where kept in the study to represent the expanding area m the northwest of the city. The amount of data for each station ranges hma low of 7 years to a high of 17 years- The average length of data is 14.5 years with 80% of the stations having 13 years or more of data. However, some of the data series were discontinuous. In order to obtain continuous data series. estimation of missing values must be performed.
4.3. Data -on
4.3.1. Introduction
Gaps in rainfAl records are common for a variety of reasons. A gauge may have been instaUed after the period of interest. it may have been cbsed down or it may not have been firnctioning correctly during the event (Durme and LeopoId, 1978). Any one of these reasons may be responsible for the gaps m a rainE1U data record.
Numerous methods are available to estimate missing rahW vdues. Singh (1992) states that kriging, optimal interpolation, and muhiquadratic interpolation methods give comparable values and are superior to other estimation methods. However, he also stated that the inverse distance and Theissen polygon methods can give satisEmory re&.
According to Dunne and Leopold (1978), the simplest way of edmation is by using both correlation and regression measurements hmthe station of interest with data from a nearby gauge when both were fimctioning. The correlation coefticient (r) is a measure of the strength of the linear relationship between two variables. I? has a range from -1 to 1 and is computed using:
The larger the absolute value of r is the stronger the linear relationship. If the correlation coeilkient is near zero it indicates that theis M) barrelationship between the values, while a value near 1 or -I means they are hstperfectly correlated. The sign of r shows whether the relationship between X and Y is direct (positive) or mverse
(negative)(Kvdi 1988).
Regression analysis is a method of studying the relationship between two (or more) variables. The purpose is to arrive at a method for estimating a value of the dependent variable (Kvanli, 1988). A muhiple linear regression model is used to explain the behaviour of a certain dependent variable using more than one predictor variable. The form of this model is:
~=8o+Btxt +B2~2+---+Bnx, 4.2
Where is the y-intercept of the line, 8, is the least square value, and XI, x2, ..., xk are the n predictor variables associated with the model The above method works well m widespread cycIonk raiddl and will be used to estimate missing data
A correlation anal@ was performed on rain stations to see which ones were
statistically related, A Pearson correlation was nm to determine which stations had a high lineat relationship with each ok- Stations were considered highly correhed if they were signilicantly related at the 0.1 lewl, using a 2-tailed test.
Stepwise regression adysis will be used to find which stations were best suited fbr estimating the missing data fbr each station. Stepwise regression is a modification of forward regression. It is the most popular and flexiile of the selection techniques
(Kvanli 1988). This method of model selection puts variables into the equation one at a time, beginning with the variable having the highest correlation. This procedure continues inserting the next best variable. At each stage any variable can be removed whose partial F value indicates that the variable does not contribute significantly to the prediction of the dependent variable. The selection of variables stops when the best variable among those remaining produces an insignificant increase in 2.
The stations used in the estimation of missing data for each station had to have two characteristics. The firs was that the station had an muaI maximum 24-hr rahfitl value for the year m which estimation had to occur. The second characteristic was that only stations which were signi6cantIy comIated wodd be used. Once the relevant stations were identified, the regression adyhwas undertaken
In some instances, it was not posiile to determine a relationship using the above methods. That was because there were too few stations available for the anaiysis. When the stepwise regression woukl reject all of the predictor variables mtroduced, stations with less than 10?4 of their data estimated were iutroduced m the w.The same stepwise -on steps were used and a rebtionship was defined. 4.3.3. Resdts
TabIe 4.2 shows the predictor variables aad the level of variance accounted fbr by the model used to estimate the missing data. The oniy stations that did not require estimates were the Airport, Downtown, Haysboro, Parkland, and West Dover. Table 4.3 shows rainfgll values between 1979 and 1997, observed and estimated, for each station.
The estimated rainfU is shown in bold italics.
Tabk 43: Stations used for the calculation of missing data Tabk 42: Observed md Estimated Annual R.iahn Maximums (mmj
West Dover 33.0 12.8 28.8 25.4 29.0 86.6 1 21.0 30.6 1 22.8 WhrPark 16.0 59.4 3f.5 39.4 29.4 86.61 53-0 64.4) 23.2 Tabk 43 (con?): Observed and Estimated Annual RaidhIl Maximuma (mm)
West Dover 29.4 ,. 32.2 39.4 38.4 22.6 24.2 1 33.0 34.8 WindsorPark 29.6 32.2 48.2 34.0 27.0 27.21 27.2 34.4 Chapter 5: RaiiVariabii
This chapter deals with the completion of the lirst objective and is broken down into four sections. The first section examines the variables selected for anaIysis. The second and third sections discuss the construction of the model to explain the variability of extreme raididl and the validation of the suggested model respectively. Finally, the redsare discussed.
5.1. Variable Selectibn
Data used in the analysis of midill variability belongs to one of three groups: (i) independent physical variables, (3 independent anthropogenic variables, and (Eii the dependent variable-
5.1.1. Independeat Physical Variables
Four physical variables were considered in this study. They are elevation, slope, aspect, and distance fiom entry of heavy mididl events. The ktthree variables are common in the study of raiddl variability (Spreen, 1947; Changnon et al., 1981;
Goldreich, 1994; Rakhecha, 1996). The fourth variable has been considered in recent middl variability studies (Goldreich, 1994), and is generally regional in effect (Longfey,
1974; Rakhecha, 1996).
The elevation. slope, and aspect data for the stations were gathered from a digital elevation model @EM) of Calgary, supplied by the University of Calgary. The general entry of heavy precipitation events into Calgary is the south (Nkemdirixn, 1998b). The distance hmthe stations to the point of ent~~,the south of tbe city, was determined. All of the physical variable information is in Table 5.1.
5.1.2. Independent Anthropogenic Variables
The most well known hpogenic emon rainfan is urbanisation (HUE 1975;
Cbaagmn et al., 1981). The diffiEuIty is to measure the degree, or IweI, of urbankition in Calgary. Based on available data, the measure of urbaaisation chosen to use for
Calgary was building density. The building density was dculated by dividing the number of dwellings located in the gauged comrmmity by the community's area. The number of dwellings in an area was obtained hrn Calgary's municipal website
[www.gov.cdgary.ab.ca(com~ty/my/p~~e/#s).The City chsdied the dwellings as totaI occupied private dwellings. Structures included in their classification are singIe detached. semidetached. row house, apartments, detached duplex, and other.
The locations of the Airport and Shepard Lagoon have a value of zero for build& density. This was because the City did not show these communities having any occupied private dwellings. The community buiIdiog densities are also listed m Table 5.1.
5.1 -3. Dependent Vdle
The dependent variable in this study was rainfaU As disc4in chapter 4, the annual maximum 24-hr vaIues were used. For comparison to the independent
variables, the time portion of the rain data was compressed. The mean annual maximum
24-hr mhMdues, which have a return period of 233 years, were calcuIated for each
station. Tabk 5.1 shows the values and Figure 5.1 shows the spatial pattern of the mean
axmud tnaxhum 24-hr values br CaIgary- -fall (mm)
Figure 5.1: Mean Annual Maximum 24-hr Raid% for CaIgary
5.2. Modd Construction
For statistical purposes the null hypothesis (&) for this research was that the independent variables had no linear relationship to mean annual maximum 24-hr rahhil.
Multiple regression adysk was used to test if the independent variables from Table 5.1 accounted for the variability of mean annual maximum 24-hr raiddl experienced in
Calgary. Before multiple regmsbn aoaIysis was performed. each of the independent variables was anaIysed to undermud the individual relationship with mean annual maximum 24-hr I;linfall. Tabk 5.1: Data lor the urban rain stations used in the determmafion ofRinWl variability StationName Mean Annual Elevation Sbp Aspect Distance Building Mirimtm24- (m) at at drom Jkmity hr- station station Storm (dwelhp (mm) ("1 ("1 EnW 1 km2) 1 Airport 40.7 1083 0.50 202 22.4 0 68 Street Lake 31.2 1058 1.20 182 22.4 158.9 Bowness 37.2 1071 1.44 60 27.7 203.4 Cedarbrae 35.8 11 17 1.46 1 75 13.1 261.9 Coach Hill 39.3 1221 2.97 59 24.9 295.2 Downtown 33.9 105 1 0.19 227 21.9 732.8 Edgemont I 48.1 1226 8.34 182 3 1.8 174.8 Forest Heights 31.7 1068 037 165 23.3 371 -0 Haysboro 37.9 1061 1.15 270 13.1 199.3 Huntington 35-1 1084 1 .M 78 29.4 246.4 Hills Lincoln Park 38.9 1116 1.67 90 18.3 71.4 Midnapore 41.5 1050 1.51 9 1 6.8 t 22.8 Mountainview 37.6 1081 0.00 260 24.3 91.9 Onden 35.7 I031 1.89 [ 62 15.1 f 78.8 Parkland 44.9 I037 I .33 8 1 9.0 92.5 Ro sscarro k 38.3 1 144 0.02 85 22.4 278.8 shepard 35.8 1032 0.49 73 13.2 0 Lagoon S ilwr Springs 39.2 1166 2.12 108 31.6 149.1 Spy Hill 47.3 1248 2.30 149 34.5 80.8 Tenrpk 38.3 1094 1.19 t 06 27.0 284.3 Tuxedo 35.0 1092 3.12 193 25.8 2282 University 37.7 1112 1.14 360 26.7 80.1 West Dover 32.0 1063 4.70 21 7 20.7 113.1 Wmdsor Park 39.3 1059 6.19 114 17.3 350.0
When elevation {E) was pIotted against the mean annual nuximum 24-hr rainfatl
(Pts)),there was a visiik hear trend (Figure 5.2). The r vaiue of the relationship was
0.568?with a significance of 0.004. The scatter pIot (figure 5.2) showed, m general, that as the station elevation iacreavs so did the Pk-) de. Tbae were some unchatacte&icaUy high whm at lower elevations. The possiile reason for the observations will be discussed later.
Figure 5.2: Scatter plot of elevation vs. mean annual maximum 2Qbr rainfall
There was a weak bear relationship between slope (9and Pb-) (Figure 5.3). The
Pearson Correlation coefficient was 0.377, which was signif?cant at the 0.07 level On its
own, slope accounted for 14% of the variability of Pb- .
When aspect (A) was plotted against PFmI.no significant relationship was present
(3= 0.0 15). This was visible in the satter pht (Fi5.4).
The distance hmstorm entry (D) had a poor linear relatiomhip to Pr 1 (r = I-
0.158). However, the Wer plot showed a ditkent relationship (Figure! 5.5). A
quadratic reIationship was ViSIiIe between the two variables. With a polynomial tit, the r value increased to 0.75 with a @,@came level of 0.0002. This relationship alone accounted for around 56% of the variab*ty of Ptrm ) m Calgary.
32.0 ,
30 0 a 00 1 00 2 00 3 00 4 00 1 00 6 00 7 00 1 00 9 00
Statma Sbpe Id,'rn*t
Figure 53: Scatter plot of slope vs. mean annual maximum 24-hr rainfall
Fire5.4: Scatter pbt of aspect YS. mean annual maximum 2ehr rrrinfnll Figure 5.5: Scatter plot of distance from storm en@ vs, mean annual maximum 21- hr rainfall
The final variable was building density (4in each community. The relationship with qi- is negative. with an r of -0.356 and significance of 0.1 I. The scatter pbt of the two variables showed that most of the stations have a relativety low building density
(Figure 5.6). The downtown station was the or@ community with a high budding density, in comparison to the other stations. The negative sbpe is consistent with the increase in rainfall observed over the highest grounds where suburban dwell@ tend to have lower density, and reduced rainfan m the downtown where densities are higher.
This outcome appears to indicate that urbanisation has not become a factor in the distriion of q-I- 1. This position is reinforced by the general lower air polhnion indu recorded downwind of the city centre (Nkedhet al, 1975; Alberta Envircimmt Web
Site).
30 0 -- 0 0 100 0 2WO 3000 4000 :XI0 0 6000 MOO 800 0 &IJdmg Demry~~afhwllmgpa~hbmarc~
Figure 5.6: Scatter plot of building density vn mean annual maximum 2Qhr rainfall
The information from the individual analysis determined the steps for the
construction of the multiple regression modeL Each variable was inserted into the
regression equation in turn. This procedure allows examination of how each of the
variables affected the fkd mdeL
The independent variables were entered in the model based on the order of their
with with the values significance Ptx. 1. The mi&Ies higher sigdicance were entered
first. If there was a tie in the signiscame, the vah~eswere entered based on their 8
due. Table 5.2 lists the independent miaides, their symbols, r, 6 si- and
order of entry. Tabk 53: Information used for the model construction
Based on the above criteria, a multiple regression analysis was performed. The model summary produced is in Table 5.3.
Tabk 5.3: Model Summary
Model Run r # Std. Error (mm) /Change , 1 0.75 0.56 3.03 0.56 2 0.84 0.70 2.54 0.15 3 0.86 0.73 2.47 0.03 4 0.86 0.73 2.53 0.00 5 0.86 0.74 2.60 0.00
The first run of the mode1 included diie from storm entry as the predictor variable. To account for the quadratic relationship discussed earlier, distance from storm entry was entered into the multiple tinear regression model as D and d.It accounted for
second 56% of the variab'i of q-sa 1. Th run of the model added elevation as a predictor. This raised the linear relationship (r) hm0.75 to 0.84. Including elevation in the model increased predictability hm56% to 70%, and decreased the standard error of estimate hm3.0 to 2.5 mm. The third and fburth nm of the regression mode1 inchded the slope and building density, respective@. In Inth cases, the linearity and 2 values had a small increase, while the standard error dunged to 2.53 mm after the fourth run. The final nm of the regression model kMed aspect. However, the variable caused no sigdicant change in the values of r or ?, but did cause a small increase in the standard error of estimate. Tbe increase m the sbmlard error of estimate occurred due to an inmare in the degrees of Worn
The 6ml equation of the qnsion amlysis gives a linear correlation to mean annual lmximm 24-hr rainfsll of 0.86, an 2 value of 0.74. with a standard error of estimate of 2.6 mm. The multipk regression equation is:
Where P(i-lk the mean annual maximum 24-h station rainfall h mm, D is tk distance fiom the storm entry point in km, E is the station elevation in metres. S is the stations sbpe m degrees, d is the building density m the community, and A is the station's aspect in degrees drrtk The next step was to determine whether equation 5.1 was a satisfictop model for estimating Pb-).
5.3. Model Verification
TIE following hypothesis was examined,
H, :flD2=Do =BE =ps=fld =PA =O
H. : At Ieast ow of the fl 's # 0
If the H, was rejected. it coufd be concluded that at least one of the independent
variab1es in equation 5.1 comnIbuted sigdhdy to the prediction of P&-). The test
statistic used to determine whether the nmhple regression mode[ contained at least one
sigdbnt exphnatory variable was the F stadstic (Kvauii, 1988)- The testing procedure
was to reject Heif F > F0.1.6.1,.The F vahae was greater than the critical vaIue, therefore, the H, was rejected. It was concluded tbat at Least one of the variables in equation 5.1 was a signiscant predictor of mean mual maximum 24-hr mhidl.
This does not imply tbat all of the variables had a s@hnt predictive ability. The next test was to see which of the variables in equation 5.1 contrthted si@kaatIy to the prediction of mean annual maximum 24-br minfU To determine the contriin of each variable, t tests were performed using the following hypothesis.
Ho:fi = 0 (variablei does not contribute)
H.: & * 0 (variablei does contribute)
Where i was each of the independent variables m equation 5.1. A two-tailed test was performed. with a significance level of 0.1. to see whether the variables contnibute to the prediction of ,, regardless of tk direction of the relationship. The test of Ho versus H, was to reject KOif It( > 10.1~17. Table 5.4 shows the dtsof the r tests for each variable. From this it was concluded that distance hmstorm entry and station elevation contriiute significantly to the prediction of mean annual maximum 24-IK
&till in Calgary. The variables of slope, building density, and aspect did not appear to contn'bute to the prediction of mean annual maximum 24-hr rahfdl.
Table 5.4: Values used in the calculation of the t-test for each of the variables in equation 5.1 Varinbk fl Std. Error 14 t~mr Reject He 0.0428 -01 1 4.027 1.740 Yes D - 1 375 -441 4.248 1.740 Yes E 0.0309 -013 2.405 1.740 Yes S 0.402 297 1355 1.740 No d -0.0014 -004 0.359 1.740 NO A 0.0019 .007 0.256 1.744 No The variabies of slope, building density, and aspect were removed hmtbe model and the multiple regression was m again (equation 52).
This gave a new equation, which had an r value of 0.838, r' due of 0.703, and a
standard emr of estimate of 2.54 mm. Figure 5.7 shows the scatter plot of the calculated
mean annual maximum 24-hr rainfdl values, using equation 5.2, against the observed.
The produced model produces relativeiy accurate resuits witfi all stations within one
standard deviation of the 1 to I line,
-- arm bmmn
Figure 5.7: Scatter pbt of calculated vs. observed P6-) using equation 5.2 The jiud test was to determine the validity of the finished model produced m equation 5.2. It was necessary to conduct a search focused on residuals to look for evidence that necessary assumptions were wt violated. In regression anab.sis, the true mrsare as& to be independent nodvalues with a mean of zero and a constant variance, If the model is appropriate for the data, the abed residuals, which axe estimates of the true errors, should have similar characteristics. The assumptions being considered are linearity and homogeneity of variance, equality of variance, and normality.
A convenient method to test for the assumptions of linearity and homogeneity of variance was to plot the residuals against the predicted vdues. If these assumptions are met, there should be no relationship between the predicted and residual values. For our modeL the assumptions of linearity and homogeneity of variance are met. This was vislible in the random distribution of the residuals around the horizontal line throu& zero
(Figure 5.8).
Figure 5.8 can also be used to check for the violations of the equality of variance.
[f the spread of the residuals increases or decreases with the predicted values, the assumption of the constant variance of the predicted variable for all values of the independent variables should be questioned (SPSS Inc., 1993). There appears to be no change m the spread of the residuals m Figure 5.8. Therefore, the equality of variance assumption does not appear to be violated.
The final assumption was normality. The simplest way to test for normality was to construct a histogram of the residuals. This plot should reveal whether the distnion of residuals was severely skewed. The distribution of residuaIs showed a general wd relationship (Figure 5.9). However, there are a higher collection of frequencies at -1 and
1.5. An exact normal djstriiution is not necessary here, problem only arise when the dktri'bution is severely skewed and does not resemble a normal distriiion (Kvauli,
Figure 5.8: Scatter plot of the residuals against the predicted values
Figure 5.9: Histogram of standardised residuals From the histogram alone (Figure 5.9), it was d3Ecult to determine if the model violated the assumption of notmaby- Another way to compare the normality of the residuals was investigated. A more sophiskated method of checking the assumption of normality involves the use of a chi-square goodness-of-iit test (Kvanli, 1988). The chi- square statistic was used to test the hypothesis that the regression residuals came hma normal diiiution. The data hmFigure 5.9 gave a chi-square value of 5.18. Wah 4 degrees of freedom and using a siguificance level of 0.1, the critical chi-square &e was
7.78. Our chi-square value did not exceed the critical value. Therefore, it can be concluded, using the chi-square statistic and Figure 5.9, that there was dcient evidence to indicate a normal distniution of the residuals.
The primary goal was to evaluate the spatial wriabiiIity of extreme raidid events in the city of Calgary. Figure 5. I shows higher levels of mean annual maximum 24-hr rainFall values m the south and north/mrthwest portions of Calgary, while lower values are found m the centre region of the city. This gives a concave or bowl shaped appearance to the raiddl variability.
5.4.1. Distance hmstom entry
Distance fiom storm entry displayed the highest significant relationship to mean armuaI maximum 24-hr rahfX It explained most of the variance m the multiple regression model with 55.7%. As mentioned m chapter 2. the importance of storm path m rainfall variability has also been hrmd in other regions of the world (Longky, 1974;
Goldreich, 1994; Rakhecha 1996). The general direction of major storm systems through Calgary is hrn south to north~noahwest. The scatter pbt of distance hm storm entry against mean annual maximum 24-hr raiddl can be re-evaluated by labelling the stations with their corresponding south-north Iocation (Figure 5.10).
Figure 5.10: Scatter plot of the mean annual masimum 24hr rainfall against distance from storm entry
In the south, the stations closest to the point of storm entry generalty experience high rainhll values. The northerly flow of the extreme storms provides the heavier rainfU experienced m the southern parts of the city. In general, storms contain more moisture and are usually strongest at the point wkethey enter an area They weaken in moisture and strength as they move horizontaUy over an area, if no sources of energy strengthen the system. Without a supply of energy, the storm system will die out and gradually disappear (Ahrens, 1994). As the storm weakens, the available moisture for rainfitll will aJso decrease as it moves north towards tbe city centre. This explained the spatial pattern of mean muaI Illitldmum 24-hr caiddI seen m the southem half of wwY (Figure 5-11. However, the stations Iocated in the north have a ddkrmt relatiomhip. If the storm continued to weaken as it moved north, the raiddl values should decrease as one gets firrther away bmthe point of stom entry. This was mt visiile m Calgary (Ti5.10).
The mean annual m;udrmrm 24-hr raiddl values can be projected (Figure 5.1 I), asstlmiag the storm weakens as the distance hm storm entry increases due to de- watering as it moves horizontally. If you compare the 0-ed to the predicted Mhres, there is a visible break in the trend. This leads to a large discrepancy between middl values in north Calgary. The observed values in the north are on average 17% larger than he predicted values. The rainfall in wrth Calgary increases in a north/northwest direction, therefore. the strength of the storm must be increasing. Energy for strengthening the storm can be derived hrn several sources (Ahrens, 1994). One of these sources is elevation,
Figure 5.11: Observed and projected PFmIvdua against distance from stom entry 5.4.2, Ekvation
The station elevation was the other variable to have a significant relationship to mean annual maximum 24-hr middL The high area of raiddl values in the northwest comer of Figure 5. I was also the location of the highest elevation (Figure 5.12).
Elevai
Figure 5.12: Elevation map of Cilgnry
The scatter plot of mean armual maximum 24-hr rahtd against station elevation was also re-evaiuated. with the stations Iabefied with their proper south-north location
(Figure 5.1 3). Here it was visl'ble that the stations in the south. which are well explained by the distance hmstorm entry, do not show a strong rehionship to elevation On the other bad, the stations in north Calgary show that as the station elevation increased the rainiacreased.
W~ a difkence of elevation over 200 meters (Fii3.3 and 5-12}, the northwest portion of Calgary wouid cause an orogxaphic tifting or upslope effect tbat can explain the higher mhMamounts experienced in tbe north. The cross-section of Calgary shows the ody significant change in eIevation in the west and northwest over the Broadcast and
Nose Hifls. These areas should increase the storm strength through upslope movement, thereby, reinvigorating the storm and increasing the trtinFall in the north region of
Calgary.
1MIo I t& I200 1300
Station Eldon(m)
Figure 5.13: Scatter plot of mean annual mhm24hr rriarjrll against station elevation
This infbrmation was consistent with literature that exmined the relationship of
rainfil and elevation (NWS, 1969; WMO, 1973; Ahem, 1994; Goldreich, 1994; Moran & Morgan, 1995; Abbs, 1999; Aguado & Brrrt, 1999). In general, the amount of precipitation received in an area increases as elevation increases. With sutficient ascent and expansional cooling, wadensation or deposition takes place (Moran & Morgan,
1995). Most of a storm's moisture is located in the low level of the column (WMO
1973). Ranges of low hills or graddy rising terrain stimulate convection and increase rainfall through movement of air up slope. If the relief of the hill or mountain is large enough, the result@ expansional cooling and compressional warming of the low level water vapour affects the development of clouds and rainfall. This effkct would cause an increase in the strength of a present storm. In HMR 45 (NWS 1969), they state that effects of upslope and broad-scale sheltering are clearly indicated tiom maximum storm events. Mountains and hills are active contributors m the effects of blocking and movement of wind. konts, and raidl. Horizontal moving air cannot go through large obstacles (mountains and hilIs), so the air must go over it (Ahrens, 1994; Abbs, 1999).
The mean annual maximum 24-hr raidid values in the north increase as elevation
than increases. On average, the north stations q-x- values were 17% larger values projected assuming the storm weakened as it moved north. The higher elevations i~ north Calgary are responsible for causing an increase in the amount of moisture received
The dBiaeaa between the observed projected during heavy rainfall events. and q-xr values ranges hm4.4% to 33.5%. The greatest increase was experienced at Edgemont and Spy Hill, which are areas of highest eIevation. While the effect of elevation m the north varies, it is respomile for recharging the storm as it moves north~northumt, explaining the spatial pattern visible in the no~northwestof Calgary (Figure 5.1). 5.4.3. Rejected Variables
The variables of slope, aspect, and building detrsity were all rejected hmthe model for having an insignificant eiEct 0.1) on the variation of mean and cnaxkmm 24-hr raint'all.
The variable of slope would have been considered signif'lcant at a p level of 0.2.
While slope had been suggested m the literature as effecting the dktri'bution of rahdhl, it did not have a signiscant effect m Calgary. This findinP may have been due to the effect of elevation, The major area of highest slope was also the main area of high elevation
(figures 3.4 and 5.12). The correlation matrix between elevation and slope showed a hear relationship that was significaut at a p level of 0.05 (Table 5.5). Therefore, the effect of slope was most Likely masked by the effect of elevation.
Table 5.5: Correlation matrix between elevation and slope
2 Elevation Slope Elevation correlation 1.00 .377 P .035 Slope correlation .377 1.00 P -035
Aspect showed no relationship to variability of annual maximum 24-hr rahfd in Calgary. This was obvious after examination of the scatter plot Ween these variabIes (Figure 5.4).
The variable of building density was also rejected fiom the regrssion mdeL This
was an unexpected result. The lit- showed that urbmisation does have an efkt on
the dktri"bution of minfidl downwind of the city centre (Huff, 1975; Changnon et aL,
1981; Lutgens and Tarbuck, 1989). In Calgary, the variable of urban density did not
afkt the distriiution of rai-It is possible that the city of Calgary is not hrge enough to have a sipbmt effect due to lItbanisation (Nkemdirim, 1981). Lncfeased rrrban density is associated to increased levels of air pohtants, which is associated to cawing increased rahfbl due to higher amounts of coadensation nuclei released into the air
(Ha 1975; Changwn et al, 1981; Lutgem and Tarbuck, 1989). There is no evidence of an urban plume of phtion downwid of the city centre to cause an increase in
mi&d (Ntemd'irim et d, 1975; Alberta Enviroaarent, 2000). This outcome appears to
that ur~tionbas not the
The distance from storm entry and station devation explains the spatial pattern of
mean annual maximum 24-hr rainfdl m Calgary. Heavy storms enter Calgary hmthe
south This provides heavier rahhll amounts for the stations in south Calgary, closest to
the point of Storm enuy. As the storm moves north towards downtown, it weakens which
decreases the amount of mhfM deposited, Riddlbxeases downwind of city centre.
The increase in rainfall downwind of city centre was caused by ekvation. The higher
eIevations m tk northwest comer of Calgary cause an upsbpe condition that
reinvigorates the strength of the storm increasing rai&L
Overall, the spatial profile of the mean annual rmchum 24-br m Figure 5.1
is consistent with the strength of the storm at entry point, a weakening of the storm
through city centre, and a rechghg of the storm in the northwest through upslope
motion. Equation 5.2 reptesents the disnion of mean annual maximum 24-hr rainfdl
m Ca%ary quite well, accounting £br roughly 700/0 of the miawe- The mode1 provides a
good base or starting point fbr deal& with the distnhtion of mean annual maximum 24-
hr &fkU in Calgary. Chapter 6: Storm Events
This chapter will consider conrmon storm mechanisms associated with heavy mididl events in Calgary. Annual msucimum 24-hr raidl events were extracted hm the daily rainfdl database. The greatest raintan amount, or extreme, was extracted for each station. Ttte station records were examined to dete!rmine the date on which the event occuned. From the above criteria, seven storm events were initially looked at. The date of occurrence of the events and the stations they affected are in the Table 6.1.
Tabk 6.1: Date of occarrence of extreme rninfrll event and stations effected
Parkland, Rosswrrok, Silver Springs,
In Calgary, most severe 24-hr rain&& are associated with cyclonic events. These storms blanket the entire city with precipitation. The seven events above must represent cyclonic storms to be included in fUrther study. The rainfitn distriion maps fbr the seven events were constructed (figures 6. la to 6. lg). If the storm produced consistent rahfbll amounts over the majority of Calgary, the storm was selected for fiuther adysis.
The storms selected were September 12, 1985; August 1, 1988; June 13 1992; and June
14, 1992. L:0
Figure blr September If 1985 RaloWl Dbtribmtk. Msp ITgmreblb: Scpctmber 16.1986 Ralrfdl Dbtributiom %lap
61. M&odology
A hydrostaticany consistent North Amxkaa radiosonde database hmthe National
Oceanic and Atmosphic AdmbktWkn (NOAA) was used, The upper-air database for
Canada was established fiom an hourly radiosonde database of North America (Schwartz d Govett, 1992). The portion of the database used hr this study was obtained hrn
Budikova (2000a). For this study, o@ data at 00:OO and 12:OO Zulu time, for 85 and 50 kPa were used hrn the original data set. These times were used because they were the most complete data sets available, after quality control (Budikova, 2000b). To allow for better understanding, the times were changed to 17:00 and 05:00 hours local time, respectiveiy. The variables included in the database are temperature, wind speed and direction, dew point, geopotential height, and sea level pressure.
The necessary data were gathered to construct 85 kPa and 50 kPa maps for the storm events, T'he maps are used to recognise the movements of pressure systems through the area The data assembled at the 85 kPa IeveI are used to construct what will be called the pseudo-surface map. Mid-atmosphere maps are constructed using the data collected at the 50 kPa [evet
The maps were comcted using the computer software Stafer. A database containing X and Y co-ordinates and multiple Z information for the upper air stations was constructed. This information was used to construct grids that would be used to create the maps. The gridd'i methods use weigbted average interpolation algorithms. There are numerous methods available to constn~ctthe grids, ranging &om inverse distance to nearest neighhur. The difference between gridding methods is in how the weighring tactors are computed aad applied to data points during grid node interpoIation. Two difkmt grid adysis methods will be examined to construct the maps.
Kriging was the first method used for the construction of the grid files. Kriging has proven usell and popular m many &Ids and is one of the more flemile methods and is usell fbr gridding almost any type of data (Golden Software, Inc., 1999). Kriging attempts to express trends suggested m the data in an efficient and naturat manner, rather than isolating infomution in a bulls-eye pattern
The last method of gridding is the Modified Shepard's method. It uses an inverse distance weighted least squares method. It is similar to the inverse distance method, but the use of local least squares eliminates or reduces the bulls-eye appearance of the generated contours. The Modied Shepard's method starts by computing a local least squares fit of a quadratic hcearound each observation. The interpolated \dues are generated using a distance-weighted average of the previously computed quadratic fits associated with neighbouring observations (Golden Software. I nc.. 1999).
After the grids where computed, the estimated values were emedhm the grid files. This was completed by computing the difkence between the Z value in the data file and the interpolated Z value on the gridded &e. This approach provides a quantitative measure of agreement between the grid file and the originaI data.
Comparison of the observed values and estimated values &om the above grid methods mill help in determining a Ievel of accuracy for the estimated values.
The two methods gave similar results when the observed and estimated values were compared. Since the methods give comparable resdts, the method of kriging wiIl be used to constxuct the maps for anatysis. This decision was based mainly on the kttbat kriging is very flexiile and usefbi for all types of data
62. September 12.1985:
The storm event of September 12, 1985 was the extreme raiddl event for many urban stations in Calgary (Table 6.1). It is the greatest storm on record m Calgary since
1979. The amount of rahl2l experienced over the city ranged hma minimum of 68 mm to a maximum of over 92 mm. The highest momts of rain on this day are located in
Mountainview and just east of Downtown, the Airport, and Bowness (Figure 6.la). The lowest rainfall occurred over Sher Springs, which received 68.8 mm of rain. The distriiution of rainfau is relatively uniform
At the 85 kPa level, there is a strong low-pressure area over Montana just south of the Alberta border at 05:W on September 12. 1985 (Figure 6.2a). This pressure system moves in a northern direction into the province of AIberta, By 17:00 hours, tbe low- pressure system has moved past Calgary and into the Edmonton area (Figure 6.2b).
There are two high-pressure areas and one low visl'ble on the 50 kPa maps (figures
6.2~& 6.2d). One high-presswe area is located over the Pacific Ocean by Alaska while the other is over the C&U.S. border straddling Saskatchewan and Manitoba. The low-pressure area is visibte over most of southem British Columbia Looking at the 5650 metre contour Line (figures 6.2~& 6-26), there is a dip hmthe Pacific Ocean back up into Idaho. Montana, and Southern Alberta. This brings the warmer moisture Men air from the Pacific into the Alberta area Figure 62a: September 12,1985 05:OO 85 kPa map
-1 60 -1 40 -1 20 -100 -80 -60 Fire 63b: September 12,1985 17:00 85 kPa map Figure 62c: Sptember 12,1985 05:00 50 kPa map
-1 60 -1 40 -120 -1 00 -80 -60 Fire 62d: September 12,1985 I7:00 SO kPa map 63. Augrrst 1, I988:
Raiddl values range hrn a low of 52 mm to a high of 69 mm on August 1,1988
(Figure 6.1~). This storm event was responsible for causing the extreme raidall value
(62 mm) at the Temple recotding station The greatest area of rainEill is in the south, centred over the Parkland rain station A second area of high raSnfgn is over the airport.
The areas of the city that have the lower mbfU values are to the east and west of the downtown station.
There is a low pressure area to the southeast of Alberta over Montana at the 85 kPa level (Figure 6.3a & 6.3b). This system becomes more pronounced at 17:00 hours over the state of Montana, stretching into the southeast corner of Alberta. The low pressure system never appears to fdy establish itself m Alberta due to a stronger high pressure system The 85 kPa maps show a high pressure area starting to develop at 0500. tt is over the West Coast of British Columbia, and hangs over the region increasing m strength (figures 6.3b).
On the 50 kPa maps, there is a low pressure area over the British Columbia-AIberta border (Figure 6.3~& 6.3d). It becomes more visible by 17:00 hours on August 1, 1988.
This system allows for the movement of air hm the northwest corner of British
Columbi down to the north portion of Idaho and over Montana, and up into southern
Alberta. Figure 63a: August 1,1988 0500 85 kPa map
-160 -140 -1 20 -1 00 -80 -60 Figure 63b: August 1,1988 17:00 85 kPa map -
20 -
7 - - -- -1 60 -140 -120 -1 00 -80 40 Figure 63c: August 1,1988 05:00 50 kPa map
-1 60 -1 40 -1 20 -1 00 Figure 6.36: August 1,1988 17:00 50 kPa map 64. June 13 and 14,1992:
These two stom events are being discussed together since tky occurred right after one another. The June 13 event caused the taiafalI at Spy Hi4 while the
June 14 storm caused the amximum value at Coach Hill. There is an interesting djstriibution pattern seen in the June 13 storm. The storm (Figure 6.Ie) caused the greatest rain accumulation m the northwest and southwest portions of the city. The lowest rain vaiues are experienced in the east by West Dover. The rahM values range hm48 to 40 mm along the river hmBowness to West Dover. One high rahMarea is in the northwest situated over Nose HiU If the northwest corner of the city is ignored, the rest of the middl values increase hmWest Dover to Cedarbrae, in a southwest direction The June 14 mididl distriion shows lower raidid values m the east and they increase towards the west (Figure 6.10. In general, the heaviest raiddl is equally distn'buted dong the western edge of the city, except for a heavy cell over the Edgemont and Spy Hill area
The data used at the 85 kPa level was from June 13 at 05:00 to June 14 at I7:00 hours. There are two system visible during this period. There is a low pressure area over Montaua. However, it is dwarfed by a stronger higb pressure system that covers most of Alberta (Figure 6.4a). The Iow pressure system extends into southern Alberta on
June 13 at 05:00, but by 17:00 hours on June 14, the system dissipates (Fii6.4b). The high pressure area increases m size to cover most of the Prairie Provinces by 17:OO.
The same data was used to analyse the 50 kPa IeveL At this level there is only one
system present. A high pressure area covers almost an of Western Canada (Figure 6.4~). One thug that can be inferred hmthese maps is that a high, or relatively stable system
aloft is usually associated with lows, or unstable, systems at the dace.
Figure 6.4a: June 13,1992 05:OO 85 kPa map
-160 -1 40 -1 20 -1 00 -80 60 Fire6.4b: Jme14,1992 17:OO 85 kPa map - High-pressure Area
7
Figure 6.4~:June 13,1992 17:M 50 kPa map
6.5. Summary
The weather patterns associated with annual &urn rainfaIl events are summarised in 6g1,u-e~6.5a through 6.5~. which themselves are based on average conditions observed in four storm. The major features are:
(a) A low pressure cell centred m Montana.
(b) -4 high pressure cell Iocated to the northeast straddling the Manitoba-
Saskatchewan border.
(c) A ridge of high pressure extending over a had zone ftom northern British
Columbia through northern Alberta and the prairies.
(d) A high pressure ridge covering Western Canada at the 50 kPa leveL
(e) Moist air abundance m the Iow pressure cell This abundance is reflected m the
si-cautly lower dew point temperantres (Figure 6%) recorded m the warm
air mass over Montana. -- -2 -1 60 -1 40 -I20 -100 ao 80 Figure 6.5~: Average of the 85 kPa data for the four storm events
Figare 6.5b: Average of the 50 kPa data for the four storm events Figure 6.5~:Average temperatures and dew point temperatures at 85 kPa
Thus aside fiom the low pressure cell, high pressure persists over the entire area tiom the surface through to the mid-troposphere. This high pressure blocks the passage of the storm eastwards and northwards. These arrangements cause the north vaveiling stom to pass through southern Alberta then veer west towards the mountains. While the northerly flow provides the heavier rainfan experienced m the southern parts of the city
(entry point). the upslope flow towards the mountains reinvigorates the stom as it moves through northwest Calgary following the Bow River valley (Figure 6.6). The spatial protile of the mean annual ma,uimum ddis consistent with the strength of storms at the entry point. a weakening of the storm through city centre, and a recbargiug of the stonn in the northwest exit through upslope motion. These storm mecmare consistent with the resutts found by Nkm(1998b). Figure 6.6: General direction of entry and movement of heavy rainfall events Chapter 7: Probable MhumPrecipitation
7.1. Selecrion of a mtthod
Several considerations must be dewhen selecting a method fbr the calcuhtion of
PMP. These can be interpreted as the project objective, project type, availability of data, and location or regional cbaracterktks (Singh, 1992). There are other considerations such as socid and economic tictors, as well as legal and environmental implications-
These other considerations will not be considered in this study.
Usually the size of the project to be constructed determines the type of design value to be used. However, since the secondary objective was to dcuIate the PMP values, the
PMP model was selected, W~ththis in mind, either the traditional or the statistical method can be utilised. The availability of data determines the method used m this study.
There are two areas of concern when considering the statistical method. More data and additiooal statistical techniques are necessary for properly estimating PMP values using the statistical approach. The data for the Calgary airport was extensive. However, the data for the urban stations were not. It is known that rainfan hquency estimates
&om brief records can be less accurate, so it may not be beneficial to estimate PMP val~~~based solely on the statistical approach. Therefore, the traditional method was considered.
The traditional method has been widely used for many years. Similar to the statistical approach, this method also requires rahM meammmts. However, the
traditionaI method also requires the use of meteorological data to estirnate the PMP duee
Upper air North American data, as we1 as surf8ce dew point data, were avaiIaMe fbr Calgary. This data provides dkient infbrmation to allow fir the estimation of PMP using the traditional method. The regional charactenstacs*. helped to determine what methods hmthe traditional PMP approach were utilkd.
7.2. MethodoIogy
The methods used for the calculation of PMP values are outlined by the WMO's
"Manual for Estimation of Probable Maximum Precipitation" (WMO, 1973). A variation of these steps will be used for the calculation of PMP values.
The storms for PMP adysis were selected in chapter 6. The next step was to maximk the extreme aamounts using the moisture adjustment index. In-situ maximhtion was used for the moisture adjustment index. It was not necessary to transpose any stom into the Calgary area because it had emmed its own extreme storm events. Maximising a stom in place conshed of &p~the observed stom
W by the R, ratio hmequation 2.2.
To obtain the maximum precipitable water for the stom location, it was necessary to determine the dew point temperature duevahKVerschuren and Wojtiw (1980) estimated the PMP for AIberta river basins. In this docmmt, a graph was created that showed the mximm persisting 12-hour dew point for each month in Calgary, in l5day periods. This graph was reproduced for the months of May to September (Figure 7.1).
The warmst situation adiabat to be expected when the extreme stom event occurred was required. The values hmthis graph were used in the moisture adjustmmt ratio for each eveat- Figure 7.1: Maximum recorded persisting 12-hour dew point temperature for Calgary (source: after Verschuren and Wojtiw 1980)
The precipitable water estimates for each of the fbur storm events in chapter 6 were calculated using the persisting 12-hour dew point temperatures hm historical records.
Hourb dew point temperature values were collected hmhistorical records for three days befbre, the day ofl and three days after each extreme storm event. Any single observation of dew pomt may include some hherent errors. For this reason, persisting
12-hour dew pomt temperatures were used. The decision to Iook three days before and after the storm was to get a good representation of the weather conditions prior to and after the storm. This allowed for the best representaton of dew point conditions associated with the extreme storm system.
While hourly values are more accurate, Iocating the 12-hr persisting dew point is more mcuk The hour@ dew point temperatures were averaged into time intends of 00 to 05,06 to 11, 12 to 17, and 18 to 23 hrmdred-hours. The redts for the September
12, 1985 storm event are in Table 7.1 below. Tbe highst persisting 12-hr dew point for this event was 9.g°C, which occurred between the 00 to 1700 horns, on September 12,
1985.
Table 7.1: 12-hoar persisting dew point for September 12,19%S eC)
A problem arises with the selection of the highest persisting 12-hr dew pomt for each station, The only historical dew point temperature data available for Calgary was at the Airport. It is well known that dew point temperature varies with changes in elevation.
In an unsaturated parcel of air, the dew point temperature would decrease 1°C for every
100 m increase in elevation (Ahrens, 1994). Therefore, as the station elevation varies over Calgary, so does the dew point temperature. For the four storm events, the highest persisting 12-hr dew point temperature at the Airport can be adjusted using the dry adiabatic lapse rate and elevation. The elevation at the Airport is 1083 metres. The elevation at the rest of the stations tangs hm I031 to 1248 metres. Therefore, the highest persisting 12-hr dew pomt temperature for September 12, 1985 would vary from
10.3 to 8.2OC.
The next step for the detembation of the mxbhtion ratio was to determine the amount of precipitable water available based on the dew point temperatures. This was done using the WMO tables of precipitable water in a saturated pseudo-adiabatic atmosphere. A reproduction of these tables is provided m Appendix A. if the repmemtive petsisting 12-hr stom dew point on September 12, 1985 was
9.g°C, the maximum hrnFigure 7.1 was 17.9C, and the rain area was at an elevation of
1083 metres abve sea level, the moisture msucimisation ratio could be computed as follows. Wm= 42-13 = 29; W, = 214 = 13; and R, = 2.23. The precipitable water values used in determining Wmand W, were for a moisture cobwith a top at 300 rnb rninus the precipitable water for a column with the top at the elevation of the rain area
As Singh (1992) suggested, it is practical to assume a column top of 300 mb, Tbis makes sense when looking at the data using a tephigram. If the temperature values were reduced, using either the moist adiabatic lapse rate or the moist adiabatic line on the rephigram there is almost no significant precipitable water in the atmosphere above 300 mb.
These calculations were done at each station for each of the four stonevents. The
ktstep in calcubting the PMP value for the station was to muitiply the rainfsll amounts
by the moisture adjustment ratio. A complete listing of atl values used in the cdcutation
of the moisture adjustment ratio and tfie PMP are m Appendix B.
The finaI step is the construction of envelopment curves. However, on& one
duration period was cdculated, so the greatest calculated PMP due was seIected hr
each station This seiected value will be considered the greatest 24-hr probable
maximum precipitation possible for the selected station.
7.3. Rex&&
Tbe compIete list of moisture adjustment ratios can be seen in Table 7.2, while the
PMP values for each station are in TabIe 7.3. Table 7.2: Moisture Adjustment Rat& hrthe Calpy Rain stations
Table 7.2 shows stations having &rent moisture ad- ratios during the same storm events. This resulted fiom inctuding the station elevation m the computation of the moisture ad- ratio and by correcting the highest persisting 12-hr dew point temperatures for elevation, didearlier.
The point PMP dues for the four events are disphyed m Table 7.3. Each station's greatest PMP value has been highlighted in bold italics. All but two of the stations greatest PMP values occurred on the August 1, 1988 storm. Bowness adLincoln Park have their greatest PMP values on September 12, 1985. Tabk 73: PMP values Lr the Calgary R8in ststions, in millimetres
These values are deemed reasonable for Calgary. Verschuren and Wojtiw (1980) found average PMP values in the Bow River watershed of 260 mm for an area of 259 km2 and 201 mm for an area of 51 80 km2, using a much larger stom base. The city of
Calgary is located in the Bow Riwr wat- and covers an area just over 700 km2. The twenty-four rain stations in Calgary give m average PMP value of 21 1.9 mm for Calgary.
This value is consistent with the values found by Verschuren and Wojtiw (1980). 7.4. Co~n
The spa?ial pattern of the PMP values over Cdgaq was compared to the spatial pattern of the mean dmahum 24-hr middl values. Tbe purpose is to detamk if the variables that &ted the spatial pattern of heavy rainfall also &kt the PMP in
Calgary. Fii7.2 shows the pattern of PMP values over the city of CaIgary- A sirnilat pattern was visible when mean annual maximum 24-hr rainfdl atad PMP were mapped side by side (Figure 7.3).
One consistency between the two maps was the location of the high areas of raidik The spatial pattern of PMP shows bigher rain vahies over the areas of
Midnapore, Parkland. Spy Hi& and Edgemont. This finding is similar to mean annual maximum 24-hr rainfdL In addition, both maps showed the lowest amount of rain over the station of 68 Street Lake in the east part of Calgary. . Whenthe~vaIuesweremxmsedfor PMP cakuIation, tbe location of the high and low values rerrrained approximately coastant. The stations closer to the point of storm entry or with higher elevations appear to have higher PMP values. The spatial profles are simiIar, but not identical. This was due to the fact that the man annual maximum 24-hr raiddi dues are mean values of extreme annual events. PMP values are the greatest possible amount of rain that codd occur based on id4 weather conditions. It was not expected that the spert$l patterns would be identkaL The important point is that the locations of the high and low areas stayed rektiveiy constant.
The spatial profiles can be consided similar and provide a starting point kr undentadq the spatid pattern of probable precipitation. Fire72: PMP values over the city of Cdga y
Figure 73: Maps of mean a~dmasimom 24hr middl md PMP vaha for c* 7.5. Kfactor rrnd its distrbdrbn
In chapter 2, the Hershtield approach was suggested as a quick way to estimate
PMP for watersheds of no more than 1000 lad. In this approach, a constant (4is
utilised for the estimation of PMP. K is the number of standatd deviations added to the
mean rainfall of an area in order to estimate its probable maximum precipitation. It was
suggested that direct application of this method should be avoided since there is no
completely objective method for determining the K due in equation 2.5. However,
where PMP is available, K can be determiaed using equation 2.6.
Using r, and PMP values hmobjectives I and 2, K values can be estimated for
the stations in Calgary. The K value for each rain station in Calgary was calculated by
substituting the PMP for 4, , in equation 2.6, K values in Calgary range hm8 to 16,
Thus, the PMP exceeds the mean annual maximum 24-hr rainfid event by between 8 and
16 standard deviations depending on the station, The values were then used to produce a
map that shows the pattern of K over the city (Figure 7.4). K is highest in the west and
northwest and lowest in the east.
The map in Figure 7.4 could be used to estimate PMP for new communities. The K
due allows for the estimation of PMP values for Calgary based on mean annual
maximum rainfall data (Figure 5. I). u.c I
Fire7.4: Map of the K values for Calgay Chapter 8: Conclusion and Recommendations
8.1. Conclusiorrs
Seventeen years of extreme raiddl records fiom twenty-four rdomly distributed stations were analysed in the greater Calgary area The purpose was to understand the variability of heavy rahM events and to help identiij bigh-risk areas and aid decisions on improvements to drainage and flood mitigation programs. The principk findings are as fouows.
i. Pf- I for Calgary varies fkom 3 1.2 mm to 48.1 mm, with a mean of 38.0 elm and
a standard deviation of 4.3 mm The spatial pattern of P(-x- in Calgary k as
follows: a) high values m the south, b) lower values m the city centre. and c)
increased values in the north/northwest.
[I. A model which Links the spatial distniution of &all to distance dong the storm
trajectory and elevation provides reahtic point estimates for mean mm
midall. The model is consistent with the strength of storms at the entry point, a
weakening through city centre bmde-watering, and a recharge in tk northwest
due to increased elevation and upslope processes.
111. Based on a weak negative correlation between urban density and mean annual
maximum 24-hr rahhll, the former does not appear to be a major forcing Emor
m the djstriiution of the mean anuual maximum 24-hr raiddl at this point. There
is also no evidence that air pollution impacts the dkviiution of mean annual rnaximum 24-hr rainfall m a tmnner suggested by HUE(1975) and Chmgmn et
al. (198 1). Evidence of signijicaut downwind transport of plhrtants into the
northwest is weak (Alberta Environment, 2000). The phme abed by
Nkemdirim et al., (1975) into the downtown area does not appear to have
impacted the dumrain$n given the lower values of P6 ) observed
downtown
IV. Heavy minidl events in Calgary are associated with a moist low pressure cell
centred near Montana, a high pressure cell located to the northeast straddhg the
Manitoba-Saskatchewan border, a ridge of high pressure extending over a broad
zone fiom northern British Columbia through northern Aiberta, and a high-
pressure ridge covering Western Canada at the 50 kPa leveL These amngements
cause the north travelling storm to pass through southern Alberta then veer west
towards the mountains. The flow causes heavy rahMstorms in southem parts of
Calgary. The veer towards the mountains moves the storm upsIope through
northwest Calgary following the Bow river valley.
V. PMP for Calgary varies from 175.6 mm to 246 rmn, with a mean of 2 1 1.9 mm
and a standard deviation of 16.89 mm. The spatial pattern of PMP is similar to
pattern Fit m Calgary. stations the of the of xo I The cbsr to point norm entry or
with higher elevations have lager PMP vab.
VI, K values in CaIgary range hm8 to 16. Thus, the PMP exceeds the mean armual
Illtudmum24-hrdeventbybetween8to 16standarddeviatioasdepending
on the station. K is highest in the west and northwest and Iowest m the east. A map of K fbr Calgary allows for the &matian of PMP based on meaa aanual
maximum mhfdl data (Fii5.1).
point data obtained Eom a single Iocation may be inadequate for its purpose udess they are adjusted to reflect the various fbrces tbat control spatial patterns of the design variables. Communities in south and northwest Calgary could be chssilied as high-risk areas that my be susceptible to more hquent £hooding due to bvy raiddl events.
Therefore, it may be necessary to re-evaluate the drainage and flood mitigation devices in these communities.
8.2. Recommendations
The following recommendations are suggested based on the above conclusions.
The distance hm storm entry was a very kcrepresentation of the e&ts of storm
paths m Calgary. Data that would represent the microcbtes of each community may
improve the relationship of storm movement and midid variability. Readings of wind
speed and direction, tempera dew point temperatrrre, preswre, and precipitation
would aiIow for a better understanding of the efkts being experienced at each station
during a heavy or extreme rainfail event.
In addition there was no evidence at this time that urbanisation in Calgary affected
the distriin of maximum rainfaa Urban areas adthe spatial raiddl pattern they
dkt can be discrete (Goldreich, 1994). This may cause problems whtrying to
quantifjr leveIs of urbanisation. IbinMI enhancement hmudmiahn is expected to
occur as a city's population reaches one minion (Mcemdirhn, 1981). Calgary is rapidly approaching this population mark, and an efkt from mimisation may soon be visl'bk.
Measummts of atnmospheric pollution, subroughness, wind direction, and llrban fabric are important Elctors related to an iatra-urban dhihtion (?&-4 1981) and urbanisation (Changnun et aL, 1981). hap rove^ in mmte sensing technology, increased microclimate data at surmu~rain stations, and detailed land udand cover data. will help identify any future impacts of uhakation in mididl patterns.
In addition, storm rainfai of simihr voband intensities can produce djikent patterns of flood damage across a city (Nkemdirim and Kendrick, 1996). In Calgary,
Silver Springs and Ranchlands experienced the greatest number of hods due to rainstorms (City of Calgary Waste Water and Drainage. Rainstorm Report Series, 1979-
I997), yet they have some of the bwer mean annual maximum 24-hr rainfitlI and PMP values in Calgary. This indicates the need for data which goes beyond design storms m flood fkquency analysis. In conjunction with a DEM and Iand use data, the extreme mhfkll variability resufts could be used to construct an appropriate minfidl-runoff model
for Calgary. This would have important impIications in the area of urban hydrology and storm sewer design for the City. Cbapter 9: References
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No. 1. Geneva: World Meteorological Organisation. Appendii A: Tables of Precipitabk Water in a Satumted Pseudo-Adiabatic
Atmosphere (WMO 1973, Verschuren and Wojtiw 1980).
The general formula for computing precipitable water, W,in cm, is:
w =q&lgp where q is the mean specific humidity m gdkg of a Iayer of moist air, Ap is the depth of the layer in mb: g is the acceleration of gravity in cm/sec2: and p is the density of water, which is equal to 1 grn/m3.
In much of hydrometeorological work the atmosphere is assumed to contain the same amount of water vapour as saturated air with a saturation pseudo-adiabatic temperature lapse rate. The precipitable water in various layers of the saturated atmosphere can be precomputed and listed in tables or in nomogram form Table A1 presents values of precipitable water (mm) between the 1000 mb surfice and various pressure kvels up to 200 rnb in a saturated pseudo-adiabatic atmosphere as a hnction of the 100 mb dew point. Table A2 Iists simibr vbbr layers between the 1000 mb surfbce, assMled to be at zero elevation, aod various heiiup to 17 km Tabk A.1: Precipitabk wder (ram) between 1080 mb SPrhcc and indiited prwsarc (mb) in 1srtamted pscud~ad.hbaticatmosphere w a function of the 1000 mb dew point eC) (source: Veneburen and Wojtiw 1980).
mb 2 4 6 8 10 12 13 14 15 16 17 18 19 20 21 22 23 24 Table kt:Precipitabk water (mm)between 1000 mb surhce md indicated height (m) above that &et in r saturated pseudo-adiabatic atmosphere as a fimction of the 1000 mb dew point eC) (saarcc: Verscharm and WojtAv 1980). -
200 400 600 800 1000 1 ZOO 1400 1600 I800 2000 2200 2400 2600 2800 3000 Appendix B: Tabks showing the V&CS Used and the Cdcuhtions of the Rm md
PMP values. 12-Sep-85 01-Aug-88 r I Station Name Station ID Elevation (m) Dew-point Wm Ws rm Max rain PMP Dew-point Wm Ws rm Max rain PMP Airport 25 1083 9.8 29.0 13.0 2.23 92.6 206.6 9.0 41 .O 12.0 3.4 65.0 222.1 68 Street Lake 12 1058 10.1 29.0 13.0 2.23 73.4 163.7 9.3 41 .O 12.0 3.4 51.4 175.6 Bcmness 4 1071 9.9 29.0 13.0 2.23 88.0 196.3 9.1 41 .O 12.0 3.4 55.5 189.5 Cedarbrae I8 1 1 17 9.5 29,O 12.5 2.32 84.8 196.7 8.7 41 ,O 12.0 3.4 62,9 215.1 Coach Hill 13 1221 8.4 26.5 10.0 2.65 83.5 221.2 7.6 38.0 9.0 4.2 55.7 235.3 Downtown 14 1051 10.1 29.0 13.0 2.23 89.8 200,3 9.3 41.0 12.0 3.4 60.1 2053 Edgemont 3 I226 8.4 26.5 10.0 2.65 73.3 194.2 7.6 38.0 9.0 4.2 57.9 244.6 Foreat Heights 10 I068 9.9 29.0 13.0 2.23 81.7 182,2 9.1 41.0 12.0 3.4 56.9 194.5 Haysboro 19 1061 10.0 29.0 13.0 2.23 79.6 177.6 9.2 41 .O 12.0 3.4 65.0 222.2 Huntington Hills 6 1084 9.8 29.0 13,O 2.23 76.2 170.0 9.0 41 .O 12.0 3.4 61.6 2103 Liacoln Park 16 1 1 I6 9.5 29.0 12.5 2,32 85.2 197.7 8.7 41.0 12,O 3.4 57.6 196.8 Midaspore 20 1050 10.1 29.0 13.0 2.23 83.6 186.5 9.3 41,O 12,O 3.4 66.8 228.2 Mountainvlew 8 1081 9,s 29.0 13.0 2.23 91.6 204.3 9.0 41 .O 12.0 3.4 62.0 21 1.8 aden 22 1031 10.3 29.0 13.0 2.23 87.2 194.5 9.5 41.0 12.5 3.3 63.0 206.6 Parkland 2 1 1037 10.3 29.0 13.0 2.23 87.2 t 94.5 9.5 41 .O 12.5 3.3 69.4 227.6 Rosmrmk 15 1 144 9.2 29.0 12.0 2.42 82.0 198.2 8.4 41 .O 1 1.5 3.6 56.6 201.7 Shepard Lagoon 23 1032 10.3 29.0 13.0 2.23 82.4 183.8 9.5 41 .O 12.5 3.3 63.1 207.1 Silver Springs 2 1 166 9.0 29.0 12.0 2.42 68.8 166.3 8.2 41 .O 1 1 ,O 3.7 56.5 210.6 Spyhill I 1248 8.2 26.5 10.0 2.65 71.4 189.1 7.4 38.0 9.0 4.2 58.3 246.0 Temple 9 1094 9.7 29.0 13.0 2.23 84.9 189.4 8.9 41.0 12.0 3.4 62.2 212.5 Tuxedo 7 1092 9.7 29.0 13.0 2.23 84,8189.2 8.9 41.0 12.03.4 60.2 205.5 University 5 1 1 12 9.5 29.0 12.5 2.32 76,8178.2 8.7 41.0 12.03.4 55.2 188.6 West Dover I I 1063 10.0 29.0 13.0 2.23 86.6 193.2 9.2 41 .O 12.0 3.4 58.7 200.5 Windaor Park 17 1059 10.0 29.0 13.0 2.23 86.6 193.2 9.2 41 ,O 12.0 3.4 64.4 220.0 13Jun-92 l4Jun-92 Station Name Station ID Elevation (m) Dew-point Wm Ws rm Max rain PMP Dew-point Wm Ws rm Max rain PMP Airport 25 1083 9.2 37.0 12.0 3.1 44.6 137.5 9.3 37.0 12.0 3.1 33.4 103.0 6% Street Lake 12 1058 9.5 37.0 12.5 3.0 42.2 124.9 9.6 37.0 12.5 3.0 34.6 102.4 Bownesn 4 1071 9.3 37.0 12.0 3.1 47.0 144,9 9.4 37.0 12.5 3.0 47.0 139.1 Cedrrbne 18 1 1 17 8.9 37.0 12.0 3.1 65.8 202.9 9.0 37.0 12.0 3.1 54.6 168.4 Cwcb Hill 13 1221 7.8 34.010.03.4 52.4 178.2 7.9 34.0 10.0 3.4 54.0 183,6 Downtown 14 1051 9.5 37.012.53.0 44.4 131.4 9.6 37.0 12.5 3.0 45.4 134,4 Edgemoat 3 1226 7.8 34.0 10.0 3.4 60.0 204.0 7.9 34.0 10.0 3.4 66.2 2251 Fonst HeighQ 10 1068 9.3 37.012.03.1 42.0 129.5 9.4 37,O 12.5 3,O 34.2 101.2 Haysborn 19 1061 9.4 37.012.03.1 60.6 186,9 9.5 37.0 12.5 3,O 53.2 157,5 Huntington Hills 6 1084 9.2 37.0 12.0 3.1 44.4 136.9 9.3 37.0 12.0 3.1 38.8 1 19.6 Lincoln Park 16 11 16 8.9 37.0 12.0 3.1 56.2 173.3 9.0 37.0 12.0 3.1 52.8 162,8 Midnapore 20 1050 9.5 37.0 12.5 3.0 61.4 181.7 9.6 37.0 12.5 3.0 46.4 137.3 Mounbinview 8 1081 9.2 37.0 12.0 3.1 46.4 143.1 9.3 37.0 12.0 3.1 41.8 128.9 wen 22 1031 9.7 37.0 13.0 2.8 47.0 133.8 9.8 37.0 13.0 2.8 40.4 1 15.0 Psrklr nd 2 1 1037 9.7 37.0 13.0 2.8 58.8 167.4 9.8 37.0 13.0 2.8 43.6 124.1 Rossarmk 15 1 144 8.6 37.0 1 1.5 3.2 55.4 178.2 8.7 37.0 12.0 3.1 58.0 178.8 Shepard Lagoon 23 1032 9.7 37.0 13.0 2.8 42.6 121,2 9.8 37.0 13.0 2.8 34.2 97,3 Silver Springs 2 1166 8.4 37.0 11.5 3.2 52.2 167.9 8.5 37.0 1 1.5 3.2 44.6 143.5 Spybill I 1248 7.6 34.0 9.0 3.8 61.8 233.5 7.7 34.0 10.0 3.4 60.0 204.0 Temple 9 1094 9.1 37.0 12.0 3.1 47.4 146.2 9.2 37.0 12.0 3.1 35.2 108.5 Tuxedo 7 1092 9.1 37.0 12.0 3.1 46.2 142.5 9.2 37.0 12.0 3.1 42.6 131.4 University 5 1112 8.9 37.012.03.1 47.2 145.5 9.0 37.0 12.0 3.1 51.2 157.9 West Dovet I I 1063 9.4 37.0 12.0 3.1 39.4 121 .S 9.5 37.0 12.5 3.0 35.0 103.6 Windaor Park 17 1059 9.4 37.0 l2,O 3.1 48.2 148.6 9.5 37.0 12.5 3.0 46.2 136.8 a