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The use of climatic data to estimate irrigation water requirements in the south central interior of British… O'Riordan, Jonathan 1966

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THE USE OF CLIMATIC DATA TO ESTIMATE IRRIGATION WATER REQUIREMENTS IN THE SOUTH CENTRAL INTERIOR OF BRITISH COLUMBIA by JONATHAN O'RIORDAN M.A., University of Edinburgh,  1964  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF ARTS i n the Department of GEOGRAPHY  We accept t h i s thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA August, 1966  In presenting  t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f the requirements  f o r an advanced degree a t t h e U n i v e r s i t y o f B r i t i s h Columbia,, I agree t h a t t h e L i b r a r y s h a l l make i t f r e e l y study.  a v a i l a b l e f o r r e f e r e n c e and  1 f u r t h e r agree t h a t permission., f o r e x t e n s i v e  copying of t h i s  t h e s i s f o r s c h o l a r l y purposes may be g r a n t e d b y t h e Head o f my Department o r by h i s r e p r e s e n t a t i v e s .  I t i s understood that  o r p u b l i c a t i o n of" t h i s t h e s i s f o r f i n a n c i a l w i t h o u t my w r i t t e n p e r m i s s i o n ^  The U n i v e r s i t y o f B r i t i s h C o l u m b i a Vancouver 8, Canada  copying  g a i n s h a l l n o t be a l l o w e d  i.  ABSTRACT Climatic data observed at six meteorological recording stations i n the south central I n t e r i o r of B r i t i s h Columbia were used to analyse the temporal and geographical v a r i a t i o n s i n the frequency,  i n t e n s i t y and duration  of various climatic phenomena that a f f e c t the supply and demand of water by growing crops. of occurrence  Rather than using average values, the r e l a t i v e frequencies of each element or combination of elements were examined, i n  order that a more objective picture of the range of conditions experienced within the region during the growing season might be obtained. An inspection of the moisture supply patterns indicated that greater amounts of p r e c i p i t a t i o n tended to occur during the e a r l i e r h a l f of the growing season at most stations, the month of June experiencing a d e f i n i t e maximum.  However, natural p r e c i p i t a t i o n would appear to be less  e f f e c t i v e f o r plant growth than i t s absolute t o t a l s suggest, due to i t s tendency to be concentrated occurrence  into a few days per month.  An analysis of the  of wet and dry s p e l l s during the grovdng season using two proba-  b i l i t y models supported  these f a c t s , the highest frequency ©f wet s p e l l s  occurring i n June, while the lower p r o b a b i l i t i e s of wet spells i n July and August indicated an increase i n the length of dry spells during the second half of the growing season. Although i t i s known that at least four weather elements a f f e c t water l o s s by crops (radiation, temperature, wind and water pressure d e f i c i t ) , d a i l y data were only a v a i l a b l e f o r two of these elements, namely a i r temperature and r e l a t i v e humidity. frequencies of t h e i r occurrence  An examination of the r e l a t i v e  showed that the evaporative power of the s  a i r remained r e l a t i v e l y low u n t i l the end of June, a f t e r which i t increased sharply as these tw© elements combined i n such a manner that they i n t e n s i f i e d evaporation l o s s .  This fact was further i l l u s t r a t e d when t h e i r j o i n t d a i l y  ii.  Abstract - Continued observations were combined i n a frequency t a b l e , both J u l y and August experienc i n g the highest r e l a t i v e frequencies of t o r r i d days (hot days w i t h low r e l a t i v e humidities). The conclusions were f u r t h e r v e r i f i e d when the a c t u a l amounts of i r r i g a t i o n water were computed at selected s t a t i o n s by estimating p o t e n t i a l evapotranspiration rates from Penman's e m p i r i c a l formula and using the s o i l budget technique.  At a l l s t a t i o n s except L y t t o n , l i t t l e i r r i g a t i o n was required  i n most years u n t i l the beginning ©f J u l y , unless the s o i l s had low moisture storage c a p a c i t i e s , but from J u l y to September the required i r r i g a t i o n amounts were considerably higher, a f a c t that was due to both the increased dryness of the atmosphere and to the previous d e p l e t i o n of the r e a d i l y a v a i l a b l e s o i l moisture.  ACHJOWLEDGMENT S Many people, both i n Vancouver and V i c t o r i a , have kindly provided assistance i n the preparation of t h i s t h e s i s .  I n Vancouver, I would l i k e  to thank Br. M.A. Melton, my supervisor, for h i s c r i t i c a l evaluation of the f i n a l draft and h i s advice i n s t a t i s t i c a l methods and computer programming; Dr. J.D. Chapman for h i s h e l p f u l comments at a l l stages of the work and Dr. A.L. Parley who, as Project Supervisor f o r Agro-Climatological studies at the University (under A.R.D.A. administration) provided both moral and f i n a n c i a l support.  In V i c t o r i a , I would l i k e to acknowledge the prompt  assistance provided by Dr. W.H. Mackie and h i s s t a f f a t Gonzales  Observatory;  Mr. D. Pearson of the Geographical D i v i s i o n , Department o f Lands and Forests for his f r i e n d l y guidance and time devoted to answering my questions, arid to members of the Water Resources Service, who supplied much useful information.  August 1966.  Jonathan O'Riordan  TABLE OP CONTENTS /  /  /  Page ABSTRACT  i .  ACKNOWLEDGIIENTS  i i i .  LIST OF TABLES  iv.  LIST OF ILLUSTRATIONS  vi.  Chapter 1  INTRODUCTION . . . South Central B r i t i s h Columbia Review of L i t e r a t u r e Outline o f Thesis  2.  AN ANALYSIS OF PRECIPITATION PATTERNS Analysis of Synoptic Weather Patterns Analysis of R a i n f a l l P r o b a b i l i t i e s Summary  *3  3.  STATISTICAL ANALYSIS OF ¥ET AND DRY SPELLS . . . . . . . The Persistency Model The Markov Chain Model Summary  26  1  k. AN ANALYSIS OF TEMPERATURE AND HUMIDITY PATTERNS . . . . Analysis of Temperature Frequencies Analysis of Relative Humidity Frequencies Combination of Weather-Type Frequencies Summary  4?  5.  65  6.  THE FREQUENCY AND INTENSITY OF DROUGHT Review of L i t e r a t u r e Analysis of PE Frequencies The S o i l Moisture Budget SUMMARY AND CONCLUSIONS  .  / . . . . .  BIBLIOGRAPHY  81 85-89  APPENDICES I.  Cumulated Frequencies of Wet and Dry Spells at Selected Stations during the Growing Season 1935-1964.  I I . Additional Uses of the Markov Chain Model.  90  91 - 9  2  iv. LIST OP TABLES Table I. \> II.  III.  Page Average Dates o f Beginning and End of Growing Season at Selected Stations . . . . . .  14  E m p i r i c a l P r o b a b i l i t i e s of Observing P r e c i p i t a t i o n Amounts (Inches) Less than or Equal to S p e c i f i e d Values at Selected Stations, 1945-1964  19  E m p i r i c a l P r o b a b i l i t i e s of Observing Monthly P r e c i p i t a t i o n Amounts (Inches) Less than or Equal to S p e c i f i e d Values at Selected S t a t i o n s ,  1945 - 1964  IV. V.  .  21 - 22  The Average Number o f Rain Days per Month during the Growing Season, 1945-1964  23  R e l a t i v e Frequencies of Monthly R a i n f a l l per Rain Day at Selected S t a t i o n s , 1945-1964  24  VI.  Frequencies of Runs of Dry Days a t P r i n c e t o n ,  VII.  Frequencies of Runs of n or More Dry Days at Princeton, 1935-1964  . .  31  VIII.  Frequencies of Runs of E x a c t l y n Dry Days at Princeton, 1935-1964 . . . .  33  IX.  Frequencies of Runs of E x a c t l y n Dry Days at P r i n c e t o n , 1935-1964  34  X.  Frequencies of Runs of E x a c t l y n Wet Days at P r i n c e t o n , 1935-1964  35  XI.  S i g n i f i c a n c e of Constant P r o b a b i l i t i e s of Wet and Dry Days at Selected S t a t i o n s during the Growing Season  35  XII.  Regression. Analysis of Dry and Wet S p e l l s during the Growing Season at Selected S t a t i o n s  38  XIII.  I n i t i a l and T r a n s i t i o n a l P r o b a b i l i t i e s at Selected Stations 2 Observed Numbers f o r Computing X S t a t i s t i c s f o r the Month of A p r i l at Princeton . . . . . . . . . . . .  XIV. XV.  Months during the Growing Season f o r which the C h i Squares were S i g n i f i c a n t at the P = 5 per cent level •  40 44  45  L i s t of Tables - Continued Table XVI. XVII.  Page R e l a t i v e Frequencies of D a i l y Maximum Temperatures at Selected S t a t i o n s , 1945-1964 . . . .  51-53  R e l a t i v e Frequencies of D a i l y Minimum R e l a t i v e Humidities at Selected Stations 1957-1964  55 " 56  XVIII.  C l a s s i f i c a t i o n of Weather Elements used i n Table XIX.  57  XIX.  Temperature-Humidity Combinations at Selected S t a t i o n s ,  1957-1964  58 - 60  XX.  Accumulated Frequencies of T o r r i d Days per Month During the Growing Season  61  XXI.  Duration of T o r r i d Days at Selected Stations 1957-1964.  63  XXII.  Relative Frequencies of Monthly PE (Inches) at Selected Stations  69  XXIII.  Empirical P r o b a b i l i t i e s of Seasonal Supplemental I r r i g a t i o n Requirements (inches) at Selected S t a t i o n s .  7  Monthly Supplemental I r r i g a t i o n Requirements at Selected S t a t i o n s  76-80  XXIV.  2  vi. LIST OP FIGURES Figure  Page  1.  Location of t h e Region  la.  2.  Summer Moisture D e f i c i t ( a f t e r Thornthwaite) . .  4a.  3.  P r e c i p i t a t i o n Regimes at Selected S t a t i o n s . . .  15a.  4.  Average May-September P r e c i p i t a t i o n .  17a.  5.  Twenty P e r c e n t i l e May-September P r e c i p i t a t i o n .  18a.  1. CHAPTER I INTRODUCTION This t h e s i s attempts to analyse s t a t i s t i c a l l y the s p a t i a l and temporal v a r i a t i o n of the various c l i m a t i c elements that influence the supply and demand of a v a i l a b l e s o i l moisture f o r crop growth i n the semi-arid plateau and v a l l e y country i n the south c e n t r a l I n t e r i o r of B r i t i s h Columbia.  The  r e s u l t s of these analyses enable an o b j e c t i v e assessment of the amounts of i r r i g a t i o n water r e q u i r e d by crops to maintain optimum growth throughout the growing season. Since s u c c e s s f u l a g r i c u l t u r e i n t h i s a r i d and s e m i - a r i d country i s almost e n t i r e l y dependent upon i r r i g a t i o n , t h i s information i s e s s e n t i a l f o r the design of storage r e s e r v o i r s and i r r i g a t i o n systems and f o r the scheduling of i r r i g a t i o n programmes. South Central B r i t i s h Columbia South c e n t r a l B r i t i s h Columbia (Figure l ) has already experienced a r e l a t i v e l y lengthy h i s t o r y of a g r i c u l t u r a l development, yet s t i l l contains considerable a g r i c u l t u r a l p o t e n t i a l . The d e f i c i e n c y of a v a i l a b l e s o i l moisture f o r optimum crop development during the growing season i s one of the two major handicaps a f f e c t i n g p r o f i t a b l e a g r i c u l t u r e w i t h i n the region, the other being the high frequency of f r o s t s during the s p r i n g and autumn months.  Although f r o s t damage causes an annual l o s s of crops of v a r y i n g  i n t e n s i t y , the inadequacy of the r a i n during the growing season i s a more u n i v e r s a l problem and consequently one more s u i t e d f o r geographical i n v e s t i gation. The d i f f e r e n c e between the amount of moisture crops require and the amount they r e c e i v e from n a t u r a l p r e c i p i t a t i o n i s known as the moisture balance.  Figure 2 shows that the south c e n t r a l i n t e r i o r l i e s w i t h i n a  3. Most of the valleys i n the region receive between 10 and 20 inches annually, Ashcroft i n the Thompson Valley, with a yearly average of 7 inches, experiencing the lowest recorded p r e c i p i t a t i o n i n the whole of Canada.  Upland  p r e c i p i t a t i o n varies considerably, ranging from about 15 inches i n the area south and west of Kamloops to 40 inches on the ranges flanking the Columbia Mountains. Temperatures also r e f l e c t the importance average, temperatures  of t e r r a i n .  Generally,  drop with increasing a l t i t u d e , thus the sheltered v a l l e y s  experience average summer temperatures between 60° and 70°F, whereas the exposed uplands tend to be 5° to 10° cooler. Several other factors such as the proximity to large water bodies and the steepness and aspect of slopes play t h e i r part i n influencing temperature patterns. Vegetation The v a r i e t y of climates r e s u l t i n g from these r e l i e f and aspect variations i s indicated by the d i f f e r e n t plant and s o i l types d i s t r i b u t e d throughout  the region.  been distinguished^.  Three major a l t i t u d i n a l zones of vegetation have  At elevations below 2,000 feet, the combination of  summer heat and low p r e c i p i t a t i o n has allowed natural grasslands to develop. An association of perennial bunch grasses i s the main vegetation, though severe overgrazing has induced a mixed covering of sagebrush  (Artemesia  t r i d e n t a t a ) , rabbit brush (Chrysothamnus nauseosus) and other unpalatable shrubs and forbs.  Between 2,000 and 4,000 feet t h i s grassland zone i s  replaced by a mixed cover of grasses and trees known as the Dry Forest.  As  the name implies, the Dry Forest i s tolerant of moderately dry conditions. Bluebunch wheat grass (Antennaria dimorpha),  Columbia speargrass (Stipa  ^ R.H. Spilsbury and E.W. Tisdale, "Soil-rPlant relationships and v e r t i c a l zonation i n B r i t i s h Columbia", S c i . A g r i c , v o l . 24 (1944), 395-435.  4. columbiana) and Kentucky bluegrass (Antennaria p a r v i f o l i a ) are the native grass species, while the predominant trees are the Yellow Pine (Pinus  ponderosa)  at lower elevations and the Douglas f i r (Pseudotsuga m e n z e i s i i ) , which climaxes above 2,500 f e e t .  Local depressions and lakeshore l o c a t i o n s support stands of  Aspen (Populus tremuloides), Maple (Acer glabrum) and Mountain B i r c h (Betula fontinalis).  Plateau ridges above 4,000 feet c a r r y a sub-alpine vegetation  dominated by Spruce (Picea engelmanni) and Balsam P i r (Abies l a s i o c a r p a ) . Soils The s o i l types represented i n the area are c l o s e l y connected to the c l i m a t i c and vegetational complexes.  The Chernozemic (grassland) s o i l s ,  subdivided i n t o Brown, Dark Brown and Black s o i l groups, are associated w i t h the warm, dry s i t e s of the v a l l e y bottoms and lower slops up to about 2,500 feet.  In the semi-arid v a l l e y f l o o r s and on the south-facing slopes, where  summer moisture d e f i c i t s exceed 12 inches (see Figure 2) the Brown s o i l s have developed.  Due to the r e l a t i v e s p a r c i t y of the vegetation there i s  l i t t l e humus accumulation and the lack of leaching has allowed lime accumul a t i o n i n the upper horizons. drainage hollows.  S a l i n e and a l k a l i n e s o i l s can be seen i n l o c a l  Where the moisture d e f i c i t s are l e s s (4 to 8 i n c h e s ) , the  Dark Brown s o i l p r o f i l e has developed, the darker colour being due to the greater proportion of humus, which r e s u l t s from the decay of the greater d e n s i t y of grassland v e g e t a t i o n .  This zone extends i n t o the Black s o i l b e l t ,  which contains the most f e r t i l e s o i l s i n the r e g i o n . These appear on the upper grassland zones i n the south and more g e n e r a l l y i n the north-eastern s e c t i o n of the r e g i o n , where the r a i n f a l l i s consistent enough to maintain growth throughout the summer, yet not s u f f i c i e n t l y great to leach the humus and inorganic n u t r i e n t s down the p r o f i l e .  Increasing p o d z o l i z a t i o n occurs  at the higher elevations as the moisture balance swings from a d e f i c i t to a surplus - a r e s u l t of the combination of increased p r e c i p i t a t i o n and lower  5. temperatures.  Since most of the s o i l s have a n u t r i e n t base and s t r u c t u r e  s u i t a b l e f o r a g r i c u l t u r e , y i e l d s are high where moisture i s a v a i l a b l e from e i t h e r p r e c i p i t a t i o n or i r r i g a t i o n . Agriculture The region may be subdivided i n t o three subregions - the Okanagan V a l l e y , the Upland Plateau ( i n c l u d i n g the Thompson V a l l e y ) and the Praser Watershed. The Okanagan V a l l e y - In terms of farm cash income, the Okanagan V a l l e y i s the second most important a g r i c u l t u r a l region i n the province, ranking behind the Lower Praser V a l l e y . The t o t a l p o t e n t i a l arable acreage w i t h i n the region i s about 400,000 acres, of which i n I960 some 50,000 acres were under i r r i g a t i o n , most of which were i n orchard.  Nearly a l l the  orchards are found on the. s l o p i n g v a l l e y benches south o f Vernon i n the Okanagan V a l l e y and south-east of Keremeos i n the Similkameen V a l l e y .  The  combination of warmer summers and a longer f r o s t - f r e e season i n the southern part of the v a l l e y (115 days at Armstrong and 151 days at Osoyoos^) favours s o f t f r u i t and apple orcharding, whereas the northern end of the v a l l e y concentrates on apple orcharding and vegetable production.  Outside t h i s  f r u i t b e l t the farming i s more extensive and the emphasis s h i f t s t o g r a i n , hay and forage crops, i n conjunction with l i v e s t o c k r a i s i n g . The Upland Plateau - The rather uneven topography and short growing season (58 f r o s t - f r e e days at Joe Rich Creek ) r u l e out most of the plateau f o r c u l t i v a t i o n . However, the Grassland and Dry Forest vegetation have promoted beef c a t t l e and sheep ranching, which remains the only important  A . J . Conner, The f r o s t - f r e e season i n B r i t i s h Columbia. Met. Div. Dept. of Transport (Toronto, 1 9 4 9 ) . '. •  7  Ibid.  6.  a g r i c u l t u r a l a c t i v i t y on , the plateau.  Irrigated hay crops, which are grown  i n conjunction with the beef c a t t l e and sheep enterprises, occupy a large portion of the cultivated land, situated mostly i n the Nicola, Similkameen, and Thompson Valleys and around the lakes of the Merritt-Princeton Basin. Small but important areas of f r u i t and vegetable production are scattered along the benches of the Thompson between Lytton and Shuswap Lake and i n the WestwoId-Falkland Area.  A l l these enterprises are c l o s e l y connected to the  a v a i l a b i l i t y of water f o r i r r i g a t i o n , though natural p r e c i p i t a t i o n i s s u f f i c ient i n the Shuswap area and on the plateau south of Kamloops to allow land farming.  dry-  The Shuswap area i s an extension of the mixed l i v e s t o c k  economy found i n the northern part of the Okanagan Valley around Armstrong and Enderby.  P o t e n t i a l l y c u l t i v a b l e land, which i s widely scattered  throughout the area, t o t a l s approximately 100,000 acres. The Fraser Watershed - This south-western section of the region has l i t t l e a g r i c u l t u r a l p o t e n t i a l due to the rugged t e r r a i n of the Coast and Cascade Mountains.  Agriculture i s r e s t r i c t e d to the Fraser Valley around  Hope, which practices the mixed-livestock  farming found i n the Lower Fraser  Valley.  Review of the Literature Factors Influencing Crop Water Requirements This thesis assumes that the only natural source of moisture supply for crops i s p r e c i p i t a t i o n . However, the amount of water a crop demands to maintain maximum growth depends upon a number of external and within i t s environment.  The external factors may  internal factors  be subdivided  into two groups, namely atmospheric or c l i m a t i c , and edaphic.  vertically The atmosphere  i s the medium through which the external supply of energy ( i . e . solar radiation)  7-  g necessary to promote evapotranspiration  reaches the evaporating surface.  It  also removes the evaporated water vapour, a process which depends upon the wind 9 speed, a i r turbulence and vapour pressure d e f i c i t  .  The external factors  operating below ground l e v e l are the texture and structure of the s o i l , which determine the amount of moisture available to the plant and the rate at which i t can be absorbed by the plant r o o t s * . 0  The internal or plant factors i n f l u e n c i n g the rate of water loss can also be subdivided v e r t i c a l l y into those factors that operate above and below ground l e v e l .  Above ground l e v e l the albedo** of the crop determines how  much energy w i l l be absorbed by the plant surface.  Since water i s l o s t through  stomata on the l e a f surface, the size of this surface and the density of these stomata are other factors determining  crop water needs.  Underground, the  concentration and the v e r t i c a l d i s t r i b u t i o n of the root system of the plant a f f e c t s the rate of water loss throughout the s o i l p r o f i l e . An examination of the energy balance enables those c l i m a t i c elements that influence the rate of evapotranspiration to be defined.  The only d i r e c t  source of radiation i s solar r a d i a t i o n , which i n turn determines d i r e c t l y and i n d i r e c t l y both the a i r temperature and the saturation vapour pressure of the 12 atmosphere  .  The a b i l i t y of the atmosphere to absorb and transport the  moisture away from the evaporating surface depends upon the v e r t i c a l gradient of the vapour pressures and the effectiveness of the turbulent mixing above  g Evapotranspiration - the combined loss of water from the s o i l and plant surfaces. Q  Vapour pressure d e f i c i t - the difference between the actual and maximum pressure that the water vapour can exert at a given temperature. *° P.J. Kramer, "Factors a f f e c t i n g the absorption of water", Plant and S o i l Water Relationships (McGraw-Hill. 1949) Ch. 9, p. 212. ** Albedo - proportion of incident r a d i a t i o n that i s r e f l e c t e d . 12 C.B. Tanner, "Energy Balance approach to the evapotranspiration from crops", Proceedings S o i l Science Soc. America,Vol. 24 (i960) p. 1-9•  8. the surface  13  .  Therefore, the major meteorological elements a f f e c t i n g evapo-  transpiration within the atmospheric environment of crops are solar r a d i a t i o n , a i r temperature, wind speed and vapour pressure  deficit.  Since the r e l a t i v e effect of each of these four climatic elements on the rates of evapotranspiration varies considerably from climate to climate, any accurate estimation of their influence requires the direct c o r r e l a t i o n of observed water use with these variables i n the f i e l d .  Fortuna-  14 t e l y , such a study has been undertaken within the region. at Summerland i n the Okanagan Valley, concluded  Wilcox  , working  that solar r a d i a t i o n and a i r  temperature were the most important variables a f f e c t i n g evapotranspiration from lysimeters and evaporation from B e l l a n i plate  atmometers, though the  best estimates required the use of a l l four elements.  P e l t o n ^ , working i n 1  a s i m i l a r l y semi-arid climate at Swift Current, Saskatchewan, found that between 70 and 80 per cent of the v a r i a t i o n i n evaporation could be accounted f o r by a linear combination of these four v a r i a b l e s . '  These researchers and o t h e r s ^ have a l l v e r i f i e d s t a t i s t i c a l l y that 1  better r e s u l t s are obtained when equating climatic variables to evapotransp i r a t i o n i f a l l four elements are used. However, e a r l i e r works (Blaney 17 lg and Criddle and Thomthwaite being amongst the better known) used only  13 R.E. Munn, "Energy budget and mass transfer theories of evapor a t i o n " , Proceedings Second Canadian Hydrology Symposium (Toronto, 1961), 8-26. 14 • J.C. Wilcox, "The effect of weather on evaporation from B e l l a n i plates and evaporation from lysimeters", Can. Journ. Plant Science, V o l . 43  (1963),  1-11. 15  W.L. Pelton, "Evaporation from atmometers and pans",;; Can. Plant Science. Vol. 44 (1964), 397-404.  Journ.  W. Baier and G.W. Robertson, "Estimation of latent evaporation from simple weather observations", Can. Joum. Plant Science, Vol. 45 (1965)9 276-284. 17 H.P. Blaney and W.D. Criddle, "Determining water requirements i n i r r i g a t e d areas from c l i m a t o l o g i c a l and i r r i g a t i o n data"; U.S. Dept. of Agric. S.C.S. - TP-96 (Washington, D.C., 1950), 1-48. 18 Thornthwaite, l o c . c i t .  a i r temperature when d e r i v i n g their empirical equations f o r estimating evapotranspiration.  Only one investigator - Penman - has produced a formula that  19 uses these climatic variables .  Since he accounted for both the energy  balance and the aerodynamic factors, h i s equation produces the most accurate 20 r e s u l t s from observed meteorological data for most climates  , and has  therefore been used to estimate water loss i n t h i s t h e s i s . Agro-Climatological Studies i n the Region U n t i l recently l i t t l e research has been undertaken into the applied aspects o f a g r i c u l t u r a l climatology i n any part of the province.  Kerr  21  presented an exhaustive study of the v a r i a t i o n i n c l i m a t i c elements across the southern part of the province and Chapman study of the climate as a natural resource.  22  followed t h i s with a detailed  The most d e t a i l e d regional 23  climatology of part o f the province to date was published by Walker which.he attempted to improve the estimation of the mean annual  , in  rainfall  amounts on the unpopulated mountainous regions, through the analysis of the dynamic climatology of the middle and upper atmosphere. Recently, agro-climatic studies within the Province have received more attention under the patronage of a Federal-Provincial programme administered under the A g r i c u l t u r a l Rehabilitation and Development Act  19 H.L. Penman, "Natural evaporation from open water, base s o i l and grass", Proceedings Royal Soc. (London), Section A, Vol. 193 (1948), 120-14-5.  20  G.F. Makkink "Testing of Penman formula by means of lysimeters", Journ. Inst. Water Eng., Vol. 11 (1957), 277-288.  21  D.P. Kerr, "Regional Climatology of Southern B r i t i s h Columbia", (unpublished Ph.D. d i s s e r t a t i o n , Dept. of Geog., U n i v e r s i t y o f Toronto 1950)« 22 J.D. Chapman, "The Climate o f B r i t i s h Columbia", B.C. Nat. Res. Cpnf., No. 5 ( V i c t o r i a , B.C., 1952), 8-37. 23 Walker, l o c . c i t .  10. (A.R.D.A.).  In each province agro-climatological committees have been set  up to assess the climatic f a c t o r s that affect a g r i c u l t u r a l production and to produce maps of climatic zones s i g n i f i c a n t to crop production.  Chapman  24 and Brown  drew up a s e r i e s of maps on a national scale, showing the d i s t r i -  bution of several o f these climatic elements, while on the p r o v i n c i a l scale 25 Rheumer and O'Riordan  prepared a more detailed set of maps showing quanti-  tative d i s t r i b u t i o n s of derived climatic v a r i a b l e s .  The most detailed  research into the effects of climate on the rates of evaporation has been undertaken by Wilcox and his associates at the experimental  farm i n Summerland.  However, he was concerned with these climatic influences at a point and did not consider t h e i r geographical v a r i a t i o n throughout the region. Outline of the Thesis It i s the task of the climatologist to depict and explain the d i f f e r e n t climates that appear on a l l or part of the earth's surface. accomplish  t h i s , he must possess knowledge of the causal r e l a t i o n s h i p s and  conditions governing the occurrence may  To  of c l i m a t i c elements i n order that he  compare the climates as they vary from place to place.  and descriptive approach to climatology has been termined  This t h e o r e t i c a l synoptic climatology  by Court However, the climate of an area can also be analysed as one of man's most v i t a l natural resources.  The a p p l i c a t i o n of these t h e o r e t i c a l and  descriptive understandings of the climates of a region f o r the benefit of man  i s known as applied climatology. This thesis deals with t h i s aspect of  climatology. 24  L.J. Chapman and D.M. Brown, Climatic Maps of A g r i c u l t u r a l Areas of Canada, Ontario Research Foundation, Dept. of Physiography ^A.R.D.A., 1964) 5 G. Rheumer and J . O'Riordan, Agro-climatic Maps of B r i t i s h Columbia. (In p r i n t , Dept. of Agriculture, V i c t o r i a , B.C.). ~ 2  ^ A. Court, Court. "Climatology" "Climatology" Complex,dynamic and synoptic". Am.  2 6  Amer. Geog., Vol. 4? (l957;, 125-136.  Assoc.  11. I t uses various s t a t i s t i c a l techniques i n order t h a t . i t might o b j e c t i v e l y quantify the i n f l u e n c e of the s e v e r a l c l i m a t i c elements that influence the supply and demand f o r water by growing crops. From these r e s u l t s the amount of i r r i g a t i o n water required to maintain optimum growth throughout the growing season can be ascertained.  As t h i s work i s e s s e n t i a l l y a geogra-  p h i c a l study i t emphasises the s p a t i a l v a r i a t i o n of these c l i m a t i c elements and the consequent v a r i a t i o n i n the supplemental water need from place to place throughout the r e g i o n . Since c l i m a t i c observations are by nature subject to considerable v a r i a t i o n s , a representative p i c t u r e of the p r e v a i l i n g c l i m a t i c conditions i n a region can only be obtained through the examination of weather records observed over some period of time.  Therefore, t h i s t h e s i s r e l i e s e n t i r e l y  upon data observed at the meteorological recording s t a t i o n s s i t u a t e d w i t h i n the areas under study and which have been observing continuously f o r at l e a s t twenty years.  The d a i l y weather data were a v a i l a b l e i n the Monthly C l i m a t i c  Summaries published by the Meteorological Branch of the Department of Transport i n Toronto and the monthly data were abstracted i n a p u b l i c a t i o n issued f o r the province by the Department of A g r i c u l t u r e i n V i c t o r i a (see data sources i n b i b l i o g r a p h y ) .  C e r t a i n more d e t a i l e d weather observations  were made a v a i l a b l e to the w r i t e r by the s t a f f of Gonzales Observatory i n Victoria. I t has been known f o r a long time that the^mean values of c l i m a t i c s t a t i s t i c s have l i t t l e value i n a p p l i e d climatology, other than as a general guide to p r e v a i l i n g c l i m a t i c c o n d i t i o n s .  Therefore, a l l observed data used  i n the work are tabulated according to t h e i r frequency o f occurrence, from which selected e m p i r i c a l p r o b a b i l i t i e s of c e r t a i n s p e c i f i e d values may be obtained.  Frequency d i s t r i b u t i o n s of the a v a i l a b l e c l i m a t i c elements a f f e c t -  i n g crop water supply and demand, namely p r e c i p i t a t i o n , maximum d a i l y  12.  temperature, minimum d a i l y r e l a t i v e humidity and monthly evapotranspiration ( e m p i r i c a l l y derived) are presented.  Since none of these v a r i a b l e s was normally  d i s t r i b u t e d , i n each case an e m p i r i c a l method of determining the selected p r o b a b i l i t i e s was used i n order that a l l derived p r o b a b i l i t i e s be r e a l i s t i c . As the only form of water supply f o r crops, the seasonal and monthly p r e c i p i t a t i o n patterns were examined f i r s t .  Recently considerable a t t e n t i o n  has been d i r e c t e d towards the use of s t a t i s t i c a l techniques f o r estimating the p r o b a b i l i t y of wet and dry s p e l l s .  Since such s p e l l s a l t e r n a t e l y a f f e c t the  supply and demand of water, i t was thought that a r e a l i s t i c estimate of the p r o b a b i l i t y of t h e i r occurrence at various points w i t h i n the region would be a necessary part of the study.  To t h i s end, two of the better-known techniques,  namely the persistency model and the Markov Chain Model, were tested at selected stations. The frequency d i s t r i b u t i o n s of the two a v a i l a b l e c l i m a t i c elements a f f e c t i n g the demand of water by crops, namely maximum a i r temperatures and minimum r e l a t i v e humidity were then analysed.  As i t has been proved s t a t i s -  t i c a l l y that both of these elements play a s i g n i f i c a n t r o l e i n promoting water l o s s , t h e i r j o i n t e f f e c t was also analysed.  Prom the r e s u l t s o f these  comparative analyses and with the use of an e m p i r i c a l formula devised by Penman i t was possible to determine o b j e c t i v e l y the water requirements f o r optimum plant growth as they vary i n both time and space w i t h i n the r e g i o n . F i n a l l y , the information obtained from these analyses on both the supply and demand f o r water was combined by means of the s o i l moisture budget technique, and selected p r o b a b i l i t i e s of the a d d i t i o n a l water requirements necessary to s u s t a i n crop growth were tabulated at s e l e c t e d s t a t i o n s on a monthly and seasonal  basis.  13. CHAPTER 2 AN ANALYSIS OP PRECIPITATION PATTERNS The only important s i n g l e c l i m a t i c element a f f e c t i n g the amount of moisture a v a i l a b l e f o r crop growth and, t h e r e f o r e , the crop water supply of any region i s p r e c i p i t a t i o n . Because drought, i n i t s a g r o c l i m a t o l o g i c a l sense,  is  perennial i n the southern I n t e r i o r of B r i t i s h Columbia, the a g r i c u l t u r a l i s t must r e l y on i r r i g a t i o n to supplement the meagre n a t u r a l r a i n f a l l during the growing season.  However, both the supply of water f o r i r r i g a t i o n and the  i n t e n s i t y of the drought depend upon the amount of p r e c i p i t a t i o n f a l l i n g w i t h i n the r e g i o n from year to year and, therefore, v a r i a t i o n s i n precipitation patterns i n both time and space are of c r i t i c a l importance to a g r i c u l t u r e . There are t h i r t y - e i g h t stations with a period of record extending over at l e a s t twenty years, most of them s i t u a t e d i n the p r i n c i p a l v a l l e y s . Out of these s t a t i o n s s i x were chosen f o r the more d e t a i l e d c l i m a t i c analyses, since they maintained d a i l y observations of the various c l i m a t i c elements that a f f e c t water l o s s .  These s i x s t a t i o n s are Hope, Lytton, P e n t i c t o n , P r i n c e t o n ,  Vernon and Kamloops and, as may be seen from Figure 2, they are r e l a t i v e l y evenly spaced across the region and therefore should present a representative c r o s s - s e c t i o n of a r e a l c l i m a t i c changes w i t h i n the more s e t t l e d a g r i c u l t u r a l sections of the r e g i o n . Since t h i s t h e s i s analyses weather elements that a f f e c t a g r i c u l t u r a l crop growth, only growing season p r e c i p i t a t i o n patterns w i l l be examined i n detail.  From Table 1 i t can be seen that the s t a r t of the growing season f a l l s  around the end of March at the s i x selected s t a t i o n s and ends i n l a t e October or e a r l y November. the r e g i o n  1  In accordance with known a g r i c u l t u r a l p r a c t i c e s w i t h i n  the growing season i s assumed t o extend from A p r i l to September  R. K. Kreuger, "The p h y s i c a l b a s i s of the orchard industry i n B r i t i s h Columbia", Geo. B u l l . , V o l . 19 (1963), 5-38. 1  14. inclusive. Table I - Average Dates of Beginning and End of the Growing Season at Selected S t a t i o n s . (Based on 42 P Threshold Temperature) Station  Average F i r s t Day  Average Last Day  Hope  March  11th  November 8th  Lytton  March 19th  November 6th  Penticton  March 27th  November 1st  Princeton  A p r i l 10th  October 22nd  Vernon  March 30th  October 28th  Kamloops  March 25th  October 29th  i  A n a l y s i s of Synoptic Weather Patterns The P a c i f i c anticyclone dominates the pressure patterns over the e n t i r e province during the six-month p e r i o d , the mean J u l y p o s i t i o n of i t s centre being 38°N and 1 5 0 ° ^ .  A ridge extends up the coast to Alaska, sending  a p r e v a i l i n g north-westerly a i r stream over the C e n t r a l I n t e r i o r .  This dry,  subsiding a i r i s f u r t h e r s t a b i l i z e d by i t s descent of the c o a s t a l mountains i n t o the v a l l e y s of the r e g i o n , b r i n g i n g the g e n e r a l l y c l e a r skies f o r which the region i s famed during the summer months.  To the south a thermal trough  extends from the C e n t r a l V a l l e y of C a l i f o r n i a i n t o the Intermontane Basin. This o c c a s i o n a l l y e s t a b l i s h e s a flow of very warm, dry, t r o p i c a l c o n t i n e n t a l a i r i n t o the region, r e s u l t i n g i n the h o t t e s t summer weather i n southern B.C. To the  n o r t h , weather disturbances from the P a c i f i c gyrate around the  a n t i c y c l o n i c c e l l o c c a s i o n a l l y b r i n g i n g cloud and showers t o the northern parts of the r e g i o n , with greater amounts of p r e c i p i t a t i o n on the h i l l s as a r e s u l t of induced c o n d i t i o n a l i n s t a b i l i t y .  By September, the P a c i f i c anticyclone  has receded southwards, while pressure deepens o f f the A l e u t i a n s , marking  Kerr, l o c . c i t .  15. the gradual return to winter conditions. The summer p r e c i p i t a t i o n regimes (Figure 3) indicate a t r a n s i t i o n from the west coast maritime pattern i n the west to a more continental pattern i n the east.  At Hope the primary maximum occurs during the cool season when  the large average p r e c i p i t a t i o n t o t a l s are a r e s u l t of moist P a c i f i c a i r being funnelled up the Fraser Valley and forced to r i s e over the Cascades. The r e s u l t i n g p r e c i p i t a t i o n on the mountains also f a l l s i n t o the narrow v a l l e y f l o o r - a phenomenon known as the "canyon effect ! • By mid-summer, however, the 1  establishment  of the more stable anticyclonic c i r c u l a t i o n lowers p r e c i p i t a t i o n  t o t a l s generally over t h i s southwestern corner of the region. A l l other i n t e r i o r stations show a marked warm season maximum i n June that deserves some comment.  An analysis of the average l a t i t u d e of the  centre of the P a c i f i c anticyclone over a period of twenty years indicates that i t maintains a p o s i t i o n of about 34°N during May and June and then i n early o 3 July i t s h i f t s abruptly northwards to about 40 N . While i t i s at i t s southe r l y May-June location, a trough at the 500 mb l e v e l develops, inducing a flow of moist maritime a i r from the P a c i f i c Ocean into the region. wet  The short  season of early summer i s the r e s u l t , but when the P a c i f i c high suddenly  s h i f t s northwards and eastwards i n early July, the c i r c u l a t i o n pattern changes, the region coming under increasing anticyclonic control with i t s associated subsidence.  This a n t i c y c l o n i c s i t u a t i o n i s maintained u n t i l the southward  movement of the Jet Stream and i t s associated weather disturbances once again increase the number o f wet days. The actual p r e c i p i t a t i o n during the growing season appears to be controlled by upper l e v e l disturbances rather than convectional influences. G.T. Trewartha, Earth's Problem Climates Press, 1962), p. 2?6. 7  (University o f Wisconsin  Fig. 3  PRECIPITATION REGIMES AT SELECTED STATIONS  10-  HOPE  PENTICTON  LYTTON  " fi-l o  2-  J F M A M J J A S O N D  J  PRINCETON  (A 0)  F M A M J  J A S O N D  VERNON  J  F M A M J J A S O N D  KAMLOOPS  42-  J F M A M J J A S O N D  J F M A M J J A S O N D  J F M A M J J A S O N D  16. Outbreaks of cold a i r from the A r c t i c are i n j e c t e d i n t o the upper atmosphere and, according to Walker , a b a r o c l i n i c zone surrounding such masses of cold a i r i s subject to small disturbances which cause i n t e n s i f i e d u p l i f t as adjacent parts of the cold core.  Since such i n s t a b i l i t y reaches maximum  amplitude i n the middle and upper troposphere, i t i s r e l a t i v e l y unaffected by surface t e r r a i n , b r i n g i n g wet weather t o h i l l s and v a l l e y s a l i k e .  Pincock^  found a c o r r e l a t i o n between such pressure systems and the height of the 500 mb surface, but no s i g n i f i c a n t c o r r e l a t i o n w i t h the 1000 mb surface.  Walker  noted that the maximum frequency of such " c o l d lows" occurred i n June ( c o i n c i d i n g w i t h the p r e c i p i t a t i o n maximum) when, on average, four such disturbances ;  may cross the southern i n t e r i o r .  The i n c r e a s i n g s t a b i l i t y of the upper atmos-  phere, coupled with the l e s s frequent outbreaks of c o l d a i r from the A r c t i c , reduces the p r o b a b i l i t y of t h e i r occurrence i n l a t e r months. Map of Average Growing Season P r e c i p i t a t i o n Since the large m a j o r i t y of the meteorological recording s t a t i o n s are s i t u a t e d on the v a l l e y f l o o r s , i t i s d i f f i c u l t t o obtain a representative p i c t u r e of the growing season p r e c i p i t a t i o n amounts over the whole area from these sources alone.  By i n s p e c t i o n of the s t a t i o n records, however, i t  appeared that the r a i n f a l l tended to increase w i t h e l e v a t i o n and l a t i t u d e , e s p e c i a l l y i n the eastern s e c t i o n of the a r e a .  Therefore, an estimation of  r a i n f a l l on the plateau surface was obtained from an a n a l y s i s of the r e g r e s s i o n of mean growing season p r e c i p i t a t i o n with l a t i t u d e and a l t i t u d e .  Eighteen  s t a t i o n s i n the Okanagan V a l l e y area were used i n the regression  analysis.  The m u l t i p l e c o e f f i c i e n t of c o r r e l a t i o n was 0.70 ( s i g n i f i c a n t at the 95$ confidence l i m i t ) and the regression equation, determined by the method of l e a s t squares,  was:  __ Walker, Loc. c i t .  >  17. A  Y  -82.26 + 0.00095X  A Y  estimate of mean growing season p r e c i p i t a t i o n i n inches,  1  +  l.?W  2  -  1.32  (1)  where  elevation i n feet. l a t i t u d e i n degrees. Since t h i s map considered plateau areas as w e l l as v a l l e y areas, the growing season was assumed to extend from May to September i n c l u s i v e . A map of the mean growing season p r e c i p i t a t i o n was prepared for the area (Figure k), using t h i s equation to estimate p r e c i p i t a t i o n t o t a l s where necessary on the plateau areas.  While almost the e n t i r e region receives l e s s  than 10 inches during the five-month p e r i o d , there are three regions that on average receive l e s s than f i v e inches.  "~~" J  These are the Thompson V a l l e y s e c t i o n ,  l y i n g between Lytton and Kamloops, the M e r r i t t Lowlands and the southern end of the Okanagan V a l l e y and Lower Similkameen V a l l e y s e c t i o n s .  Local topographic  i n f l u e n c e s play t h e i r part f o r a l l three areas l i e i n the immediate lee of high mountain chains, which increase the drying and s t a b i l i s i n g e f f e c t s on the P a c i f i c a i r masses as they descend over the c o a s t a l mountains.  The Thompson  dry b e l t l i e s behind the Marble Mountains and the South Okanagan and S i m i l kameen behind the Cascades.  Often convectional cumulus and cumulo-nimbus  clouds w i l l appear above the ridges i n response to intense heating, but seldom do such cloud systems produce measurable r a i n f a l l i n the v a l l e y s . Apart from these areas, the map does i n d i c a t e a tendency f o r the r a i n f a l l to increase towards the north and east due to the i n c r e a s i n g frequency of weather disturbances i n the n o r t h and the "approach e f f e c t " of the P u r c e l l Mountains i n the east.  This equation i s e f f e c t i v e for e l e v a t i o n s between 1,000 and 4,000 feet and l a t i t u d e s between 49 N and 51 N.  18. Analysis of R a i n f a l l P r o b a b i l i t i e s I t i s w e l l known that mean values of p r e c i p i t a t i o n have l i t t l e value i n semi-arid regions, since the r a i n f a l l d i s t r i b u t i o n s are invariablyskewed from the normal.  Although u s e f u l as a general summary of r a i n f a l l  c o n d i t i o n s , they cannot be used to make statements about the p r o b a b i l i t y that p r e c i p i t a t i o n of a c e r t a i n magnitude w i l l occur i n a given month or season. To make such statements an a n a l y s i s of the p r o b a b i l i t y d i s t r i b u t i o n s i s required. Several techniques f o r making p r o b a b i l i t y estimates were i n v e s t i g a t e d . One of the simplest, the logarithmic transformation, was found t o be s u i t a b l e to estimate c e r t a i n selected confidence i n t e r v a l s f o r a large number of s t a t i o n records and therefore could be used for mapping purposes.  Figure 5 shows the  d i s t r i b u t i o n of the 20 p e r c e n t i l e i s o l i n e s w i t h i n the r e g i o n .  This e m p i r i c a l  p r o b a b i l i t y means that the stated amount of p r e c i p i t a t i o n or l e s s w i l l occur during two growing seasons i n t e n .  The map does show how meagre the r a i n f a l l  can be during the five-month p e r i o d , l e s s than 5 inches o c c u r r i n g at a l l low e l e v a t i o n s , but i t emphasises more strongly the i n c r e a s i n g a v a i l a b i l i t y of r a i n f a l l towards the north-eastern p o r t i o n of the r e g i o n . To o b t a i n more d e t a i l e d p r o b a b i l i t y estimates f o r the s i x selected s t a t i o n s , an e m p i r i c a l method of data a n a l y s i s f o l l o w i n g Kanglesir and  7 Green  was chosen.  Each r a i n f a l l s e r i e s was arranged i n order of i n c r e a s i n g  values, and the p r o b a b i l i t y value assigned to each of the ordered observat i o n s i s equal to pfo = 100m/(n + l ) , where m i s the order of the observation Q and n the t o t a l number of the s e r i e s .  Table I I  shows the amounts of  7 P.C. Kangleser and C,R. Green, P r o b a b i l i t i e s of P r e c i p i t a t i o n at Selected Points i n Arizona, Tech. Report No. 16, I n s t . Atmos. Physics (TucsonJ U n i v e r s i t y of Arizona, 1965), 1-7• 8 U n i v e r s i t y Press, E . J . Gumbel, 1958), Sp.29. t a t i s t i c s of Extremes, (New York: Columbia  19. r a i n f a l l to be expected during the s i x months growing season ( A p r i l t o September) at various s p e c i f i e d p r o b a b i l i t i e s at each of the s i x synoptic s t a t i o n s w i t h i n the r e g i o n . Table I I - E m p i r i c a l P r o b a b i l i t i e s of Observing P r e c i p i t a t i o n Amounts (inches) Less than or Equal to S p e c i f i e d Values f o r the Growing Season at Selected S t a t i o n s ,  (1943 - 1964).  Hope  Lytton  Penticton  9.69  2.91  4.28  3.67  5.57  3.45  13.78  3.53  4.61  4.67  5-58  4.13  50  15.60  4.31  5.41  5.39  6.73  5.23  75  18.26  5.08  6.69  6.24  9.32  6.28  90  21.65  5.72  8.13  8.30  11.28  7.25  95  26.81  7.22  13.28  11.87  13.09  9.80  10  Princeton  Vernon  Kamloops  The t a b l e i n d i c a t e s that Hope and the Lower Praser Canyon area r e c e i v e f a i r l y large amounts of p r e c i p i t a t i o n i n most years compared with the other s t a t i o n s .  I t a l s o shows j u s t how inadequate the n a t u r a l r a i n f a l l can be  f o r a g r i c u l t u r e i n other parts of the region, l e s s than 3" occurring at Lytton once a decade on average, while the i n c r e a s i n g r e l i a b i l i t y of r a i n f a l l east o f Kamloops i s underlined by the f i g u r e s f o r Vernon (over 9" once i n four y e a r s ) . The e f f e c t i v e n e s s of p r e c i p i t a t i o n f o r crop growth depends both upon i t s absolute amount and the t i m i n g of i t s occurrence during the growing season.  Therefore monthly p r o b a b i l i t i e s of p r e c i p i t a t i o n amounts were  tabulated f o r each of the s i x months of the growing season at each of the selected s t a t i o n s (Table I I I ) .  E x a c t l y the same procedure was used t o o b t a i n  the e m p i r i c a l p r o b a b i l i t i e s of these t o t a l s as was o u t l i n e d e a r l i e r . The prominence of June as the only "wet" month at a l l s t a t i o n s can  20. be seen from an examination of the t a b l e , though L y t t o n s t i l l may receive l e s s than h a l f - a n - i n c h once i n every four years.  The p r e c i p i t a t i o n t o t a l s of a l l  other months are extremely u n r e l i a b l e , any one of them r e c e i v i n g no r a i n at a l l at most stations apart from Hope.  However, despite the r e l a t i v e l y large  6-month t o t a l s at Hope (see Table I I ) ,  the i n c r e a s i n g dominance of the stable  a n t i c y c l o n i c a i r masses over the area from May to August i s i n d i c a t e d by the observation of low amounts (less than an inch) at the lower p r o b a b i l i t i e s .  In  any year any of these months may be extremely dry, making i r r i g a t i o n e s s e n t i a l i f f u l l crop growth i s t o be maintained. this table.  Two other f a c t s should be noted from  F i r s t l y , the prominence of the June maximum appears to increase  towards the north of the region, as i n d i c a t e d by the f i g u r e s f o r that month at Vernon and Kamloops and, t o a l e s s e r extent, at L y t t o n .  This i s i n accord-  ance w i t h the paths of the " c o l d low" weather disturbances, which migrate down from the n o r t h .  Secondly, the highest maxima (95?^ p r o b a b i l i t y ) do not  always occur i n June but o f t e n i n August, when cT a i r from the south i s a more frequent v i s i t o r , accompanied by thunderstorm a c t i v i t y . Number of Days per Month with S p e c i f i e d L i m i t s of P r e c i p i t a t i o n Increasing the d e t a i l of the a n a l y s i s of p r e c i p i t a t i o n patterns another step, the a c t u a l d i s t r i b u t i o n of the r a i n f a l l throughout each month was also examined.  P r e c i p i t a t i o n e f f e c t i v e n e s s f o r crop growth depends  9 upon t h i s f a c t o r r a i n days*  0  and, t h e r e f o r e , the a c t u a l d i s t r i b u t i o n of the number of  per month during the growing season was analysed (Table  IV).  L. C u r r i e , "The c l i m a t i c resources of i n t e n s i v e grassland farming", Geog. Review, V o l . 52 (1962), 174-194. * ° Rain day i s defined as a day when at l e a s t 0.01 inch of r a i n fell.  21. Table I I I  - E m p i r i c a l P r o b a b i l i t i e s of Observing Monthly P r e c i p i t a t i o n Amounts (inches) Less than or Equal to S p e c i f i e d Values at Selected Stations, (1945 - 1964).  Hope M  April  10  May  June  July  August  September  1.46  0.79  0.66  0.48  0.51  0.76  5  2.36  1.06  1.61  0.83  1.15  2.28  50  4.23  1.72  2.00  1.15  1.53  3.18  75  5.65  3-18  2.95  1.87  2.48  5-57  90  7.75  4.32  4.05  2.91 .  3.39  7.06  95  10.22  4.92  4.09  3.11  5.71  7.85  2  Lytton  SL'-  April  May  June  July  August  September  10  0.07  0.02  0.16  0.06  0.07  0.21  25  0.26  0.17  0.45  0.11  0.24  0.52  50  0.52  0.50  0.84  0.46  0.44  0.82  75  0.97  1.03  1.06  0.89  0.90  1.26  90  1.65  1.47  1.62  1.00  1.93  1.76  95  1.71  1.6?  2.02  1.13  3.12  2.69  September  Penticton Ffo  April  May  June  July  August  10  0.08  0.1?  0.54  0.27  0.05  0.11  25  0.36  0.61  1.22  0.51  0.33  0.18  50  0.66  0.89  1.42  0.95  0.69  0.50  75  1.42  1.65  1.82  1.29  1.30  1.04  90  2.32  2.04  2.62  1.86  1.77  1.47  95  2.74  2.26  2.88  2.02  2.84  2.17  22.  Table I I I  - Continued  Princeton April  May  June  July  August  September  10  0.08  0.08  0.67  0.19  0.12  0.28  25  0.22  0.34  O.76  0.59  0.40  0.45  50  0.39  0.91  1.09  0.81  0.78  0.57  75  0.78  1.49  1.83  1.48  1.24  1.07  90  1.28  2.15  2.29  2.41  2.26  1.51  95  1.36  3.0?  2.92  2.50  3.48  2.1?  p£  April  May  June  July  August  September  10  0.33  0.47  0.70  0.32  0.29  0.33  25  0.38  0.96  0.88  0.43  0.34  0.68  50  0.52  1.35  1.91  1.11  1.09  0.87  75  0.94  1.81  2.05  1.33  1.66  1.66  90  1.69  2.08  2.98  1.88  2.38  2.80  95  2.43  2.42  4.97  2.04  3.43  3.09  ?1  April  May  June  July  August  September  10  0.09  0.14  0.34  0.15  0.15  0.04  5  0.25  0.39  0.63  0.31  0.63  0.15  50  0.35  0.60  1.14  0.94  0.96  0.59  75  0.60  0.94  2.18  1.62  1.48  1.09  90  1.15  1.39  3.10  1.86  1.84  1.67  95  1.78  1.53  3.25  2.89  3.14  2.20  Vernon  iCamloops  2  '  23. Table IV - The Average Number of Rain Days per Month During the Growing Season,(1945 - 1964). Station  . A_  _M  J  J  A_  18  13  15  7.  10  11  74  6  6  6  4  .5  7  34  Penticton  10  10  11  6  7  8  52  Princeton  8  8  10.  6  7  8  47  Vernon  9  9  11  6  7  8  50  Kamloops  6  8  10  8  7  7  46  Hope Lytton  Total  The r e l a t i v e l y high t o t a l number of r a i n days at Hope (74) and low number of r a i n days at Lytton (34) i s emphasized, the other s t a t i o n s f o l l o w i n g t h e i r own remarkably s i m i l a r p a t t e r n .  However, the a c t u a l number of days per month i s  subject t o remarkable f l u c t u a t i o n s from year to year;  f o r example, at Kamloops  40% of the J u l y and August r a i n f a l l occurs on one day i n each month on average**. Although the summer r a i n f a l l amounts d i s p l a y a tendency to be concentrated i n t o a few days, there does not appear to be a high convectional c h a r a c t e r i s t i c about them. Tables showing the r e l a t i v e frequencies of selected amounts o f r a i n f a l l per r a i n day (Table V) i n d i c a t e that at a l l the s t a t i o n s , apart from Hope, 60% or more of the t o t a l r a i n days measure 0.1" or l e s s , and over 80% measure under 0.25".  With t h e i r low monthly t o t a l s one  would expect p r o b a b i l i t i e s of large amounts per r a i n day to be very low. Admittedly, the a c t u a l time span of d a i l y r a i n f a l l amounts was not considered (hourly i n t e n s i t i e s were hot a v a i l a b l e at any s t a t i o n ) , but high frequencies of such low amounts are not g e n e r a l l y associated w i t h semi-arid c l i m a t i c conditions.  The t a b l e s do show a greater frequency of l a r g e r d a i l y amounts  during the mid-summer months at a l l s t a t i o n s apart from Hope, which again emphasises 'that'-this s t a t i o n belongs to the maritime c l i m a t i c type r a t h e r than the i n t e r i o r type. * * Kerr, l o c . c i t .  Table V - R e l a t i v e Frequencies of Monthly R a i n f a l l per Rain Day at Selected Stations,(1945 - 19,64). Hope  Percent June July  Inches  April  May  > 0.12 0.12 - 0.25 0.25 - 0.50 0.50-1.00 1.00 + •  47.57 21.93 17.25 11.25 2.00  50.12 25.56 16.70 7.34 0.05  52.17 27.43 10.98 8.69 0.60  61.15 19.83 12.80 5.78 0.50  50.16 26.40 13-20 8.25 1.93  41.57 18.97 19.27 12.95 7.22  69.79 14.58 10.41 4.68 0.55  59.05 22.32 10.63 6.38 1.59  59.13 21.50 13.97 5.37 0.00  58.82 17.64 11.76 4.54 0.00  60.24 22.98 9.93 6.21 1.50  52.83 28.77 11.32 7.07 0.00  Penticton > 0.12 0.12 - 0.25 0.25 - 0.50 0.50 - 1.00 1.00 +  74.14 13.26 9.18 3.06 0.33  63.63 23.05 8.44 4.22 0.66  62.42 23.96 6.21 7.10 0.33  58.06 23.11 12.90 4.83 1.07  69.16 15.85 11.89 3.08 0.00  69.13 19.13 8.69 3.04 0.00  Princeton ' >0.12 0.12 - 0.25 0.25 - 0.50 0.50 - 1.00 1.00 +  79.66 14.40 5-50 0.50 0.00  64.23 23.46 8.84 2.69 0.05  60.32 24.83 10.00 4.51 0.33  61.49 20.85 12.29 4.27 1.02  59.54 25.00 10.00 4.54 1.04  62.99 25.55 8.81 2.64 0.00  75.53 16.90 6.83 0.30 0.30  60.00 23.57 12.14 3.92 0,30  61.6? 23.65 8.98 4.79 1.00  60.20 19.89 13.77 6.12. 1.00  59.32 23.30 12.28 4.23 1.00  61.94 23.48 11.33 2.02 1.21  71.83 20.34 6.56 0.?1 0.76  67.77 24.71 5.12 2.40 0.00  53-60 27.55 14.84 3.91 0.00  61.11 19.15 14.14 4.68 0.92  62.55 20.65 12.05 4.37 0.48  62.57 24.22 10.21 2.80 0.00  '  August  September  Lytton . 0.12 0.25 0.50 1.00  > +  0.12 0.25 0.50 1.00  Vernon 0.12 0.25 0.50 1.00  > +  0.12 0.25 0.50 1.00  Kamloops 0.12 0.25 0.50 1.00  > +  o.u 0.25 0.50 1.00  25. Summary An a n a l y s i s of p r e c i p i t a t i o n patterns during the growing season i n d i c a t e s that while r a i n f a l l amounts are g e n e r a l l y inadequate f o r vigorous crop growth throughout the lower parts of the area, the drought i n t e n s i t y v a r i e s from place to place w i t h i n the r e g i o n .  The Thompson V a l l e y , M e r r i t t  Lowlands and South Okanagan V a l l e y are notable dry spots  w h i l e , i n comparison,  the Horth Okanagan and Shuswap areas receive considerably more moisture, e s p e c i a l l y i n May and June. Although high i n t e n s i t i e s were infrequent, there was a tendency f o r 12 e f f e c t i v e r a i n f a l l s ( i . e . more than 0.1") days per month.  to be concentrated i n t o a few  This suggests that the r a i n f a l l i s l e s s  plant growth than i t s absolute t o t a l s suggest.  effective for  However, no general statements  on p r e c i p i t a t i o n e f f e c t i v e n e s s and plant growth can be made, since t h i s depends upon the i n f i l t r a t i o n capacity of the s o i l , s o i l moisture holding c a p a c i t y and the r o o t i n g systems of the p l a n t s .  These l a r g e r amounts g e n e r a l l y a l l o w moisture i n f i l t r a t i o n i n t o the s o i l and subsequent absorption by the plant r o o t s , whereas the smaller amounts are evaporated d i r e c t l y o f f the s o i l and p l a n t surfaces.  26. CHAPTER 3 STATISTICAL ANALYSIS OP WET AND DRY SPELLS This chapter concentrates upon determining the p r o b a b i l i t y of the occurrence of wet (and dry) s p e l l s during the growing season at the s i x selected s t a t i o n s i n the r e g i o n .  Not only does t h i s information amplify the  material i n the previous chapter, but i t provides an o b j e c t i v e method f o r assessing the duration  of such s p e l l s throughout the growing season.  Wet  s p e l l s being periods o f supply and dry s p e l l s being periods o f demand, t h i s chapter a l s o a c t s as a n a t u r a l bridge between the two sections of the t h e s i s . Problems i n v o l v i n g the estimation of the p r o b a b i l i t y d i s t r i b u t i o n s of lengths of wet and dry s p e l l s have received an i n c r e a s i n g amount of attention recently.  Several i n v e s t i g a t o r s have set up and confirmed a number  of hypotheses concerning such p r o b a b i l i t i e s which, g e n e r a l l y speaking, conform to two mathematical models - a persistency model e s t a b l i s h e d Carruthers  1  by Brooks and  2 and the Markov Chain Model as presented by G a b r i e l and Neumann .  This chapter attempts to test these models against the observed frequencies of wet and dry days recorded at the s i x synoptic s t a t i o n s i n the region f o r the six-month period A p r i l to September i n c l u s i v e . The Persistency Model I t i s w e l l known that the p r o b a b i l i t y of a wet or dry day i s not independent of previous c o n d i t i o n s , i . e . there i s a greater p r o b a b i l i t y that r a i n w i l l f a l l on a given d a y , i f the previous day was wet than i f the previous  * C.E.P. Brooks and N. Carruthers, Handbook of S t a t i s t i c a l Methods i n Meteorology (London: H.M.S.O., 1953), Chapter 16, p. 309. 2  K.R. G a b r i e l and J . Neumann, "A Markov chain model f o r d a i l y r a i n f a l l occurrences at T e l A v i v " , Quart. Journ. Royal Met. S o c , V o l . 88 (1962), 90-95.  •  2  7  .  3  day was dry. Jorgensen , studying the persistency e f f e c t s o f r a i n and nonr a i n days i n San F r a n c i s c o , noted that the number of observed frequencies of wet and dry days d i d not agree with that c a l c u l a t e d on the basis of constant p r o b a b i l i t y , equal to the r a t i o of the number of wet (or dry) days d i v i d e d by the t o t a l number of wet o r dry days.  4 Williams  applied the hypothesis that the longer the s p e l l has  l a s t e d , the more l i k e l y i t w i l l l a s t another day, and f i t t e d a logarithmic s e r i e s t o h i s observations.  Longley^ concluded from h i s study of wet and  dry days i n various Canadian c i t i e s that the p r o b a b i l i t y of a wet day, the previous day being wet, was constant, no matter how long the s p e l l l a s t e d . However, he did n o t i c e a s l i g h t increase i n the p r o b a b i l i t y of a dry day, with i n c r e a s i n g length of the dry s p e l l . Method o f I n v e s t i g a t i o n Since the same mathematical procedures were used at a l l s i x s t a t i o n s to t e s t t h e persistency model, a d e t a i l e d a n a l y s i s of the data processing w i l l only be presented f o r one s t a t i o n , v i z . P r i n c e t o n , and the r e s u l t s of the other s t a t i o n s w i l l simply be t a b u l a t e d .  A wet day i s defined as a day  when at l e a s t 0.01" r a i n f e l l , and a s p e l l i s taken to mean an unbroken succession o f occurrences (or non-occurrences) of such days.  The data were  tabulated from the Monthly C l i m a t i c Summaries published by the Meteorological Branch of the Department of Transport f o r the 30-year period 1935 - 1964. Since the dry s p e l l s f r e q u e n t l y overlapped from month t o month, the data  3  D.L. Jorgensen, " P e r s i s t e n c y of r a i n and non-rain days in. San F r a n c i s c o " , Monthly Wea. Rev., V o l . 77 (1949), 302-30?.  4  C.B. Williams, "Sequences of wet and dry years considered i n r e l a t i o n t o the logarithmic s e r i e s " , Quart. Journ. Royal Met. S o c , V o l . 78,  (1952), 91-96.  ^ R.W. Longley, "Lengths of wet and dry p e r i o d s " , Quart. Journ. Royal Met. S o c . V o l . 79 (1953), 91-98.  28. were cumulated over the t o t a l g r o w i n g season, a l l s p e l l s b e i n g assumed t o b e g i n and end on A p r i l 1 s t and September 3 0 t h  respectively.  Ho:  No p e r s i s t e n c e e f f e c t between e v e n t s .  Hi:  P e r s i s t e n c e e f f e c t between e v e n t s .  I f a s e r i e s has no p e r s i s t e n c e e f f e c t s , both t h e p r o b a b i l i t y p_ t h a t an event w i l l o c c u r , and the p r o b a b i l i t y £ = 1 - p t h a t the event w i l l o c c u r are independent of what has gone on b e f o r e . p_ ( t h e p r o b a b i l i t y of any day b e i n g d r y ) was  0.738.  not  At P r i n c e t o n , f o r d r y days, S i n c e no p e r s i s t e n c e i s  assumed, t h e chance t h a t any day w i l l be wet i s q = 0.262.  The chance o f  a n o t h e r day b e i n g d r y i s a l s o equal t o p_ and, c o n s e q u e n t l y , the p r o b a b i l i t y 2 o f the o c c u r r e n c e o f a t l e a s t two d r y days i s qp .  S i m i l a r l y , the chance of  3  a t l e a s t t h r e e c o n s e c u t i v e d r y days i s qp , and so on.  I f the t o t a l number  o f days over a c e r t a i n p e r i o d i s N, the expected number o f r u n s o f a t l e a s t one day, o f a t l e a s t two days, o f at l e a s t t h r e e days over t h a t p e r i o d a r e 2 Nqp  Nqp,  3  , Nqp  ....... p r o v i d e d t h a t t h e r e i s no p e r s i s t e n c e .  p = 0.738, q = 0.262 and N = 5^90;  t h u s Npq = 1061.  For P r i n c e t o n ,  These e x p e c t e d  f r e q u e n c i e s a r e shown i n the f i r s t column o f T a b l e V I .  The  differences  between s u c c e s s i v e v a l u e s i n t h i s column g i v e the e x p e c t e d number o f r u n s o f at l e a s t n days (n = 1 , table.  2, 3  ) and a r e shown i n the second column of the  The observed f r e q u e n c i e s are g i v e n f o r comparison i n t h e t h i r d column. The X  confidence l i m i t .  f o r 18 degrees of freedom was not s i g n i f i c a n t at the  0.05  I t i s obvious t h a t t h e s h o r t r u n s a r e much l e s s f r e q u e n t ,  and the l o n g r u n s much more f r e q u e n t t h a n would be e x p e c t e d on the h y p o t h e s i s of independence,  i . e . of no p e r s i s t e n c e .  T h e r e f o r e the h y p o t h e s i s o f no  p e r s i s t e n c e between e v e n t s i s r e j e c t e d and i t s a l t e r n a t i v e , persistence, i s accepted. other f i v e  that there i s  A s i m i l a r p e r s i s t e n c e e f f e c t was noted a t the  stations. The observed r u n s of a t l e a s t n days a t P r i n c e t o n were t h e n c o n v e r t e d  29.  Table VI - Frequencies of Runs of Dry Days at Princeton, (1935 - 1964).  n days  Runs of n & more days  Expected runs of n days  Observed runs of n days  Observed Expected  )C  1  1061  277  172  105  39.801  2  784  206  116  90  39.320  3  578  151  6  ?  84  46.728  4  427  114  61  53  24.640  5  313  82  57  25  7.621  6  231  60  37  23  8.816  7  171  45  26  19.  8.022  8  126  33  29  4  0.484  9  93  24  19  5  1.041  10  69  18  24  6  2.000  11  51  14  22  8  4.571  12  37  10  13  3  0.900  1  3  27  7  9  2  0.571  14  20  6  5  1  0.167  15  14  4  8  4  4.000  16"  10  2.1  3  0.9  3.857  17  7-9  2.0  4  2.0  2.000  18  5.9  1.6  5  3.4  7.225  19  4.3  1.1  5  3.9  13.821  20  3.2  0.9  5  4.1  18.677  =  234.262 N.S.  30. i n t o observed runs of n or more days to give a s e r i e s of cumulative frequencies shown i n Table VII.  The second column gives the r a t i o s between successive  frequencies, I.e.  i s the p r o b a b i l i t y of a dry day when the k days immediately  preceding i t were a l s o dry.  I t should be noted that a l l of these r a t i o s exceed  the general p r o b a b i l i t y (p = 0.738) of a dry day. In attempting to f i t a t h e o r e t i c a l persistence model to the dry (and wet) s p e l l s at P r i n c e t o n , three hypothese.s were considered: 1.  Hj>:  P r o b a b i l i t y of a dry day f o l l o w i n g a dry day i s constant f o r a l l values of k.  2.  H>>:  P r o b a b i l i t y of a dry day a f t e r two dry days i s constant f o r a l l values of k greater than 1.  3.  H3:  P r o b a b i l i t y of a dry day increases as l e n g t h of s p e l l increases, i . e . p^ c o n t i n u a l l y increases as k increases.  Considering the f i r s t hypothesis, i f the p r o b a b i l i t y of the occurrence of a dry day i s constant a f t e r the f i r s t day, the frequencies of runs of 1, 2, . . . . n or more days are 68? ( l , p,  » P]_'  the observed data, the number o f dry days i s 4050.  Therefore 687/(l - p^) =  4050, from which p  = 0.830.  1  • • • • P-^  )•  Prom  Using t h i s value f o r p^, the c a l c u l a t e d s e r i e s  of runs of •exaetlyn days are shown against t h e i r observed frequencies i n 2 Table V I I I .  The X  t e s t with 18 degrees of freedom showed that the expected  r e s u l t s c a l c u l a t e d on the b a s i s of constant p r o b a b i l i t y were s i g n i g i c a n t l y d i f f e r e n t from the observed frequencies at the 95f° l e v e l of confidence. Since the l a r g e s t discrepancies are at low values f o r n, i t was thought that the second hypothesis, i . e . the p r o b a b i l i t y of a dry day f o l l o w i n g two dry days i s constant might f i t the observed d i s t r i b u t i o n more closely. ( l , p , Pg 2  The frequencies of runs of 2, 3> ....)  n or more days are now 515  (2 or more days) + (3 or more) +  = 3363, from which p_ = 0.847.  , then 515 ( l - P )  A comparison between expected numbers of  2  Table VII - Frequencies of Runs of n or more Dry Days at Princeton, (1935 - 1964).  n days  Runs of n or more days  1  687  2  515  3  399  4  332  5  271  6  214  7  177  8  151  9  122  10  103  11  74  12  57  Ratio = p.  0.750 0.775 0.832 0.816 0.790 0.827 0.853 0.808 0.844 0.767 0.722 0.772  44 0.795  14  35  15  30  16  20  0.857 0.733  32. runs c a l c u l a t e d on the b a s i s of t h i s p r o b a b i l i t y and the observed number of 2 runs i s shown i n Table IX.  The X  test f o r 17 degrees of freedom showed that  the two d i s t r i b u t i o n s were s t a t i s t i c a l l y the same at the 95$ l e v e l of c o n f i dence.  No simple law of increase i n p^ with k i s l i k e l y to improve appreciably  on t h i s value of X  when allowance i s made f o r the decrease i n the number of  degrees of freedom required f o r each a d d i t i o n a l assumption. The wet s p e l l frequency d i s t r i b u t i o n s were subjected to the same treatment.  For the f i r s t hypothesis, i . e . p  Q  - the p r o b a b i l i t y of a wet day  f o l l o w i n g a wet day i s constant f o r a l l values of k, the sum of the wet s p e l l s e r i e s was 298/(l - p ) = 1440, from which p Q  Q  = 0.535.  The X  t e s t (Table X)  i n d i c a t e s a close c o r r e l a t i o n between observed and expected frequencies, which i s s i g n i f i c a n t at the 95$ l e v e l of confidence.  Since the p r o b a b i l i t y of  accepting t h i s f i r s t n u l l hypothesis was greater than the p r o b a b i l i t y f o r accepting the second, i . e . the p r o b a b i l i t y of a wet day f o l l o w i n g two wet days i s constant, the f i r s t hypothesis was allowed to stand. The same set of hypotheses was tested f o r the frequency d i s t r i b u t i o n s of both wet and dry s p e l l s at the other f i v e s t a t i o n s .  Table XI  summarizes  the r e s u l t s . The d r i e r s t a t i o n s a t Lytton and Kamloops r e s p e c t i v e l y did not show a s i g n i f i c a n t constant p r o b a b i l i t y i n t h e i r dry s p e l l frequencies on t h i s persistence model.  Their observed frequencies showed a tendency f o r proba-  b i l i t i e s of dry days to increase as the length of the s p e l l increased, though t h i s was not a constant tendency (see Appendix I ) .  Local s t a b i l i z i n g con-  d i t i o n s may be maintained f o r l o n g periods at these s t a t i o n s d u r i n g the growing season - a 49 dry day s p e l l o c c u r r i n g at L y t t o n i n 1940 and a 44 dry day s p e l l at Kamloops i n i 9 6 0 .  Altogether there have been 10 dry s p e l l s that  have exceeded 30 days at Lytton over the.past t h i r t y years and 8 such s p e l l s at Kamloops, while over the same period of time there have been 6 s p e l l s at  Table V I I I - Frequencies of Runs of E x a c t l y n Dry Days at P r i n c e t o n , (1935 - 1964 ).  1 Ho:  p  n days  k  "  P  k  l  0  Obs.  Exp.  1  172  117  55  25.85  2  116  97  19  3.72  3  67  80  13  2.11  61  68  7  0.72  5  57  55  2  0.07  6  37  45  8  1.42  7  26  39  13  4.33  8  29  31  2  0.13  9  19  27  8  2.37  10  2k  22  2  0.18  11  22  18  4  0.88  12  13  X  5  2  0.27  12  3  0.75  13  .  9  Obs. - Exp.  5  9.9  4.9  2.42  8  8.5  0.5  0.03  3  7.1  4.1  2.36  4  5.9  1.9  0.61  18  5  4.9  0.1  0.01  !9  5  4.1  0.9  0.19  20  5  3.4  1.6  0.76  14 15 16  •  x  2  =  49.18  N.'S. '  34. Table IX - Frequencies of Runs of E x a c t l y n Dry Days at . P r i n c e t o n , (1935 - 1964).  (b)  Ho:  p  =  k  p  for k ^ »  2  1 2  days  Exp.  2  116  139  23  3.81  3  67  6?  0  0.00  4  61  56  5  0.45  5  57  48  9  1.69  6  37  41  6  0.88  7  26  34  8  1.88  8  29  29  0  0.00  9  19  25  6  1.44  10  24  21  3  0.43  11  22  17  . 5 '  1.4?  12  13  15  2  0.27  13  9  13  4  1.23  14  5  10.8  5.4  2.70  15  8  9.3  x  -3  0.18  16  3  7.4  4.4  2.62  4  6.4  2.4  0.89  18  5  5.6  0.6  0.0?  19  5  4.7  0.3  0.02  20  5  4.0  1.0  0.25  y  X.  Obs. - Exp.  X  Obs.  2  *  =  20.28  * S i g n i f i c a n t at the 95% confidence l e v e l  35. Table X - Frequencies of Runs of E x a c t l y n Wet Days a t P r i n c e t o n , (1935 - 1964). Ho:  p  k  days  =  l  P  Obs.  E x  o  k  = 0.535 P«  Obs. - Exp,•  2  X  1  298  ,311  13  0.543  2  174  16?  7  0.293  3 4  93  89  49  47  31 8  5  1  6.  >  0.180  2  0.085  25  6  1.440  13  1.923 1.371  7 8  8  5.3  5 2.7  6  4.0  2.0  1.000  9  2  2.1  0.1  0.001  x  2  •=  6.836  *  Table XI -• S i g n i f i c a n c e of Constant P r o b a b i l i t i e s of Wet and Dry Days at Selected Stations during the Growing Season  Pl  Note:  Wet Spells  Dry Spells  Station  P  2  p  l  P  2  *  -  *  -  Hope  0.794 N.S.  0.823 *  0.689  Lytton  0.877 N.S.  0.888 N.S.  0.492  Penticton  0.816 N.S.  0.829 *  0.543  Princeton  0.832 N.S.  0.84? *  0.535  Vernon  0.813 N.S.  0.829 *.  0.541  Kamloops  0.839 N.S.  0.857 N.S.  0.419 N.S.  0.560  p^ = p r o b a b i l i t y of a dry (or wet) day f o l l o w i n g a dry (or wet) day. P  2  = p r o b a b i l i t y of a dry (or wet) day f o l l o w i n g 2 dry (or wet) days.  NS = not s i g n i f i c a n t at 95$ l e v e l of confidence, s i g n i f i c a n t at 95$ l e v e l of confidence.  36. P e n t i c t o n or Vernon r e s p e c t i v e l y , k s p e l l s at P r i n c e t o n and 3 at Hope. The p r o b a b i l i t i e s of wet s p e l l s during the growing season f o l l o w a more consistent p a t t e r n across the r e g i o n , a l l s t a t i o n s except Kamloops having a constant p r o b a b i l i t y of a wet day, provided the previous day was wet.  The  c o n s i s t e n t l y shorter s p e l l s of wet weather compared with dry weather at a l l s t a t i o n s might account f o r t h i s s i m p l i f i e d constant p r o b a b i l i t y .  Similar  r e s u l t s were obtained i n a study undertaken by the B r i t i s h Meteorological O f f i c e i n South East England^. The constant p r o b a b i l i t i e s shown i n Table XI i l l u s t r a t e the v a r i a t i o n s i n the moisture supply and demand by crops at selected points w i t h i n the region during the growing season.  I n the case of both wet and dry s p e l l s ,  high p r o b a b i l i t i e s i n d i c a t e a tendency towards a greater duration of such s p e l l s and, as expected, s t a t i o n s with high p r o b a b i l i t i e s of wet s p e l l s have low p r o b a b i l i t i e s of dry s p e l l s and v i c e - v e r s a .  Thus these f i g u r e s contrast the  r e l a t i v e l y unfavourable moisture supply and demand p a t t e r n f o r crop growth i n the Thompson V a l l e y and at Princeton against the more favourable balance at Hope, Vernon and P e n t i c t o n . Since there appeared to be a constant p r o b a b i l i t y of a dry (or wet) day f o l l o w i n g a c e r t a i n number of dry (or wet) days at most s t a t i o n s , i t was thought that there might be a r e l a t i o n s h i p between the frequency of occurrence 2 of such dry (or wet) days and the length of the run.  Using the X. goodness  of f i t t e s t and the appropriate degrees of freedom, a l l the observed frequencies of both wet and dry s p e l l s at a l l the s t a t i o n s f i t t e d the negative binomial distribution relatively well.  Accordingly, the frequency d i s t r i b u t i o n s were  normalized by transforming the cumulative frequencies i n t o t h e i r l o g a r i t h m i c S p e l l s of Dry Weather i n Eastern England. Agro. Met. Branch (London: Met. O f f i c e , 1953), 1-20.  37. values.  Regression analyses were then carried out between the dependent  variable - the logarithm of the cumulative  frequency and the independent  variable - the length of s p e l l (wet or dry) i n days.  The various regression  equations, standard errors of the estimate and c o r r e l a t i o n c o e f f i c i e n t s are summarized i n Table XII. A l l regression analyses are highly s i g n i f i c a n t at 18 and 8 degrees of freedom f o r the dry and wet s p e l l s respectively, i n a l l cases over 90$ of the v a r i a t i o n i n the s p e l l frequencies being explained by t h e i r duration.  It i s  therefore thought that f a i r l y accurate forecasts of the recurrence i n t e r v a l s of wet and dry s p e l l s . o f any length less than approximately made from these  a month could be  equations.  The relevance of these equations to the study can be seen from an examination of the regression constants (the number followed by n i n each equation), which indicate the slope of the regression l i n e .  For both wet  and d r y . s p e l l s , the lower t h i s figure,the greater i s the tendency for the s p e l l to continue.  These f i g u r e s support the conclusions r e s u l t i n g from an  analysis of the constant p r o b a b i l i t i e s , namely that Lytton, Princeton and Kamloops tend to experience the longest dry s p e l l s during the six-month growing season, and that Hope i s the only s t a t i o n that can expect wet  spells  of some considerable length. However, such r e s u l t s can only be applied f o r data covering lengthy time i n t e r v a l s which avoid the awkward overlapping of dry spells from month to month.  The a g r i c u l t u r a l i s t i s also concerned with the p r o b a b i l i t i e s of  wet and dry s p e l l s over shorter periods of time (say a monthly b a s i s ) , which requires the use of the Markov Chain Model.  Table XII - Regression A n a l y s i s on Dry and Wet S p e l l s during the Growing Season at Selected S t a t i o n s . Dry S p e l l s Station  Regression Equation  Hope  l o g y = 2.909 - 0.112311  Ly t t on  l o g y = 2.927 - 0.0956n  Penticton  Wet S p e l l s S.E.  R_  Regression Equation  0.103  0.989  l o g y = 3.063 - 0.1702n  0.151  0.968  l o g y a 3.099 - 0.3308n  A  S.E. 0.117  0.989  0.070  0.997  A  A  A  0.999 l o g y = 2.991 - 0.1076n  0.107  0.98?  l o g y ~ 3.104 - 0.25l6n  0.027  Princeton  0.994 l o g y = 2.960 - 0.1020n  Vernon Kamloops  R  O.O65  0.995  l o g y - 3.186 - 0.2985n  0.136  0.982  l o g y = 3.031 - 0.24l9n  0.168  O.967  l o g y = 2.950 - 0.2534n  A  l o g y = 3.027 - 0.1l45n  A  A  l o g y = 2.983 - 0.1055n  0.099 .0.091  A  0.108  0.993 0.994  CO  39o  The Markov Chain Model Recently, the f i r s t order Markov Chain Model has been used as a f i r s t approximation to describe the s t a t i s t i c a l dependence already v e r i f i e d i n sequences of wet and dry days.  Evidence of the f e a s i b i l i t y of such a model has  been presented by Gabriel and Neumann, Caskey, Weiss, Hopkins and Robillard  7 and Peyerherm and Dean Bark . This section attempts to present evidence f o r and ( f o r some stations) against the use o f a simple Markov Chain p r o b a b i l i t y model, and to present the operational procedures necessary to estimate the i n i t i a l and t r a n s i t i o n a l p r o b a b i l i t i e s used i n such a model. The Markov Chain model deals with any process that can only be i n one state at one time and i t assumes that t h i s state i s dependent upon some previous condition.  Any day can be either wet or dry, and i t has been v e r i f i e d  that the probability of a day being wet or dry i s dependent upon whether the previous day was wet or dry.  Let q. represent a day type (wet or dry) and  J p.. the probability of t h i s outcome i n any given sequence, given that the outcome q. appeared on the previous day. This quantity p.. i s known as a t r a n s i t i o n a l probability, since i t indicates the p r o b a b i l i t y of moving from one state (wet or dry) to another or remaining i n the same state as time passes. References dealing with the Markov Chain model. Gabriel and Neumann, l o c . c i t . J.E. Caskey, "The Markov chain model f o r the p r o b a b i l i t y of p r e c i p i t a t i o n occurrence i n i n t e r v a l s of various lengths", Monthly Wea. Rev., V o l .  91 (1963), 298-301.  L.L. Weiss, "Sequences of wet and dry days described by a Markov chain p r o b a b i l i t y model", Monthly Wea. Rev., V o l . 92 (1964), 109-176. J.W. Hopkins and P. Robillard, "Some s t a t i s t i c s of d a i l y r a i n f a l l occurrence f o r Canadian P r a i r i e Provinces", Journ. Applied Met., Vol. 3 (1964),  600-602.  A.M. Feyerherm and L.D. Bark, " S t a t i s t i c a l methods for persistent p r e c i p i t a t i o n patterns", Journ. Applied Met., V o l . k (l96^)s 320-328.  The t r a n s i t i o n a l p r o b a b i l i t i e s may be set up i n a matrix form, from which the following formula may be derived, assuming that the t r a n s i t i o n  probabilities  depend only upon the previous day's weather.  hJ - (V < t l/V P  P  < t> i»l X  X  P  X  P ( X  +  t*n/ t n-l> ' X  +  Where X = states (wet or d r y ) . P(X  X  ,...) denotes the probability.that the sequence shown i n  i n parenthesis w i l l occur. P(X ) i s the i n i t i a l p r o b a b i l i t y of a wet or dry day. t  P(X  t+1  / X ^ ) i s a t r a n s i t i o n a l probability,  the sign (/) meaning  "given that" i . e . P(W^ /W ) i s the t r a n s i t i o n a l probability of +1  a wet day, the previous day being wet. Thus i t can be seen that the right-hand side of ( l ) i s the product of an i n i t i a l probability and a set of t r a n s i t i o n a l p r o b a b i l i t i e s . above model assumes that the probability  Since the  of r a i n f a l l on any day depends only  on whether the previous day was wet or dry, i t i s known as the f i r s t  order  Markov chain. In order t o estimate the p r o b a b i l i t i e s of wet and dry s p e l l s of lengths n days, equation ( l ) may be s i m p l i f i e d by assuming the t r a n s i t i o n a l p r o b a b i l i t i e s of the right hand side to be equal, i . e . Pw/w = Pw/w,w ( i n the case o f vret s p e l l s ) .  This assumption i s sometimes part of the d e f i n i t i o n of  Q a f i r s t order Markov Chain . Such a model only requires two parameters: Pw/w = P (wet day/ the previous day wet) Pw/d  = P (wet day/ the previous day dry)  W. F e l l e r , An Introduction to Probability Theory and i t s Applications (2nd Ed.; New York! John Wiley and Sons, Inc., 1957), Vol. 1  41. The p r o b a b i l i t y of a wet s p e l l of length n days i s : (1 - Pw/v) Pw/w" " 1  1  .  .(2)  and the p r o b a b i l i t y of a dry s p e l l of length k days i s Pw/d (1 " P w / d )  k_1  (3)  Before t h i s model can be s t a t i s t i c a l l y v e r i f i e d f o r each of the s i x synoptic s t a t i o n s w i t h i n the r e g i o n , the procedure f o r estimating the i n i t i a l and c o n d i t i o n a l p r o b a b i l i t i e s must be discussed.  This i s best i l l u s -  t r a t e d by means of a p r o b a b i l i t y " t r e e " .  where: Pw  = p r o b a b i l i t y of an i n i t i a l wet day on random s e l e c t i o n .  Pd  = p r o b a b i l i t y of an i n i t i a l d r y day on random s e l e c t i o n .  Pw/d  = p r o b a b i l i t y of a wet day, the previous day being dry.  Pw/w  = p r o b a b i l i t y of a wet day, the previous day being wet.  Pw/d,w  = p r o b a b i l i t y of a wet day, the previous days being dry and wet r e s p e c t i v e l y .  and Pw/w,w  = p r o b a b i l i t y of a wet day, the two previous days being wet.  42. Using the appropriate branches of this tree, the p r o b a b i l i t i e s of any consecut i v e combination  of wet and dry days may be estimated.  Since the sum  of the  p r o b a b i l i t i e s on any two branches away from a single outcome i s 1 (e.g. + Pw/d  Pw/w  = l ) only the p r o b a b i l i t i e s of wet days following the various combina-  tions of wet and dry days were calculated (Table X I I I ) . An analysis of the table underlines two points already noted i n e a r l i e r chapters.  F i r s t l y , the various t r a n s i t i o n a l p r o b a b i l i t i e s vary by  larger or smaller amounts, both from month to month and from place to place across the region.  The lower p r o b a b i l i t i e s of wet days are associated with  the drier months and d r i e r areas i n accordance with e a r l i e r r e s u l t s . the persistence e f f e c t s are immediately t r a n s i t i o n a l p r o b a b i l i t i e s f o r Pw/w Pw/w  Secondly,  obvious from a comparison of the  against Pw or Pw/d.  and Pw/d,w are the highest p r o b a b i l i t i e s at most  Generally speaking, stations.  It has already been mentioned that one of the conditions o f the f i r s t order Markov Chain i s that the p r o b a b i l i t y of a wet day i s constant, provided the previous day was wet, i . e . Pw/w  = Pw/w,w, e t c .  An  examination  of the tables shows that t h i s assumption i s remarkably consistent for most months at most places, though there appear to be a few exceptions. i t was  Therefore,  decided to test s t a t i s t i c a l l y whether the differences between these  p r o b a b i l i t i e s were s i g n i f i c a n t l y different or not. S t a t i s t i c a l methods used to test hypotheses concerning the Markov  9 Chain model have been discussed by Anderson and Goodman Dean B a r k ^ .  In accordance with their r e s u l t s , the 2 x 2  and, Feyerherm and contingency table  for both wet and dry days r e s p e c t i v e l y was used to test the n u l l hypothesis s  T.W.  Anderson and L.A. Goodman, " S t a t i s t i c a l  Markov Chains", Am. Math. Stat.. Vol. 28 (1957), 89-110. Feyerhern and Bark, l o c . c i t .  Inference about  43. Table X I I I - I n i t i a l and T r a n s i t i o n a l P r o b a b i l i t i e s at Selected Stations Probability  . Station  April  June  July  August  September  Pw  Hope Lytton Penticton Princeton Vernon Kamloops  0.553 0.177 0.230 0.205 0.287 0.168  0.384 0.163 0.266 ' 0.255 0.264 0.203  0.418 0.237 0.327 0.312 0.367 0.293  0.271 0.148 0.190 0.213 0.234 0.203  0.313 0.171 0.197 0.232 0.255 0.210  0.363 0.208 0.200 0.217 0.258 0.185  Pw/w  Hope Lytton Penticton Princeton Vernon Kamloops  0.684 0.302 0.391. 0.293 0.413 0.257  0.647 0.347 0.455 0.462 0.488 0.373  0.606 0.387 0.464 0.428 0.514 0.520  0.536 0.304 0.390 0.455 0.469 0.333  0.547 0.330 0.361 0.444 0.468 , 0.369  0.628 0.416 0.433 0.413 0.452 0.387  Pw/d  Hope Lytton Penticton Princeton Vernon Kamloops  0.391 0.150 0.182 0.182 0.236 0.130  0.220 0.127 0.198 0.184 0.184 0.160  0.284 0.190 0.260 0.259 0.282 0.204  0.173 0.121 0.143 0.148 0.161 0.170  0.211 0.138 0.157 0.168 0.182 0.167  0.212 0.183 0.142 0.162 0.191 0.139  Pw/w,w  Hope Lytton Penticton Princeton Vernon Kamloops  0.656 0.250 0.389 0.306 0.451 0.346  0.623 0.343 0.467 0.452 0.538 0.362  O.566 0.400 0.462 0.375 0.514 0.505  0.456 0.179 0.326 0.483 0.441 0.333  0.471 0.371 0.364 0.454 0.392 0.352  0.606 0.269 0.269 0.370 0.414 0.372  Pw/w,d  Hope Lytton Penticton Princeton Vernon Kamloops  0.390 0.216 0.156 0;218 0.254 0.138  0.274 0.167 0.267 0.224 0.190 0.266  0.333 0.195 0.352 0.346 0.364 0.163  0.256 0.187 0.153 0.181 0.169 0.250  0.233 0.127 0.244 0.275 0.190 0.195  0.284 0.192 0.162 0.239 0.247 0.206  Pw/d,w  Hope Lytton Pentict on Princeton Vernon Kamloops  0.743. 0.324 0.393 0.28? 0.387 0.262  0.690 0.348 0.444 0.470 0.440 0.380  0.666 0.628 0.379 . 0.359 0.431 0.467' 0.467 0.431 0.494 0.495 '0.333 0.535  0.611 0.310 0.359 0.413 0.538 0.378  0.66? 0.521 0.559 0.44? 0.482 0.397  Pw/d,d  Hope Lytton Penticton Princeton Vernon Kamloops  0.393 0.138 0.188 0.177 0.229 0.129  0.205 0.119 0.185 0.176 0.183 0.157  0.189 0.177 0.227 0.229 0.249 0.215  0.205 0.140 0.141 0.146 0.179 0.162  0.193 0.147 0.138 0.14? 0.236 0.128  0.155 0.112 0.142 0.142 0.161 O.I54  44. Ho:  P(X / I ,  Hi:  P(X / X _  w  X ._ )  =  P(X  X _ )  =  P(X /X  t  2  A  t  T  l  )  against t  t  l f  t  2  t  t - 1  )  Again, data at P r i n c e t o n for the 20-year period 1945 - 1964 are shown 2 i n Table XIV as i l l u s t r a t i v e of the method used f o r computing the X.  statistic.  2 Two X  were computed, one f o r sequences i n which the middle day was dry and  one f o r sequences i n which the middle day was wet. 2 Table XIV - Observed Numbers f o r Computing X. S t a t i s t i c s for the month of A p r i l at P r i n c e t o n , (1945 - 1964). X  t-i D  =  D  X  V  t-1 D  =  w w  D  321  69  390  D  62  25  87  W  69  19  88  W  25  11  36  390  88  4?8  87  36  123  5C D 2  =  0.0010 * *  >c w 2  =  0.0001 **  Using the 5% l e v e l of s i g n i f i c a n c e Ho would be accepted i n both instances i . e . the f i r s t order Markov Chain holds f o r both wet and dry s p e l l s at Princeton during A p r i l .  However, i t must be stated that accepting  this  hypothesis does not prove that the data f o l l o w a f i r s t order chain but rather suggest that the observed departures from a f i r s t order chain model are probably random. Similar X  2  t e s t s were run f o r each month of the growing season at 2 each of the s i x chosen s t a t i o n s . The months f o r which the X were  45. s i g n i f i c a n t at the 5% l e v e l are tabulated i n Table XV * * each month being denoted by a number. Table XV - Months during the Growing Season f o r which the Chi-Squares were S i g n i f i c a n t at the P = 5 per cent Level Conditions X  t-l -  D  Hope  Lytton  Penticton  Princeton  Vernon  Kamloops  5,8,9  4,5,6,7,8,9  4,5,7,9  4,5,7,9  4,5,7,8,9 4,5,6,8,9  5,6,9  4,5,6,7,8  4,5,6,7,8 4,5,6,7,8,9 4,5,6,7,9 4,5,6,7,8,9  I t i s d i f f i c u l t t o r a t i o n a l i z e why the f i r s t order chain i s r e j e c t e d f o r c e r t a i n months at the v a r i o u s s t a t i o n s , since no month i s c o n s i s t e n t l y r e j e c t e d throughout the whole area and no two s t a t i o n s have the same monthly p a t t e r n of accepting and r e j e c t i n g the n u l l hypothesis (except i n the case of dry s p e l l s at P e n t i c t o n and P r i n c e t o n ) .  However, i n judging the r e s u l t s of  Table XV, i t should be noted that there are 12 independent t e s t s f o r each s t a t i o n (2 conditions and 6 months).  Thus i t would not be s u r p r i s i n g t o f i n d  one or two months per s t a t i o n f o r which the n u l l hypothesis would be r e j e c t e d . The r e s u l t s suggest that although the f i r s t order Markov Chain i s an imperfect model f o r p r e d i c t i n g p r e c i p i t a t i o n patterns w i t h i n the region on a monthly b a s i s , i t does provide a r e l i a b l e approximation t o the problem:.  Con-  sequently, the p r o b a b i l i t i e s o f wet and dry s p e l l s of any length may be obtained with a c e r t a i n degree of v a l i d i t y from equations (2) and ( 3 ) . I t i s thought that f o r some months and a t some s t a t i o n s t h i s approximation might be improved by a second order Markov Chain, i . e . a day's weather depends on events o c c u r r i n g two days p r e v i o u s l y , though i t i s doubtful whether t h i s improvement would be worth the a d d i t i o n a l computational e f f o r t . Threshold o f 0.01 inch was s t i l l used. I t was hoped that the 0.1 i n c h threshold could also be used, since such r a i n f a l l i s more u s e f u l f o r crop growth but when using such a threshold the observed frequencies i n some c e l l s were not large enough to provide trustworthy. ^ statistics. 1 1  46. Summary An analysis of the d i s t r i b u t i o n of daily p r e c i p i t a t i o n data at selected and  points within the region indicates  that both the persistency model  the Markov Chain model may be used to estimate p r o b a b i l i t i e s of wet and  dry s p e l l s .  Both hypotheses reject overwhelmingly the, hypothesis of  independence i n daily r a i n f a l l occurrence.  The frequencies o f wet and dry  s p e l l s over the entire length of the growing season appear t o follow a cons i s t e n t pattern, the probability probability  of a dry day following two dry days and the  of a wet day following a single wet day being r e l a t i v e l y constant.  From l i n e a r relationships  between the cumulated frequencies of wet and dry  s p e l l s and the lengths o f these s p e l l s , p r o b a b i l i t i e s o f the occurrence of a s p e l l (wet or dry)  can be determined.  However, the analysis  of t r a n s i t i o n a l p r o b a b i l i t i e s on a monthly  basis indicate that one must take into account v a r i a t i o n i n the matrix of such p r o b a b i l i t i e s with time. and  For short sequences, one might consider the i n i t i a l  t r a n s i t i o n a l p r o b a b i l i t i e s constant, without biasing f i n a l estimates, but  aggregation over several months might produce severely biased r e s u l t s . The Markov chain technique i s a useful t o o l i n quantitative climatology, since through i t s application  direct comparisons of p r e c i p i t a t i o n  patterns from place to place can be made.  Furthermore, cumulative p r o b a b i l i t i e s  and expected return periods of both wet and dry s p e l l s can be forecast the formulae described i n Appendix I I .  by using  47. CHAPTER 4 AN ANALYSIS OP TEMPERATURE AND HUMIDITY PATTERNS Evaporation and t r a n s p i r a t i o n , that i s the conversion of water i n l i q u i d form i n t o a gaseous form, requires a considerable amount of heat energy (approximately 590 c a l o r i e s per gram of water at normal temperatures and pressures).  Under f i e l d conditions, t h i s a v a i l a b l e heat comes from two sources,  namely d i r e c t s o l a r and sky r a d i a t i o n and that conveyed to the crop from the surrounding a i r by turbulent f l o w . By f a r the more important source of energy i s d i r e c t solar radiation"''. 2 Several i n v e s t i g a t o r s  have noted high c o r r e l a t i o n s between observed evapora-  t i o n and t r a n s p i r a t i o n from crop covers and the d i f f e r e n c e i n water loss from the black and white B e l l a n i atmometers.  Since these instruments d i f f e r prim-  a r i l y i n t h e i r r a d i a t i o n c h a r a c t e r i s t i c s , i t would appear that evapotranspirat i o n (the combined processes of d i r e c t evaporation from the s o i l plus t r a n s p i r a t i o n from the crop) and s o l a r r a d i a t i o n are h i g h l y c o r r e l a t e d .  Stricly  speaking, i t i s net r a d i a t i o n rather than i n s o l a t i o n upon which evaporation 3 4 rates are l a r g e l y dependent.. However, i t has been shown by Shaw that s o l a r  • ^ U.S. Geological Survey. Water Loss I n v e s t i g a t i o n s , V o l . 1 Lake Hefner Studies, U.S.G.S., C i r . 299 (1952), pp. 154. 2 N.H. Halkias, E.T. Veihmeyer and - A.H. Hendrickson, "Determining water needs f o r crops from c l i m a t i c d a t a " , H i l g a r d i a , V o l . 24 (l955)s 207-233. R.M. Holmes and G.W. Robertson, "Conversion of l a t e n t evaporation to p o t e n t i a l e v a p o t r a n s p i r a t i o n " , Can. Journ. Plant Science, V o l . 38 (1958),  164-172.  J.C. Wilcox, Comparative Monthly I r r i g a t i o n Requirements i n Southern B r i t i s h Columbia, S o i l s 5> Summerland, B.C. (1963). (mimeographed). 3 J  Mukaramel and Bruce, l o c . c i t .  ^ R.H. Shaw, "A comparison of s o l a r r a d i a t i o n and net r a d i a t i o n " , B u l l . Amer. Met. S o c , V o l . 37. (1956), 205-207.  48. r a d i a t i o n and daytime net r a d i a t i o n over grass are p r a c t i c a l l y d i r e c t l y proportional. As was mentioned e a r l i e r , the other source of heat energy i s the' t u r b u l e n t flow of heat between the ground and the a i r .  Mukammel and Bruce  noted that on dry, windy days the observed water l o s s from B e l l a n i P l a t e s was four times as much as the water l o s s c a l c u l a t e d from the net r a d i a t i o n energy supply alone. .R  Examination of the heat balance equation explains t h i s d i f f e r e n c e ^ . =  LE • + K  + A . . . . . . . . . . .  .  ;  (l)  where R i s the net r a d i a t i o n , LE i s the l a t e n t heat of evaporation, K i s the turbulent f l u x of heat between the surface and the atmosphere and A i s a heat f l u x between the surface and the lower l a y e r s .  Since the component A  i s g e n e r a l l y n e g l i g i b l e when d e a l i n g with evaporation from plant surfaces^, t h i s turbulent advection of heat (K) i s the p r i n c i p a l a d d i t i o n a l component o f energy other than net r a d i a t i o n a f f e c t i n g the loss of water from moist surfaces. The importance of these two heat components vary from climate to 7 climate.  Pelton  working i n the semi-arid climate at Swift Current, Saskat-  chewan estimated that only 50% of the B e l l a n i P l a t e evaporation was due t o net r a d i a t i o n .  Mukammel and Bruce, working w i t h the same instrument, but i n  the more humid c l i m a t e at Ottawa, suggested t h a t t h i s f a c t o r accounted for 80% of the evaporation (the lengths of the. records were not s i m i l a r , but they were comparable).  These r e s u l t s suggest that i n the d r i e r c l i m a t i c  regions a l a r g e r ..proportion of Lthe t o t a l r a d i a t i o n balance f a l l s i n t o the sensible heat component and a l e s s e r proportion i n t o the l a t e n t heat component. 5 M.T. Budyko, The Heat Balance of the E a r t h ' s Surface, T r a n s l a t i o n PB 131692 (Washington, D.C.: U.S. Dept. of Commerce, 1 9 5 5 ) . ~ ^ Mukammel and Bruce, l o c . c i t . 7 Pelton, loc. c i t .  49. Should t h i s be t r u e , then a i r temperature should be more s i g n i f i c a n t l y c o r r e l a t e d w i t h evaporation i n dry areas than i n humid areas.  At Swift Current,  the c o r r e l a t i o n between B e l l a n i P l a t e evaporation and a i r temperature was 0.739 ( s i g n i f i c a n t at 95$ l e v e l of confidence), while at Ottawa i t was only 0.460 (not s i g n i f i c a n t ) .  The incoming r a d i a t i o n recordings were only a v a i l -  able at one s t a t i o n w i t h i n the area (Summerland), but since t h i s t h e s i s emphasises the s p a t i a l v a r i a t i o n i n the c l i m a t i c parameters a f f e c t i n g evapot r a n s p i r a t i o n , other r e l a t e d c l i m a t i c elements recorded at the s i x synoptic s t a t i o n s were used.  Judging from the above r e s u l t s , a i r temperature i s the  best s i n g l e element a f f e c t i n g evapotranspiration i n t h i s dry area.  Relative  humidity patterns are also analysed since they are an expression of the s a t u r a t i o n d e f i c i t of the a i r , which i s i n t u r n an i n d i c a t o r of the a b i l i t y of the atmosphere t o accept the evaporated moisture. Since by f a r the g r e a t e r proportion of water l o s s from plant and s o i l surfaces occurs during the day than at n i g h t , i t was thought that the d a i l y maximum temperature and the d a i l y minimum r e l a t i v e humidity were the most representative c l i m a t i c " c o n d i t i o n s a f f e c t i n g crop water l o s s e s . Although, as maxima and minima r e s p e c t i v e l y , they w i l l overemphasise the average cond i t i o n s p r e v a i l i n g throughout the daylight hours, since these  observations  are recorded i n a shaded screen, four feet about the ground, they are l i k e l y to be underestimates of the p r e v a i l i n g c o n d i t i o n s at ground l e v e l at any point i n time.  Therefore, they are probably the most representative f i g u r e s  of a l l the d a i l y c l i m a t i c data commonly observed at synoptic recording s t a t i o n s f o r estimating evaporating c o n d i t i o n s . Analysis of Temperature Frequencies . As w i t h p r e c i p i t a t i o n patterns, the frequency and p r o b a b i l i t y d i s t r i b u t i o n s o f maximum temperatures rather than t h e i r means are discussed.  50. I t i s b e l i e v e d that much of the d i f f i c u l t y that i s experienced i n c o r r e l a t i n g f i e l d observations of c l i m a t i c parameters with evaporation l i e s i n the i n d i s criminate use of d a i l y averages. B a s i c a l l y the same procedure was followed to obtain the p r o b a b i l i t i e s of maximum temperatures as was used to determine the p r o b a b i l i t i e s of p r e c i pitation.  The d a i l y maxima were tabulated i n 5°F classes f o r each of the s i x  growing season months at each of the s i x synoptic s t a t i o n s over the 20-year period 1945 - 1964.  These 5°*' frequencies were then cumulated from the lowest  c l a s s , each of the cumulated frequencies being d i v i d e d by the t o t a l monthly s i z e sample plus one to y i e l d t h e i r desired p r o b a b i l i t i e s of occurrence. An a n a l y s i s of the Table XVI shows that Lytton and Kamloops are notably warmer than the other s t a t i o n s f o r a l l months except A p r i l .  This  i s mainly due t o t h e i r l o c a t i o n i n the r a t h e r confined Thompson V a l l e y , yet these towns occupy s i t e s representative of much of the p o t e n t i a l arable land i n the v a l l e y . Although the p r o b a b i l i t i e s of cooler maxima (below 75°F) are lower at these s t a t i o n s from May onwards, the p r o b a b i l i t i e s of the warmer maxima (80°F and above) are not n o t i c e a b l y greater u n t i l J u l y .  The u n s e t t l e d ,  cloudy weather of June i n the I n t e r i o r keeps the maxima on a par with Hope, but when the more s e t t l e d a n t i c y c l o n i c conditions p r e v a i l i n the I n t e r i o r during the. middle and l a t e r summer, accompanied by outbreaks of CT a i r , Lytton and Kamloops can experience extremely high maxima (over 100°F).  A  comparison between the temperature p r o b a b i l i t i e s at Kamloops, Penticton and Vernon q u i c k l y shows how the climate i s g e n e r a l l y cooler towards the north and east of the r e g i o n .  The differences i n height between the s t a t i o n s  (Kamloops 1133 f e e t , Penticton 1140 f e e t , Vernon 1580 f e e t ) would hardly account f o r these r e s u l t s , e s p e c i a l l y as P r i n c e t o n (2283 f e e t ) p a r a l l e l s Vernon's p r o b a b i l i t i e s i n a l l months except J u l y , when i t i s considerably warmer.  51. Table XVI - Relative Frequencies of D a i l y Maximum Temperatures at Selected S t a t i o n s , (1945-1964). Hope April  TV 30 35 4045 50 55 60 65 70 75  -  80 85 90 95 100 105  -  35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110  1.41 7.97 28.01 51.77 70.04 . 82.45 93.44 97.87 99.82  May  June  1.95 9.51 21.36 43.83 62.33 75-92 89.71 95-34 98.45 99.61 99.81  1.95 7.39 25.88 49.42 73.54 87.74 93.97 97.47 99.42 99.80  May  June  July  August  0.92 7.02 19-59 39-56 68.39 87.25 93.53 96.49 98.71 99.81  1.28 10.09 23.85 48.07 69.54 85.50 94.86 97.80 99.81  July  August  Septembi  1.63 11.20 28.92 46.84 65.17 80.45 87-58 97.75 99.18 99.80  Lytton T°F 30 35 40 45 50 53 60 65 70 75 80 85 90 95 100 105 110  April  -  —  _  — — —  -  —  --  35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115  0.73 3.10 14.75 34.24 59.39 77.05 89.98 95.45 99.63 99.81  0.40 1.74 8.93 20.24 39.28 56.75 72.82 85.91 93.25 99-60 99.80  0.40 1.01 8.45 21.13 46.68 64.78 81.29 90.54 96.37 98.79 99.59 99.80  0.36 0.90 5.61 17.36 34.54 51.36 67.09 82.64 92.77 98.37 99.45 99.82  2.25 7.30 23.97 42.88 56.93 73.97 86.70 97.94 99.81  September  1.29 4.97 17.49 31.86 50.28 65.01 79.37 91.53 99.08 99.81  • I.  I  52. Table XVI - Continued Penticton April  t l  30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105  -  35 40 45 50 55 '• 60 65 70 75 80 85 90 95 100 105 110  0.82 5.77 21.07 44.93 73.76 96.66  99.01 99.81  May  0.36 2.?2 10.31 27.72 46.38 68.12 86.96 95.65 99.82  June  1.07 8.21 21.07 46.25 68.39 87-86 95.71 99.46 99.82  July.  1.04 4.58 11.85 29.83 52.20 78.20 94.07 99.23 99.61 99.81  August  0.34 3.40 9.17 21.56 44.14 71.64 89.13 97-79 99.82  Septeml  1.18 4.74 18.38 34.78 59.68 83.40 97.23 99.41 99-81  Princeton April  T°F 30 35 40 45 50 •'55 60 65 70 75 80 85 90 95 100 105  -—  —  -  -  35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110  0.54 4.75 17.55 40.76 64.17 80.26 89,76 95.98 98.53 99.45 99.82  May  0.37 2.21 10.11 26.47 43.75 59.38 76.10 87-50 95.04 98.71 99.81  June  0.36 0.72 6.32 24.19 42.96 64.26 82.31 91.52 97.11 99.10 99.82  July  August  0.17 0.87 5.05 12.19 26.83 43.21 62.72 82.93 94.25 98.95 99.48 99.82  0.37 1.31 7.68 18.73 39.33 56.55 73.60 87.45 96.44 99.62 99.81  Septeml  0.57 4.92 16.48 31.44 43.75 57.76 73.86 89.01 97-35 99.81  53. Table XVI - Continued  Vernon April 30 35 4o 45 50 55 60 65 70 75 80 85 90 95 100 105  - 35 - 40 - 45 - 50 - 55 - 60 - 65 - 70 - 75 - 80 - 85 - 90 - 95 - 100 - 105 - 110  0.37 1.69 7.50 22.51 50.09 74.48 88.55 97.18 99.80  May  0.90 3.81 27.77 48.64 69.87 86.75 93.10 98.91 99.82  June  August  July  0.19 1.69 8.60 25-98 48.60 73.46 87.29 96.82 99.44 99.82  0.41 1.64 6.78 36.75 59.34 80.29 94.04 98.97 99.80  June  July  .  0.53 2.81 11.78 29.17 53.60 73.46 88.93 98.77 99.81  Septeml  0.53 4.27 12.10 26.33 44.84 65.30 87.19 96.44 99.81  Kamloops T°F 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105  April - 35 - 40 - 45 - 50 - 55 - 60 - 65 - 70 - 75 - 80 - 85 - 90 - 95 - 100 - 105 - 110  Rote:  2.29 6.11 16.41 38.55 66.22 82.82 92.75 98.28 99.81  May  0.37 2.40 9.59 24.1? 37.82 57-74 78.41 89.48 95.94 99.45 99.82  0.19 2.06 7.88 19-70 39.96 62.85 82.18 91.18 98.50 99-62 99.82  1,25 6.26 14.13 29.52 49.91 68.69 86.68 96.24 99.10 99.82  August  0.54 1.43 6.44 21.65 43.47 65.12 81.75 95.52 99.81  Septemb<  0.56 2.10 6.50 19-85 35-95 49.06 66.29 86.70 95.88 99.61 99-80  The p r o b a b i l i t i e s are tabulated i n percentages and represent the e m p i r i c a l p r o b a b i l i t y of obtaining maximum temperatures i n the stated range or l e s s .  54. Analysis of R e l a t i v e Humidity Frequencies According to the mass t r a n s f e r process, evaporation i s a f u n c t i o n of both the v e r t i c a l gradient of the vapour pressure at the evaporating surface and at some distance away from that surface, and the e f f e c t i v e n e s s of turbulent mixing above the surface. E o where E  q  .(2)  » . f (u) (e - e ) o  a  i s the evaporation, f (u) i s a f u n c t i o n of the wind speed at some  height 2 above the ground and e  and e o  and height 2 r e s p e c t i v e l y .  are vapour pressures at the surface a  8  According to Leighly , the r e l a t i v e dryness  of the a i r rather than i t s absolute dryness i s important.  Consequently, the  frequencies of d a i l y minimum r e l a t i v e humidities are analysed i n Table XVII. As can be seen from the t a b l e , d a i l y observations of r e l a t i v e humidity were only a v a i l a b l e at three of the s i x stations (Lytton, Penticton and Princeton) f o r a period of 8 years - 1957-1964. An analysis of the t a b l e shows that both Lytton and Princeton experience considerably d r i e r atmospheric conditions than Penticton during the growing season. For example, at Lytton 33.5$ and 45.2$ of the days during June and J u l y r e s p e c t i v e l y record humidities below 25$ and at Princeton 32.4$ and 48.2$ of the days record s i m i l a r l y low h u m i d i t i e s , while at Penticton such conditions only p r e v a i l 13.0$ to 18.6$ of the time.  Undoubtedly the  occurrence of higher humidities at Penticton i s due to the advection of moist a i r o f f the Okanagan Lake, but such conditions are presumably experienced a l l along the lake shores were most of the p r i n c i p a l orchards are situated.  However, the general r e l a t i v e humidity f i g u r e s are so low that  i t i s doubtful whether t h i s d i f f e r e n c e would s i g n i f i c a n t l y a f f e c t J . Leighly, "A note on evaporation", Ecology, V o l . 18 (1937), 180-198.  55. Table XVII - R e l a t i v e Frequencies of D a i l y Minimum R e l a t i v e Humidities at Selected S t a t i o n s i n the I n t e r i o r , (1937-1964.). Lytton R.H.  fo  April  5 - 10 10 - 15 15 - 20 20 - 25 25 - 30 30 - 3 5 35 - 40 40-45 45 - 50 50-55 55-60 60 - 65 65 - 70 70 - 75 75-80  2.46 10.66 21.31 34.25 52.46 68,44 82.79 90.57 94.67 97.54 98.36 98.36 99.59  J  May  June  July  August  September  0.80 6.37 28.84 44.28 63-75 77.29 88.84 91.24 96.41 98.00 99.20  1.05 6.28 18.85 33.51 50.79 65.45 84.29 92.67 97.38 98.95 99.48  2.15 13.44 30.11 45.16 55.38 69.35 81.72 88.71 94.62 97.85 99.40  0.81 7.29 18.62 36.84 48.99 62.35 74.49 83.80 90.69 94.33 97-57 99.60  June  July  August  September  0.42 3.78 13.03 38.66 56.30 74.37 86.13 91.18 94.96 97.48 99-16 99.50  0.81 6.85 18.55 47.18 68.15 81.85 90.73 93.95 96.77 98.39 99.60  2.09 10.88 28.45 51.05 69.26 84.02 94.26 96.31 97-54 99-18 99.60  0.37 10.78 33.47 46.10 64.31 79-18 86.25 90.71 95.17 97-40 98.88 99.26 99.60  5-85 16.45 32.91 49.39 62.04 71-31 83.34 88.61 96.20 97.89 99.50  Penticton ,4  R.H. 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80  i°  -  10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85  April  2.09 9.62 24.25 44.75 64.44 77.59 82.88 94.56 97.07 98.33 99.50  May  1.60 14.00 33.20 52.00 • 67.20 80.40 86.80 92.40 95.20 96.40 98.40 98.80 99.60  56. Table XVII - Continued Princeton R.H. fo 5 10 15 20 25 30 35 40 '+5 50 55 60 65 70 75  _  April  10  - 15 - 20 25 - 30 35 -- 40 - 45 - 50 - 55 - 60 - 65 - 70  75 - 80 -  Rote:  May  1.25 8.75 17.50 33.33 49-58 70.41 84.16 90.83 93.33 94.58 95-83 99-16 99.60  5-75 15-70 25.67 42.15 60.15 75.48 83.14 88.89 91-57 95.01 96.55 98.08 98.85 99.65  June  July  August  September  0.41 3.32 14.94 32.37 46.89 62.66 73.03 82.16 89.63 92.53 95.02 97.93 98.76 99.65  2.04 10.61 28.98 48.16 59.59 71.49 82.45 88.57 93.47 96.33 98.38 99.68  4.45 19.03 35.63 49.80 61.54 70.45 83.81 89.07 93.93 97.17 98.79 99.63  1.27 10.55 18.99 38.40 50.21 63.29 76.37 85.23 90.30 96.62 97.89 99-58  '  P r o b a b i l i t i e s are tabulated i n percentages and represent the empirical p r o b a b i l i t y of obtaining minimum r e l a t i v e humidities i n the stated range or l e s s .  57. t r a n s p i r a t i o n losses along the lake shore. Combination of Weather-Type Frequencies Since evaporation i s known to be a f f e c t e d by at l e a s t f o u r c l i m a t i c elements, v i z . temperature, humidity, wind and net r a d i a t i o n , i t was thought that a more r e a l i s t i c representation of the evaporating conditions i n the I n t e r i o r might be obtained from an analysis of the frequencies of occurrence  9 of combinations of these weather types .  Unfortunately, d a i l y data were  a v a i l a b l e f o r only two of the four weather elements, v i z . temperature and humidity.  Frequency tables were tabulated at the three s t a t i o n s f o r the 8  years when both d a i l y minimum humidity and d a i l y maximum temperature observat i o n s were a v a i l a b l e (Table XIX).  The c l a s s i f i c a t i o n system used i n the t a b l e s  f o r each of the two elements i s presented i n Table X V I I I . Table XVIII - C l a s s i f i c a t i o n of Weather Elements used i n Table XIX D a i l y Maximum Temperature Class Number Range  D a i l y Minimum Relative Humidity Class Number Range  1  below  50 F  1  0  -  10%  2  51  -  60°F  2  11  -  20%  3  61  -  70°F  3  21  -  30%  4  71  -  80°F  4  31  -  40%  5 6  81  -  90°F  41  -  50%  91  - 100°F  5 6  51  -  60%  7  above 100°F  7  above  60%  The diagonal patterns apparent i n Table XIX i n d i c a t e that there i s a pronounced negative c o r r e l a t i o n between the two weather elements - the h i g h e r the maximum temperature, the lower the minimum r e l a t i v e humidity. other f a c t o r s being equal, these conditions would combine to i n t e n s i f y the rates of evaporation loss and, accordingly, the greater the frequency of occurrences towards the right-hand top corners of the t a b l e s , the greater w i l l be the evaporation r a t e .  All  58. Table XIX - Temperature-Humidity Combinations at Selected S t a t i o n s , (1957-1964) 1.  LYTTON 3  4  1  4  2  2  5 '24 31 32  14  1  -P •H  Tl •H  j  3  2  4  40  31  5  5 17  7  7  1  7  1  13  •H  4  •H  11  4  9  ?  6  5  8  10  1  4  2  1  4  9  2  1  2  12  38  18  2  2  48  21  32  1  •rl  4  2  5  3  2  4  15  21  3  3  17  48  15  3  4  1  23 40  6  5" 6  8  7  7  2  Temperature  2  1  10  2  4  2  19  29  18  5  25  7  5  6  9 4  7  3  •H  3  9  2.  8  35  1  6  7  7  12  5  2  >5  11  4  1  •H  49  3  7  -P  24  3  September  8  1  6  6  23  18  5  5  25  17  10  7  1  1  3 25  1  4  7  4  7  3  6  28  6  2  5  4  23  4  Temperature  3  3  15  1  2  3  5 6  August  Temperature 1  1  .  4  31  1  7  1  x  7  1  7  34  6  4  5  13  5  -p  3  3  June  •H  7  18-  .4  8  6  20  7  3  5  10  1  Temperature  4  3  1  3  3  2  6  2  2  1  8  1  -P •H 'd •H  6  1  June  -P •rl Tj •H  5.  Temperature  May  Temperature  April  16  7  59Table XIX - Continued  2.  PENTICTON May  Temperature 4.  5  13  2  1  29 41  14  1  2  3  7  6  Temperature 1  7  2  3  4  5  6  1 2 •H  3 1  40  33  5  1  20  8  6  1  14  1  7  3  1  •H  1  •H  3  4  1  2  •H  1  6  5  1  •H  Temperature  July-  June  7  3  3  43  12  1 46  4  16  37  18  5  13  8  1  6  6  4  7  1  11  •p •H •rt  w  4  5  2  3  11  3  25  4  9 40  1 2  3  4  5  2  2 4  1  2 15 25 18 61 44 2 28 26  5 6  4  10  2  5  3  September 6  1  7  1  Temperature 2  3  4  5  1  5  2  22  40  9  5  37  35  14  4  34  20  6  16  2  5  4  1 >M1 •P •H TJ •H  5 6 7  11 50 22 2 32  5 15 11 2 5  t>3| -P •H •H  6  1  7  Temperature  August  2,3  7  2 1  60. Table XIX - Continued PRINCETON  3.  April  Temperature  1  >»  •p •rl  m  2  3  6  1  1  2  9 23  8  2  3  3  3  4  5  6  2  3  4  4  9 18  4  1  2  41  18  6  3  1  31  37  18  16  61  6  1  4  3  25  14  3  4  5  5 6  1  13  1  2  2  7  3  7  2  2  1  4  13 1  7  7  3  w  July  Temperature  2  3  1 2  4  1  3  4  5  6  2  3  3  27  31 11  7  25  35  24  19  2 20  4  4  •rl  5 6  8  7  1  1  2  •rl •H  4  4  5  6  7  1  9  1  13  43  23  f»4 -P  3  1  •rl  4  5 31 37 4 23 24 18 5 1 2  1  4  13  24  5  5  1  13  6  2  5 2  September  2  4  3  7  3  3  1  •rl  2  3  2  1  4  3  4  27  10  31  5 6  12  17 6  7  7  4  6  7  7  18  1  1  5  Temperature  1  •rl  5  9 52 31 6 28 20 5  2  1  1  2  2  1 -P  7  Temperature 1  7  Temperature  August  7  2  12  5 6  5 6  Temperature 1  7  1  1  •rl  5  1  June  •p  4  May  8  4  5  2 1 21 15 30 13 1 19 4  6 1  7  61. At a l l s t a t i o n s , such frquencies increase sharply during J u l y and August.  Lytton appears to have the greatest frequency of low humidities and  high temperature, and while Penticton has a higher frequency of hot days than Princeton, i t seldom experiences humidities below 10%. The occurrences of hot days w i t h low humidities deserve c l o s e r s c r u t i n y . An Analysis of T o r r i d Day Frequencies The hot, sunny day w i t h low r e l a t i v e humidity and a gentle breeze i s known to extract the greatest amounts of moisture from a crop cover.  Such  a day i s c a l l e d a " t o r r i d day" and i s here defined as a day on which the maximum temperature i s 86°F or above and the minimum r e l a t i v e humidity 30% or less.  A t o r r i d s p e l l i s defined as any t o r r i d day or uninterrupted succession  of t o r r i d days, i . e . the i s o l a t e d t o r r i d day represents a one-day t o r r i d s p e l l . As with the other c l i m a t i c elements, the frequencies of t o r r i d days and s p e l l s are analysed i n terms of t h e i r monthly, seasonal and geographical v a r i a t i o n s . The a c t u a l number of t o r r i d days, accumulated over the 8-year period 1957-1964, are tabulated f o r each of the months of the growing season at each of the three s t a t i o n s . (Table XX) Table XX - Accumulated Frequencies of T o r r i d Days per Month During the Growing Seasons, 1957 - 1964. Station  April  May  June  Lytton  July  Aug.  Sep.  Season  -  21  63  126  44  32  286  Penticton  -  10  46  101  51  5  213  Princeton  _  9  28  108  62  13  220  The prominence of Lytton as the warmest and d r i e s t s t a t i o n i n the I n t e r i o r i s again emphasised, but the i n t e r e s t i n g f a c t emerging from the table i s that Princeton i n the plateau experiences more t o r r i d days over the  seasons (ZZO) than Penticton  i n the v a l l e y (213), that i s approximately 28  days per season at Princeton against 27 per season at P e n t i c t o n . Lytton averages %  days per season.  By comparison,  However, the year t o year v a r i a t i o n i n the  frequency of t o r r i d days at the i n d i v i d u a l s t a t i o n s i s so great as to make the statement f o r the seasonal averages f o r each s t a t i o n v i r t u a l l y meaningless. Lytton had a range from 20 t o 57 days per season;  P e n t i c t o n 9 to 43 and  Princeton 6 to 44. This v a r i a t i o n r e s u l t e d from the f a c t t h a t , while during the e a r l i e r months, t o r r i d days occurred as single events, by f a r the larger number occurred i n a s s o c i a t i o n w i t h other t o r r i d days to form t o r r i d s p e l l s .  Prolonged t o r r i d  s p e l l s tended t o be concentrated i n t o a few seasons, other seasons only experi e n c i n g short s p e l l s .  In f a c t , three out of the eight seasons analysed  accounted for approximately 70% of the t o t a l number of t o r r i d days at these stations. An a n a l y s i s of these t o r r i d s p e l l frequencies shows t h a t , as w i t h t o r r i d days, t o r r i d s p e l l s are most frequent at L y t t o n , (Table XXI).  They  also tend to be longer at t h i s s t a t i o n - 2.3 days over the season on average against 1.8 days and 1.7  days at Penticton and P r i n c e t o n r e s p e c t i v e l y .  Thus,  although Princeton experienced more t o r r i d days per growing season than P e n t i c t o n , the l a t t e r s t a t i o n tended to have the greater frequency and the greater proportion of longer s p e l l s , e s p e c i a l l y during J u l y and August.  At  a l l s t a t i o n s , t o r r i d s p e l l s are more frequent and l a s t longer during the month o f J u l y , which i s i n keeping with the high incidence of a n t i c y c l o n i c weather during t h i s period of the growing season.  I n f a c t , L y t t o n experienced more  than h a l f of i t s t o r r i d days i n J u l y during s p e l l s l a s t i n g f o r f i v e days or longer.  Note the r e l a t i v e l y infrequent occurrences of t o r r i d days at Princeton during May and June, a r e f l e c t i o n of the c o o l e r springs on the plateau.  63. Table XXI - Duration of T o r r i d Days at Selected Stations, (1957 - 1964)  Duration of T o r r i d S p e l l s (Days) Station  1  2  3  4  5  6  7  8  9  3  2  June  14  10  5  3  1  1  -  -  July  10 10  6  4  5  3  3  2  5  2  3  -  1  -  5  10  1  1  T o t a l No. of s p e l l s  Average Duration  9  Lytton May  August September  14  1.5  -  34  1.9  2  1  36  3.5  -  -  21  2.1  17  1.9  Season  122  2.31  Penticton May  6  2  June  16  7  4  1  July-  20  11  9  4  August  15  10  6  1  3  1  September  -  -  -  -  -  1 1 1  8  1.2  28  1.6  47  2.2  32  1.4  4  1.1  Season  1.79  119  Princeton May  5  2  June  6  1  1  July  25  14  11  August  20  16  2  9  2  September Season  2 1  _  1 -  -  _  -  7  1.3  16  1.7  54  2.0  39  1.6  11  1.2  127  1.73  6k.  Summary The a n a l y s i s of temperature and humidity frequency patterns at selected points w i t h i n the region tends to emphasize the a r e a l d i f f e r e n c e s i n crop water requirements suggested from an; a n a l y s i s of p r e c i p i t a t i o n p a t t e r n s . The d r i e r areas are generally warmer and l e s s humid than the moister areas and experience more frequent and longer t o r r i d s p e l l s , and therefore one assumes that the consumptive use of water by crops i n these areas w i l l be greater.  In other words, moisture conditions are even more l i m i t i n g i n the  d r i e r areas than the study of p r e c i p i t a t i o n p r o b a b i l i t i e s alone would suggest. However, t h i s s i t u a t i o n i s not e n t i r e l y true throughout the area, since the tempering e f f e c t s of the Okanagan Lake are r e f l e c t e d i n the higher humidities and the r e l a t i v e l y small number of t o r r i d days at Penticton and presumably other lakeside s t a t i o n s .  I t remains to be seen i n the next chapter  whether t h i s m i c r o c l i m a t i c influence s i g n i f i c a n t l y a f f e c t s crop water r e q u i r e ments.  65. CHAPTER 5 THE FREQUENCY AND INTENSITY OF DROUGHT The term "drought" can have several meanings^".  In t h i s chapter i t  i s defined as a s o i l moisture concept, a drought o c c u r r i n g when there i s no longer s u f f i c i e n t moisture i n the s o i l to s u s t a i n vigorous plant growth. Obviously any analysis of drought frequency and i n t e n s i t y so defined w i l l require some measure of the s o i l moisture content and the v a r i a t i o n s i n the s o i l moisture content i n both time and place w i t h i n the r e g i o n . Although procedures f o r measuring s o i l moisture have improved r e c e n t l y and new ones have been made a v a i l a b l e , a l l commonly used techniques have i n herent shortcomings and require considerable c a l i b r a t i o n and r e p l i c a t i o n to provide representative s o i l moisture data.  Furthermore, since the d i r e c t  measurements of s o i l moisture w i t h i n the area only provide point readings, they do not i n t e g r a t e s o i l moisture content i n r e l a t i o n to both time and space. To overcome the d i f f i c u l t i e s encountered with d i r e c t s o i l moisture measurements, various methods have been developed f o r c a l c u l a t i n g t h i s water l o s s from meteorological data.  Most of these techniques make use of the w e l l -  known concept of p o t e n t i a l evapotranspiration (PE) as an i n d i c a t o r of the maximum loss of water from a s o i l (a combination of both evaporation and t r a n s p i r a t i o n ) under conditions where the s o i l moisture supply i s not l i m i t i n g . 2 According to Thornthwaite  PE i s independent of crop type and s o i l type, being  determined s o l e l y by meteorological f a c t o r s , provided the crop completely covered the ground and has an adequate moisture supply. * U.S. Geological Survey, Drought: The Meteorological Phenomenon of Drought i n the South West, U.S.G.S. P r o f . Paper'372!A (1962;. Thornthwaite, l o c . c i t .  66. Review of Literature Early workers based their c a l c u l a t i o n s of PE on a few selected 3 c l i m a t i c elements.  Hedke  suggested a method from a study of available heat  expressed i n degree days, the base temperature depending upon the minimum growing temperature of each crop.  4  Lowry and Johnston  undertook a broader  study which indicated a linear r e l a t i o n s h i p between consumptive use and o accumulated maximum temperatures above 32 P.  Blaney and Criddle  5  expressed  monthly PE as proportional to the product of the mean monthly temperature and the monthly percentage of daylight hours i n the year. constant took d i f f e r e n t values f o r d i f f e r e n t crop types.  The proportionality Also using mean  monthly temperatures, Thornthwaite^ developed h i s formula which included a correction factor for l a t i t u d e .  These methods that use mean monthly tempera7  tures have been subjected to some c r i t i c i s m  since the i r r e g u l a r l a g of a i r  temperature behind solar r a d i a t i o n means that such methods cannot be generally applied i n different areas. In 19^8  Penman developed a more sophisticated technique which con-  sidered the energy balance and the influence of wind and the vapour pressure difference on the t r a n s f e r of water vapour into the atmosphere.  However, he  s i m p l i f i e d h i s technique so that PE could be calculated from commonly recorded meteorological observations - a i r temperature, r e l a t i v e humidity, wind speed  ^ C.R. Hedke, "Use of water by crops", New Mexico State Engineer's Office, 1924. (unpublished)  4 R.L. Lowry and A.P. Johnston, "Consumptive use o f water f o r agriculture", Amer. Soc. C i v i l Eng., V o l . 107 (1942), 1243-1302. ^ Blaney and Criddle, l o c . c i t . 6 ' Thornthwaite, l o c . c i t . 7 W.R. van V/ijk and D.A. de Vries, "Evapotranspiration", Neth. Journ. Agric. Science, V o l . 2 (1954), 105-118.  67. and the percentage of the possible hours of sunshine.  Many investigators  have concluded on both theoretical grounds and as a r e s u l t of p r a c t i c a l experiments that Penman's method provides the most accurate estimation of crop  Q water requirements on a monthly basis .  Since t h i s method also combines the  effects of the climatic elements already analysed i n previous chapters,  it  was chosen as an empirical estimator of PE at the selected stations within the region. Analysis of PE Frequencies Since a l l the necessary climatic information was not available at all  six stations for the complete 20-year period of record 1945-1964, the  frequency tables of Penman's PE estimates are perhaps not as consistent for all  stations as were  the other frequency t a b l e s .  The minimum period of  continuous record thought necessary to produce r e s u l t s that would be accurate enough to be used i n this study was ten years and since Vernon could not produce adequate data over a 10-year period, i t was dropped from the drought frequency analysis.  The results were compiled on an I . B . M . 1740 computer  9 following the method outlined by Criddle . The empirical p r o b a b i l i t i e s of monthly PE (Table XXII) were tabulated i n i d e n t i c a l manner as those f o r the maximum temperature occurrences. expected from the analysis of temperature and humidity frequencies,  As  PE rates  8 W.O. P r u i t t , "Relation of consumptive use for water to climate", Trans. Amer. Soc. Agric. E n g . , V o l . 3 (i960), 9-17. W.C. Munsen, "Method for estimating consumptive use of water for  agriculture", Amer. Soc. C i v i l E n g . , V o l . 127 0-962), 200-212. K. Smith,"A long-term assessment of the Penman and Thornthwaite potential evapotranspiration formulae", Journ. H y d r o l . , V o l . 2 (1964),  277-290.  C . B . Tanner and W.L. Pelton, "Potential evapotranspiration estimates by the approximate energy balance method of Penman", Journ. Geoph. Rest,  Vol. 65 (i960), 3391-3413. q  W.A. C r i d d l e , "Methods for computing consumptive use of water", Proc. Amer. Soc. C i v i l Eng. ( i r r i g a t i o n and Drainage), V o l . 84 (1958}, 1-27  68. are highest at Lytton and Kamloops.  However, values are r e l a t i v e l y high at  Hope during June, July and August which, coupled with i t s notable summer minimum  i n r a i n f a l l , would suggest that s o i l moisture conditions at this s t a t i o n  may be l i m i t i n g i n most years by the end of July.  The table also indicates  that PE rates at Penticton are d e f i n i t e l y greater than rates at Princeton, verifying earlier results*  0  that a i r temperature i s a more important element  a f f e c t i n g water loss than the r e l a t i v e humidity.  However, the differences  are generally less than PE rates estimated from Thomthwaite's formula, but not reported here. The S o i l Moisture Budget The components necessary f o r the computation of the s o i l moisture budget have now been analysed.  This budget f o r cropped s o i l s under i r r i g a t i o n  i s obtained by balancing the moisture losses by evapotranspiration against the moisture gains from r a i n f a l l and i r r i g a t i o n .  The bookkeeping  procedure  for estimating s o i l moisture and f o r scheduling the time of i r r i g a t i o n from PE data has been described elsewhere**. However, the use of weather data i n connection with i r r i g a t i o n planning requires the acceptance of certain fundamental concepts i n connection with the gain and loss of water from the s o i l .  F i r s t l y , i n order that they  maintain maximum growth rates, crops must have an adequate supply of water and, therefore, by d e f i n i t i o n , they w i l l lose water at PE rates.  It i s not  easy to define exactly what i s meant by adequate s o i l moisture. Penman  12  *° Wilcox, l o c . c i t . ** O.W. Thomthwaite and J.R. Mather, The Water Budget and i t s Use i n I r r i g a t i o n , U.S. Dept. of Agriculture Yearbook (Washington, D.C., 1955), 3 -358. c.H.M. van Bavel, "A drought c r i t e r i o n and i t s application i n evaluating drought incidence and hazard", Agron. Journ. Vol. 45 (1953), 167-172  12  s  H.L. Penman, Vegetation and Hydrology, Tech. Comm. No. (Harpenden, England: Commonwealth Agricultural Bureau, 1963).  53  69. Table XXII - R e l a t i v e Frequencies of Monthly PE (inches) at Selected S t a t i o n s . HOPE  - Period of Record 1945-1964  P.E. (Inches) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0  6.5  7.0 7.5 8.0 8.5  -  1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5-5 6.0  April 8.33 33.30 72.00 96.00  May  4.16 16.67 37.50 62.50 83.33 95-83  6.5  June  4.00 28.00 44.00 72.00 84.00 88.00 96.00  7.0 7.5 8.0  8.5  July  12.50 25.00 41.66 62.50 75.00 83.33 91.66 95.83  August  4.00 12.00 20.00 36.00 60.00 80.00 92.00 96.00  Sept ember 4.16 20.83 58.33 87-50 95.83  9.0  LYTTON - Period of Record 1946-1964 P.E. (Inches) 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5  - 1-5 - 2.0 -2.5 -3.0 - 3.5 - 4.0 - 4.5 - 5-0  - 5-5  - 6.0 - 6.5  - 7.0  - 7.5 - 8.0  - 8.5  - 9.0  April  20.00 50.00 70.00 95.00  May  8.30 23.80 47.62 80.95 90.48  June  4.75 9.52 14.29 38.10 57.11 71.42 76.19 90.47 95-24  July  10.00 30.00 35.00 75-00 80.00 95.00  August  September  10.00 25.00 40.00 65.00 75.00 95.00  The p r o b a b i l i t i e s are tabulated i n percentages and represent the empirical p r o b a b i l i t i e s of obtaining PE of the stated amount or less.  4.76 23.81 61.90 90.47 95.23  70. Table XXII - Continued PENTICTON - Period of Record 1946-1964 P.E. (inches)  1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5-5 6.0 6.5 7.0 7.5 8.0 8.5  -  -  -  1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0  April  16.67 45.83 79.17 95-83  May  17.39 52.17 60.87 91.30 95.65  August  June  18.18 40.91 63.64 81.82 90.91 95.45  27.2? 45.45 68.18 81.82 90.91 95.45  4.35 34.78 39.13 69.56 86.95 91.30 95-65  September  16.6? 37.50 79.17 87.50 95-83  PRINCETON - Period of Record 1945-1964 P.E. (Inches)  1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5-5 6.0 6.5 7.0 7.5  - 1.5 - 2.0 - 2.5 - 3.0 - 3.5 - 4.0 - 4.5 - 5.0 - 5.5 - 6.0 - 6.5 - 7.0 - 7.5 - 8.0  Anril  23.07 61.54 92.31 96.15  May  4.00 20.00 52.00 84.00 92.00 96.00  June  4.00 24.00 52.00 80.00 92.00 96.00  KAMLOOPS - Period of Record 1954-1964 May June April P.E. (Inches)  1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 8.5  - 1.5 - 2.0 - 2.5 - 3.0 - 3.5 - 4.0 -4.5 - 5.0 - 5.5 - 6.0 - 6.5 - 7.0 - ?o - 8.0 - 8.6 - 9.0  5.88 11.76 41.18 76.47 94.11  11.76 29.41 52.94 82.33 94.11  17.65 29-41 47.06 79.59 88.24 94.11  July  8.00 32.00 60.00 72.00 92.00 96.00  July  12.50 25.00 43.75 56.25 75.00 93.75  August  4.00 16.00 48.00 68.00 . 92.00 96.00  August  25.00 31.25 37.50 81.25 93-75  September  4.00 24.00 68.00 88.00 96.00  September  5.88 23.52 35.29 82.33 88.24 94.11  71. i n reviewing extensive l i t e r a t u r e pertaining to moisture loss under conditions of non-limiting water supply noted that some investigators considered the water supply to be l i m i t i n g as soon as i t dropped below f i e l d capacity ( i . e . the TO  amount the s o i l can hold against gravity), while others continue to transpire at PE rates almost throughout c i t y to permanent w i l t i n g point.  showed^tKat'^crops can  the range from f i e l d  capa-  Moisture available for a plant depends upon  both the v e r t i c a l root d i s t r i b u t i o n of the plant and the porosity of the s o i l within the root zone. may be  very  Adequate water f o r a shallow-rooted crop on a sandy s o i l  much d i f f e r e n t  s o i l , f o r the  from  that  for  a  deep-rooted crop  on  a clay loam  amount of moisture available to a shallow-rooted crop on a sandy  s o i l w i l l not last as many days as w i l l the larger amount of water available to the deep-rooted crop on the clay loam.  Working i n the area under study,  14 V/ilcox and Korven  have suggested that s o i l moisture content adequate for  crop growth should not f a l l below 50 per cent of the t o t a l s o i l water a v a i l able to the crop. The second assumption i n connection with the use of s o i l moisture budget i s that PE rates under the above conditions are independent and s o i l factors and are s o l e l y a function of the climate.  of plant  Therefore,  fluctuations i n PE rates should vary d i r e c t l y with the fluctuations i n the climatic elements a f f e c t i n g evapotranspiration. Thus, the required amount of i r r i g a t i o n to maintain maximum crop growth within the area w i l l be the difference between that amount of water available to the crop from  soil  storage and r a i n f a l l , and that amount lost through potential evapotranspiration.  __ P.J. Veihraeyer and A.H. Hendrickson, "Does transpiration decrease as s o i l moisture decreases?" Trans. Amer. Geoph. Union, Vol. % (l°55)> 425-  448.  14  J.C. V/ilcox and H.C. Korven, "Effects of weather fluctuations on the scheduling of i r r i g a t i o n " , Can. Journ. Plant Science, V o l . 44 (1964),  439-445.  72. Table XXIII - Empirical P r o b a b i l i t i e s of Seasonal Supplemental I r r i g a t i o n Requirements (Inches) at Selected Stations (assuming no s o i l storage capacity). Princeton  Kamloops  18.1  14.8  24.2  27.6  21.1  18.2  27.2  29.2  24.1  19.3  28.9  33.6  25.7  20.9  32.0  35.5  30.2  25.1  34.2  Hope  Lytton  90  9.3  24.5  75  10.2  50  11.1  25  15.1  10  17.9  .  Penticton  The general tendency f o r water income ( r a i n f a l l ) to decrease i n areas where the expenditure (PE) i s greatest i s emphasized  i n Table XXIII.  Here are  shown the supplemental water requirements cumulated over the e n t i r e growing season, as calculated by the s o i l moisture budget method at various p r o b a b i l i t y levels.  The r i s k (P) i s shown i n percentages and can be interpreted as the  number of years i n 100 when at most a certain amount of supplemental water w i l l be required.  For example, at Hope the amount of i r r i g a t i o n water req-  uired w i l l exceed 17.9 time.  I t i s important to note that the above table does not include s o i l  moisture c a p a c i t i e s . the  inches only once i n 10 years, or 10 percent of the  Once these are known (see r e s u l t s of s o i l surveys),  necessary amount can simply be deducted.  Thus i f a s o i l had an 8 inch  s o i l moisture storage at Hope, the actual amount of supplemental i r r i g a t i o n required once a decade would be 9«9 inches. Even i n this dry region few crops require i r r i g a t i o n throughout the growing season, beginning i n A p r i l , thus when estimating the amounts of supplemental i r r i g a t i o n for short season crops such as hay i t would be advantageous  to use Table XXIV, which shows the p r o b a b i l i t i e s of monthly  supplemental water requirements f o r crops at various s o i l moisture storage capacities.  73. The f a c t that s o i l moisture capacity i s d i f f i c u l t to quantify has already been discussed and, since the various f a c t o r s a f f e c t i n g i t vary g r e a t l y throughout the region, a range of p o s s i b l e s o i l moisture c a p a c i t i e s has been 15 used i n t h i s t a b l e .  According t o Wilcox  these c a p a c i t i e s cover most of the  range represented by the a g r i c u l t u r a l l y productive s o i l s w i t h i n the r e g i o n . However, remembering that PE r a t e s only continue as long as 50 per cent or more of the a v a i l a b l e moisture remains i n the s o i l , and that t h i s t a b l e has been c a l c u l a t e d assuming-loss at PE r a t e s , the s o i l moisture storage c a p a c i t i e s i n d i c a t e d i n the table w i l l only equal approximately h a l f of the t o t a l amount of water a v a i l a b l e to the crops, i . e . that amount of water held i n the s o i l at tensions between f i e l d capacity and permanent w i l t i n g p o i n t .  For example,  the s o i l with a 2 inch s o i l moisture storage capacity w i l l , i n f a c t , contain 4 inches of a v a i l a b l e moisture. An analysis of Table X X I V  16  i n d i c a t e s that there are considerable  s p a t i a l v a r i a t i o n s i n the timing and the amount of supplemental i r r i g a t i o n requirements w i t h i n the r e g i o n .  Because A p r i l and May are cool months at most  i n t e r i o r l o c a t i o n s (see Table XVI), and because the summer maximum r a i n f a l l accompanied by periods of c o o l , cloudy weather, keep PE rates down during June (see Table XXII), the supplemental i r r i g a t i o n requirements remain reasonably low f o r the heavy s o i l s at most s t a t i o n s apart from Lytton and Kamloops u n t i l J u l y . At Hope the high frequency of wet s p e l l s i n A p r i l and May maintain the s o i l moisture storage at or near f i e l d c a p a c i t y u n t i l earlyJune.  However, the incidence of prolonged dry s p e l l s i n June and J u l y , as  noted i n Chapter 3, allows considerable water d e f i c i t s t o be b u i l t up by l a t e J u l y i n most s o i l s , with the r e s u l t that i n order to maintain maximum J.C...,,.Wile ox, " I n d i r e c t determination .of f i e l d capacity, f o r moisture", S c i e n t i f i c A g r i c u l t u r e , V o l . 29 (19^9), 563-578. In the table a l l s o i l s are assumed to be at f i e l d capacity at the beginning of the growing season. 1 6  74. growth throughout the summer supplemental i r r i g a t i o n i s a necessity i n most years. The lack of large i r r i g a t i o n requirements for the heavier s o i l s u n t i l l a t e June throughout the area suggests that short-season crops such as hay could be economically grown.  However, the long-season crops, such as  orchard production, w i l l c e r t a i n l y r e q u i r e large amounts of supplemental i r r i g a t i o n once the s o i l moisture storage has been exhausted and such crops should only be grown where there i s an adequate supply of water.  An estimation  of t h i s t o t a l amount and the various p r o b a b i l i t i e s of the amounts can be made by cumulating the monthly i r r i g a t i o n requirements f o r the appropriate p r o b a b i l i t y levels at Penticton.  Although the appropriate f i g u r e s were not a v a i l a b l e  f o r Vernon, the combination of a higher incidence of p r e c i p i t a t i o n throughout the summer and lower maximum temperatures would suggest that i r r i g a t i o n would not only be delayed but would also be required i n smaller amounts as one moves up the Okanagan. The same combination of c l i m a t i c f a c t o r s reduce the i r r i g a t i o n requirements at Princeton, the only s t a t i o n studied which represents conditions i n the p l a t e a u . Unfortunately, the advantage of smaller i r r i g a t i o n amounts i s o f f s e t by the predominance of t h i n , l i g h t s o i l s which seldom hold more than 8 inches of a v a i l a b l e water w i t h i n t h i n p r o f i l e s , i . e . 4 inches of s o i l 17 storage capacity  .  However, at higher elevations one would expect the t i m i n g  of the water d e f i c i t to be delayed u n t i l J u l y and August, a l l o w i n g a system of transhumansce to enable c a t t l e to feed on f r e s h pastures u n t i l the middle of summer. I t was hoped that the e m p i r i c a l r e s u l t s expressed i n Table XXIV could be compared w i t h f i g u r e s f o r the a c t u a l use of i r r i g a t i o n water i n the region.  Unfortunately, d e t a i l e d information of t h i s nature was not a v a i l a b l e 17  Spilsbury and T i s d a l e , l o c . c i t .  75. f o r these s t a t i o n s .  However, the Water Resources Service i n V i c t o r i a issue  water l i c e n c e s f o r each i r r i g a t o r i n the province and, although t h i s i s u s u a l l y a f i x e d amount from year to year (and therefore not v i a b l e f o r comparative purposes), the e m p i r i c a l r e s u l t s generally agree with the Water Resource Services estimates.  Since such d e t a i l e d information i s l a c k i n g , i t i s thought  that these e m p i r i c a l r e s u l t s could act as an important f i r s t approximation to the very important problem of estimating i r r i g a t i o n water requirements i n t h i s semi-arid r e g i o n .  76. Table XXIV - Monthly Supplemental I r r i g a t i o n Requirements at Selected S t a t i o n s . HOPE (a)  1" S o i l Moisture Storage Capacity  n 90 75 50 25 10 (b)  April  May  _  _  —  0.9 1.9 3.9  1.2 1.6 2.7 4.2  0.6  90 75 50 25 10  90 75 50 25 10  2.2 2.8 3.9 5.0 6.6  0.8 2.1 2.4 3.7 4.3  September — —  0.1 1.7  mm  May  June  *m  mm  0.9 2.9  0.2 1.3 2.7 4.2  July  August  2.2 2.8 3.9 5.0 6.6  0.8 2.1 2.4 3-7 4.3  September  — —  0.1 1.7  April  May  _  _  June —  0.8 1.2 3.3  September  July  August  1.2 2.2 3.5 4.8 6.2  0.8 2.1 2.4 3.7 4.3  0.1 1.7  August  September  -  -  .  —  8" S o i l Moisture Storage Capacity ._Pji  90 75 50 25 10 (e)  August  4" S o i l Moisture Storage Capacity Ffo  (a)  July  2" S o i l Moisture Storage Capacity  April  (c)  June  July  April  May  June  -  —  -  -  —  -  _  —  —  —  -  —  0.3 1.3 5.1  0.2 1.2 2.2 3.5 4.0  -  -  0.1 1.7  12'" S o i l Moisture Storage Capacity April  May  June  July  August  September  77. Table XXIV - Continued LYTTON (a)  l  w  p%_  April  May  June  July  August  September  90  1.4 1.6 2.3 2.5 3.2  4.2 4.6 5.0 5.8 6.5  3.6 4.8 5.9 6.9 7.7  5.2 6.3 7.0 7.6 8.7  3.3 4.3 5.8 6.1 6.8  1.3 2.1 2.7 3.6 3.8  75 50 25 10 (b)  S o i l Moisture Storage Capacity  2" S o i l Moisture Storage Capacity P%_  April  May  June  July  August  September  90 75 50 25 10  0.4 0.6 1.3 1.5 2.2  4.2 4.6 5.0 5.8 6.5  3.6 4.8 5-9 6.9 7.7  5.2 6.3 7.0 7.6 8.7  3.3 4.3 5.8 6.1 6.8  1.3 2.1 2.7 3.6 3.8  August  September  5.2 6.3 7.0 7.6 8.7  3.3 4.3 5.8 6.1 6.8  1.3 2.1 2.7 3.6 3.8  June  July  August  Sept ember  3.4 4.4 5.9 6.9 7.7  5.2 6.3 7.0 7.6 8.7  5-3 4.3 5.8 6.1 6.8  1.3 2.1 2.7 3.6 3.8  S o i l Moisture Storage Capacity  (c)  90 75 50 25 10  April  May  June  -  3.2 4.1 4.4 4.9 6.1  3.6 4.8 5.9 6.9 7.7  0.3  July  8" S o i l Moisture Storage Capacity  (e)  Si  April  May  90 75 50 25 10  _  —  -—  0.6 1.0 2.3  12' • S o i l Moisture Storage Capacity P%  90 75 50 25 10  April  May  • —  -  -  --  -  -  -  June  July  August  September  0.4 1.8 2.7 4.7 6.4  5.2 6.0 6.9 7.5 8.7  3.3 4.3 5.8 . 6.1 6.8  1.3 2.1 2.7 3.6 3.8  78. Table XXIV - Continued PENTICTON (a)  1" S o i l Moisture Storage Capacity p£  90 75 50 25 10  April  May  June  July  August  September  0.7 1.6 2.1 2.7  1.8 3.0 4.0 4.2 5.4  2.7 3.2 4.0 4.6 6.2  4.2 5.0 5.4 5-9 7.5  3.4 4.0 4.4 5.5 6.0  1.3 2.3 2.9 3.4 4.1  2 S o i l Moisture Storage Capacity n  (c)  Si  April  May  June  July  August  September  90 75 50 25 10  -  1.8 3.0 4.0 4.2 5-4  2.7 3.2 4.0 4.6 6.2  4.2 5.0 5.4 5.9 7.5  3.4 4.0 4.4 5.5 6.0  1.3 2.3 2.9 3.4 4.1  June  July  August  September  1.6 3.2 4.0 4.6 6.2  4.. 2 5.0 5.4 5.9 7.5  3.4 4.0 4.4 5.3 6.0  1.3 2.3 2.9 3.4 4.1  July  August  3.6 4.6 5.2 5.9 7.5  3.4 4.0 4.4 5.3 6.0  4" S o i l Moisture Storage Capacity .5  90 75 50 25 10 (d)  0.6 1.1 1.7  April  May  _  _  -  1.6 2.4 3.1 4.4  8" S o i l Moisture Storage Capacity April  90 75 50 25 10 (e)  -  May  -, 0.5  June _  0.9 2.9 3.8 6.0  Septembei  1.3 2.3 2.9 3.4 4.1  12" S o i l Moisture Storage Capacity  90 75 50 25 10  April  May  -  -  June _  -  0.3 2.2  July  August  0.2 2.0 4.2 5.1 6.1  3.4 4.0 4.4 5.3 6.0  Septembe]  1.3 2.3 2.9 3.4 4.1  79. Table XXIV - Continued PRINCETON (a)  1" S o i l Moisture Storage Capacity P£  90 75 50  25 10 (b)  April  May  June  July  August  September  0.2 0.7 1.3 1.7  1.2 1.8 2.6 3.7 4.7  2.2 3.1 3.7 4.1 5.0  2.7 4.0 4.6 5-5 6.5  2.0 3.1 3.9 4.6 5.6  0.6 1.4 2.1 2.5 3.0  2" S o i l Moisture Storage Capacity April  90 75 50 25 10 (c)  90 75 50 25 10  July  August  September  1.2 1.8 2.6 3.7 4.7  2.2 3.1 3.7 4.1 5.0  2.7 4,.0 4.6 5-5 6.5  2.0 3.1 3.9 4.6 5.6  0.6 1.4 2.1 2.5 3.0  April  -  May  June  July  August  September  0.9 2.0 3.2  2.1 2.4 3.6 4.0 4.7  2.7 4.0 4.6 5.5 6.5.  2.0 3.1 3-9 4.6 5.6  0.6 1.4 2.1 2.5 3.0  July  August  September  2.4 3.4 4.2 5.^ 6.2  2.0 3.1 3-9 4.6 5-6  0.6 1.4 2.1 2.5 3.0  July  August  September  -  0.6 3.1 3-7 4.6 5.6  0.1 1.3 2.1 2.5 3.0  V  8" S o i l Moisture Storage Capacity  Si 90 75 50 25 10 (e)  0.3 0.7  June  4" S o i l Moisture Storage Capacity  *L  (d)  -  May  April  May  -  -  June —  - .  1.0 2.1 3.5  12" S o i l Moisture Storage Capacity 2L  90 75 50 25 10  April  May-  June  1.6 2.5 5.6  80« Table XXIV - Continued KAMLOOPS (a)  1" S o i l Moisture Storage Capacity ffo  April  May  June  July  August  September  90  2.2 2.5 2.6 3.2 3.8  4.3 4.7 5.1 6.2 6.8  4.0 4.7 5.8 6.4 6.8  5.1 5.2 5.7 7.6 8.1  3.2 4.4 5-9 6.5  1.4 2.5 3.2 4.0 4.6  75 50 25 10 (b)  2" S o i l Moisture Storage Capacity  H 90  75 50 25 10 (c)  April  May  June  July  August  September  1.1 1.5 1.6 2.2 2.8  4.3 4.7 5.1 6.2 6.8  4.0 4.7 5-8 6.4 6.8  5.1 5.2 5.7 7.6 8.1  3.2 4.4 5.0 5-9 6.5  1.4 2.5 3.2 4.0 4.6  4" S o i l Moisture Storage Capacity  \± 90 75 50 25 10  (d)  April  May  June  July  August  September  0.3 0.9  4.3 4.7 4.9 5.5 6.5  4.0 4.7 5.8 6.4 6.8  5.1 5.2 5.7 7.6 8.1  3.2 4.4 5.0 5-9 6.5  1.4 2.5 3.2 4.0 4.6  8" S o i l Moisture Storage Capacity P$  April  90 75 50 25 10 (e)  5.0  May  June  July  August  September  0.7 0.9 1.2 1.7 2.5  4.0 4.7 5.8 6.4 6.8  5.1 5.2 5-7 7.6 8.1  3.2 4.4 5.0 5.9 6.5  1.4 2.5 3.2 4.0 4.6  August  September  3.2 4.4 5-0 5.9 6.5  1.4 2.5 3-2 4.0 4.6  12' S o i l Moisture Storage Capacity 1  April  90 75 50 25 10  -  -  -  May  June  July  0.9 1.6 2.6 3.5 4.7  5.1 5.2 5.7 7.6 8.1  81. CHAPTER 6 SUMMARY AND CONCLUSIONS The temporal and geographical v a r i a t i o n s i n the frequency, i n t e n s i t y and d u r a t i o n of some of the meteorological phenomena a f f e c t i n g the supply and demand of water by growing crops have been analysed at selected s t a t i o n s i n the south-central I n t e r i o r of B r i t i s h Columbia.  The a n a l y s i s of the mois-  ture supply patterns showed that greater amounts of p r e c i p i t a t i o n tended to occur during the e a r l i e r h a l f o f the growing season at most s t a t i o n s , the month of June experiencing a d e f i n i t e maximum.  P r o b a b i l i t i e s of wet and dry  s p e l l s supported t h i s f a c t , the highest frequency of wet s p e l l s o c c u r r i n g i n June, while the lower p r o b a b i l i t i e s of wet days i n J u l y and August i n d i c a t e d an increase i n the length of dry s p e l l s during the second h a l f of the growing season. The r e s u l t s of the analyses of the two weather elements promoting water l o s s , namely maximum a i r temperature and minimum r e l a t i v e humidity, suggested that these elements also followed t h i s p a t t e r n .  The evaporative  power of the a i r * remained r e l a t i v e l y low u n t i l the end of June, a f t e r which i t increased sharply as these two elements combined i n such a manner t h a t they i n t e n s i f i e d evaporation l o s s .  This conspiracy was i l l u s t r a t e d when t h e i r  j o i n t d a i l y observations were combined i n a frequency t a b l e , both J u l y and August experiencing t h e highest r e l a t i v e frequencies of t o r r i d days (hot days with low r e l a t i v e h u m i d i t i e s ) . The conclusions were v e r i f i e d when the actual amounts of i r r i g a t i o n water were computed at selected s t a t i o n s , by estimating p o t e n t i a l evapotransp i r a t i o n r a t e s from Penman's e m p i r i c a l formula and using the s o i l moisture * Evaporative power - the dynamic capacity or power of the surrounding a i r t o permit or promote the evaporation o f water.  82. budget technique.  At a l l s t a t i o n s except L y t t o n , l i t t l e i r r i g a t i o n was r e q -  u i r e d i n most years u n t i l the beginning of J u l y , unless the s o i l s had low moisture storage c a p a c i t i e s , but from J u l y to September the required i r r i g a t i o n amounts were high, a f a c t that was due both to the increased dryness of the atmosphere and to the previous d e p l e t i o n of the r e a d i l y a v a i l a b l e s o i l moisture. This s o i l mosture budget technique provides a systematic ( i f not wholly accurate) method f o r applying weather data to the problems of i r r i g a t i o n scheduling and to the v a r i a t i o n s of such amounts i n both time and space. For s o i l s of s i m i l a r moisture storage c a p a c i t i e s , there are considerable v a r i a t i o n s i n water need from place to place throughout the region, the dry areas of the Thompson Valley and South Okanagan r e q u i r i n g greater amounts of i r r i g a t i o n water throughout the growing season than the Princeton and (presumably) Vernon areas. Evaporating processes are shown to be a complex m u l t i - v a r i a t e system r a t h e r than a mere sum of averaged c l i m a t i c data.  Each i n d i v i d u a l element of  the o v e r a l l complex of elements that i s known c o l l e c t i v e l y as the weather varies  independently to f i t i n t o a general e q u i l i b r i u m that forms a weather 2  type or n a t u r a l p e r i o d , e.g. hot, sunny s p e l l .  I t has been shown  that a  higher proportion of the v a r i a t i o n of evaporating r a t e s can be explained through the v a r i a t i o n of chosen c l i m a t i c v a r i a b l e s , i f such c o r r e l a t i o n analyses are conducted only during n a t u r a l weather periods, r a t h e r than calendar periods.  For example, Drinkwater and Jones noted a s i g n i f i c a n t l y b e t t e r  c o r r e l a t i o n between maximum d a i l y temperature, s o l a r r a d i a t i o n and the durat i o n of sunshine with atmometer and lysimeter evaporation when the a n a l y s i s was only conducted during dry periods than when the same analysis wae W.O. Drinkwater and B.E. Jones, " R e l a t i o n of p o t e n t i a l evapot r a n s p i r a t i o n to environment and kind of p l a n t " , Trans. Amer. Geoph. Union, V o l . 38 (1957), 524-528.  83. conducted over a 7-day p e r i o d .  I t would appear that the various meteorological  elements that a f f e c t evaporation adjust themselves to produce a p a r t i c u l a r evaporation r a t e , and that a change i n one of these elements i s not accompanied by an immediate corresponding change i n evaporation r a t e s , but rather a r e adjustment of the other r e l a t e d v a r i a b l e s and the subsequent adoption of a new energy balance, that i n t u r n induces a d i f f e r e n t r a t e of evaporation. Obviously the type of data recorded at the meteorological s t a t i o n s i s so general that i t obscures such d e t a i l e d f l u c t u a t i o n s .  However, i t i s  thought that the data are s u i t a b l e to produce r e s u l t s i n keeping w i t h the s c a l e of the study, and to provide a valuable f i r s t approximation of the  3 amounts of water required to maintain maximum crop growth,  Wilcox and Korven  have noted the importance of these f l u c t u a t i o n s i n the energy balance on the rates of evaporation, however, and have suggested that more d e t a i l e d c l i m a t o l o g i c a l i n v e s t i g a t i o n s should be made to quantify t h e i r e f f e c t . Such information most c e r t a i n l y would improve the forecasts of i r r i g a t i o n amounts required throughout the area, therefore providing more r e a l i s t i c estimates of r e s e r v o i r c a p a c i t i e s and i r r i g a t i o n layout.  Undoubt-  edly future growth i n the a g r i c u l t u r a l economy w i l l be c l o s e l y r e l a t e d to the a v a i l a b i l i t y of i r r i g a t i o n water, e i t h e r by pumping from the main r i v e r s or through large scale upland water d i v e r s i o n . Consequently more e f f i c i e n t use of such water w i l l a l l o w a greater proportion of the p o t e n t i a l l y c u l t i v a t a b l e land to be u t i l i z e d f o r p r o f i t a b l e a g r i c u l t u r e .  Furthermore, the increased  d e t a i l of the estimates would allow the p o s s i b l e maximum d a i l y rates of water l o s s t o be ascertained.  These would be invaluable to the i r r i g a t o r who  wishes to know how q u i c k l y he must complete one c y c l e , i . e . i r r i g a t e a l l h i s acreage to f i e l d capacity, and yet renew h i s cycle before h i s crops begin to Wilcox and Korven, l o c . c i t .  84. s u f f e r from water deficiency'. U n t i l such studies are c a r r i e d out, the knowledge of the p h y s i c a l processes of the atmosphere a f f e c t i n g the demand of water by plants w i l l be too incomplete to enable an evaluation of evaporation r a t e s on t h e o r e t i c a l considerations alone.  Thus, i t appears that e m p i r i c a l methods such as were  used i n t h i s t h e s i s w i l l remain part of the s o l u t i o n f o r some time i n the future.  I t i s hoped that the techniques employed w i l l serve as valuable t o o l s  i n applied climatology and that through t h e i r development there w i l l be a greater c o - o r d i n a t i o n of a c t i v i t i e s between the meteorologist, the f o r e c a s t e r , the s t a t i s t i c i a n and the geographer-climatologist.  85. BIBLIOGRAPHY A.  Books  Brooks, C.E.P., and Carruthers, N. Handbook of S t a t i s t i c a l Methods i n Meteorology. Ch. 16. Persistence. London: H.M.S.O., 1953.  PP. 309-329.  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Science, V o l . 2 (1954), 105-119.  Neth. Journ.  Weiss, L.L. "Sequences of wet or dry days described by a Markov chain probability model", Monthly Wea. Rev., V o l . 92 (1964), 169-176.  88. Wilcox, J.C.  "Indirect determination of f i e l d capacity f o r moisture", S c i .  A g r i c , Vol. 29 (1949), 563-578.  Wilcox, J.C. "Effects of weather on evaporation from B e l l a n i plates and evaporation from lysimeters", Can. Journ. Plant Science, V o l . 43  (1963), 1-11.  V/ilcox, J . C , and Korven, H.C. "Effects of weather fluctuations on the schedu l i n g of i r r i g a t i o n " , Van. Journ. Plant Science, V o l . 44 (1964),  439-445.  Williams, C.B. "Sequences of wet and dry years considered i n r e l a t i o n to the logarithmic series", Quart. Journ. Royal Met. S o c , V o l . 78 (1952),  91-96.  C.  Reports  B r i t i s h Meteorological Office, Spells of Dry Weather i n Eastern England. A report prepared by the Agro-Met. Branch. London, 1953Budyko, M.T. The Heat Balance of the Earth's Surface. Translation PB 131692. U.S. Dept. of Commerce, O f f i c e of Technical Services. Washington, D.C, 1955The Canada Land Inventory A.R.D.A. Report No. 1 (January, 1965). Dept. of Forestry, Publ. No. 1088.  Ottawa:  Chapman, L.D., and Brown, D.M. Climatic Maps o f A g r i c u l t u r a l Areas i n Canada. Ontario Research Foundation, Dept. of Physiography. Ottawa, 1964. Conner, A.J. The Frost-Free Season i n B r i t i s h Columbia. Met. Branch. Toronto, 1959.  Dept. of Transport,  Kangieser, P.C., and Green, C.R. P r o b a b i l i t i e s of P r e c i p i t a t i o n at Selected Points i n Arizona. University of Arizona, Inst, of Atmos. Physics, Tech..Report No. 16, Tucson, 1965. MacPhee, E.D. The Report of the Royal Commission on the Tree-Fruit Industry i n B r i t i s h Columbia. B.C. Dept. of Agriculture, V i c t o r i a , B. C ,  1958.  Penman, H. L. Vegetation and Hydrology. Tech. Comm. No. 53, Commonwealth A g r i c u l t u r a l Bureau, England, 1963. Quartermaster Research and Engineering Centre. Winter Weather Type Frequencies i n the Northern Great P l a i n s . U.S. Army Tech. Report, EP-64. Natick, Mass., 1957. Rheumer, G. and O'Riordan. J . Agro-Climatic Maps of B r i t i s h Columbia. (in preparation). Dept. o f Agriculture, V i c t o r i a , B. C. 1966. Thomthwaite, C.W. and Mather, J.R. The Water Budget and i t s Use i n I r r i g a t i o n . U.S. Dept. of Agriculture Yearbook, Washington, D.C.,  1955, PP. 346-358.  89 . Thornthwaite, C.W., and Mather, J.R. The Water Balance. Publ. i n Climatology, Drexel I n s t , of Technology, No. 8, Centerton, New Jersey, 1955• U.S. Navy E l e c t r o n i c s Laboratory. Water Loss Investigationst a Review of Evaporation Theory and Development of Instrumentation. U.S. Navy E l e c t r o n i c s Laboratory Report No. 159, pp. 71 > 1950. U.S. Geological Survey. Water Loss I n v e s t i g a t i o n s : U.S.G.S. C i r . 229, 1952.  Lake Hefner Studies.  U.S. Geological Survey. Drought: The Meteorological Phenomenon of Drought i n the South West. U.S.G.S. Prof. Paper, 372-A, 1962. Walker, E.  The Synoptic Climatology of the Western C o r d i l l i e r a . Research Group, M c G i l l U n i v e r s i t y , Montrel, 1961.  D.  A r c t i c Met.  Data Sources  B r i t i s h Columbia, Department of A g r i c u l t u r e . V i c t o r i a , B. C.  Climate of B r i t i s h Columbia,  Canada, Department o f Transport, Meteorological Branch. Monthly Record of Meteorological Observations i n Canada. Toronto, Ontario.  E.  Unpublished Sources  Hedke, C.R. "Consumptive Use of Water by Crops", O f f i c e , 1924 (unpublished). Kerr, D.P.  New Mexico State Engineers  "Regional Climatology of Southern B r i t i s h Columbia", Unpublished Ph.D. d i s s e r t a t i o n , U n i v e r s i t y of Toronto, 1950.  Wilcox, J . C . "Comparative Monthly I r r i g a t i o n Requirements i n Southern B r i t i s h Columbia",. S o i l s 5, Summerland, B.C., 1963. (mimeographed).  90.  APPENDIX I Cumulated Frequencies of Wet and Dry S p e l l s at Selected S t a t i o n s during the Growing Seasons 1935-1964. Length i n days  Hope Wet Dry  Lytton Wet Dry  Penticton Wet Dry  Princeton Wet Dry  Yernon Wet Dry  Kamloops V/et Dry  1  167  212  261  108  251  160  298  172  306  188  261  168  2  193  125  163  61  184  117  174  116  199  122  137  106  3  118  72  69  68  101  65  93  67  110  101  97  89  4  67  56  25  54  51  52  49  61  55  76  34  45  5  49  40  15  39  33  60  31  57  25  4?  22  53  6  40  40  6  28  21  37  8  37  8  36  15  35  7  17  20  5  32  11  29  8  26  7  32  6  23  8  14  22  2  21  4  27  6  29  3  26  26  9  8  10  1  24  3  20  2  4  18  10  6  13  -  12  4  21  24  5  19  11  5  12  -  20  22  -  14  12  8  10  -  14  -  13  6  11  10  -  14  -  5  15  2  16  -  12  -  13  10  11  -  9  5  21  16  4  5  7  8  -  -  7  7  17  1  3  8  6  18  -  4  3  1  -  10  6  3  3  19 20  4 2  -  -  5  -  13  8  7  3  2  4  7  5  5  -  5  3  -  5  2  13 26 11 14 8 6 10 12 6 •4 6 2  91. APPENDIX  II  A d d i t i o n a l Uses of the Markov Chain Model 1.  Cumulative d i s t r i b u t i o n of wet s p e l l s through n i s : 1 - Pw^w and f o r dry s p e l l s i s :  where Pw/w = P (wet day / the previous day wet). Pw/d = P (wet day / the previous day d r y ) . 2.  Formulae f o r computing the lengths of dry and wet s p e l l s (n days) at selected cumulative p r o b a b i l i t i e s * .  3.  Wet S p e l l s  Dry S p e l l s  98  -1.698? l o g 10 Pw/w  -1.6987 l o g 10 (1 - Pw/d)  90  -1.0000  -1.0000  l o g 10 Pw/w  l o g 10 ( l - Pw/d)  50  -0.3010 l o g 10 Pw/w  -0.3010 l o g 10 ( l - Pw/d)  10  -0.0458 l o g 10 Pw/w  -0.0458 l o g 10 (1 - Pw/d)  P r o b a b i l i t i e s expressed as r e t u r n periods. The p r o b a b i l i t i e s of dry and wet s p e l l s may a l s o be expressed i n terms of an average recurrence i n t e r v a l T, which i s the r a t i o of the number of years of record to the t o t a l number of sequences of more than n days. Dry S p e l l s :  T  =  1 - Pw/w + Pw/d Sp w/d ( l - Pw/w)(l - Pw/d)  n  The p r o b a b i l i t i e s are tabulated i n percentages and represent the e m p i r i c a l p r o b a b i l i t y of o b t a i n i n g the computed length of s p e l l i n days or l e s s .  92. Appendix II - Continued Wet S p e l l s :  T  =  1 - Pw/w + Pw/d Sp w/d ( l - Pw/w) Pw/w  n  S = number of days i i i sub i n t e r v a l f o r which the sequences are counted, e.g. monthly,  S = 30 or 31•  A d d i t i o n a l References A. H. Eichmeter and W.D. Baton, " R a i n f a l l p r o b a b i l i t i e s during the crop season i n lower Southern Michigan", Monthly Wea. Rev.. V o l . 90 (1962J, 277-281. A.G. T o p i l , " P r e c i p i t a t i o n p r o b a b i l i t y i n Denver r e l a t e d to month of p e r i o d " , Monthly Wea. Rev., V o l . 91 (1963), 293-297.  

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