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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 in the Department of GEOGRAPHY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1966 I n p r e s e n t i n g 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 of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia,, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. 1 f u r t h e r agree t h a t permission., f o r extensive 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 granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood t h a t copying or 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 g ain s h a l l not be allowed without my w r i t t e n permission^ The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada i . ABSTRACT Climatic data observed at six meteorological recording stations in the south central Interior of British Columbia were used to analyse the temporal and geographical variations i n the frequency, intensity and duration of various climatic phenomena that affect the supply and demand of water by growing crops. Rather than using average values, the relative frequencies of occurrence 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 precipitation tended to occur during the earlier half of the growing season at most stations, the month of June experiencing a definite maximum. However, natural precipitation would appear to be less effective for plant growth than i t s absolute totals suggest, due to i t s tendency to be concentrated into a few days per month. An analysis of the occurrence of wet and dry spells during the grovdng season using two proba-b i l i t y models supported these facts, the highest frequency ©f wet spells occurring i n June, while the lower probabilities 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 affect water loss by crops (radiation, temperature, wind and water pressure d e f i c i t ) , daily data were only available for two of these elements, namely air temperature and relative humidity. An examination of the relative frequencies of their occurrence showed that the evaporative power of the s a i r remained relatively low until the end of June, after which i t increased sharply as these tw© elements combined in such a manner that they intensified evaporation loss. This fact was further illustrated when their joint daily i i . Abstract - Continued observations were combined i n a frequency tab le , both Ju ly and August experien-c ing the highest r e l a t i ve frequencies of t o r r i d days (hot days with low r e l a t i v e humidit ies). The conclusions were further 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 stat ions by estimating potent ia l evapotranspiration rates from Penman's empir ical formula and using the s o i l budget technique. At a l l stat ions except Lytton, 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 Ju ly, unless the s o i l s had low moisture storage capac i t ies , but from Ju ly to September the required i r r i g a t i o n amounts were considerably higher, a fact that was due to both the increased dryness of the atmosphere and to the previous depletion of the read i l y ava i lable s o i l moisture. ACHJOWLEDGMENT S Many people, both i n Vancouver and Victoria, have kindly provided assistance i n the preparation of this thesis. In Vancouver, I would l i k e to thank Br. M.A. Melton, my supervisor, for his c r i t i c a l evaluation of the f i n a l draft and his advice i n s t a t i s t i c a l methods and computer programming; Dr. J.D. Chapman for his helpful comments at a l l stages of the work and Dr. A.L. Parley who, as Project Supervisor for Agro-Climatological studies at the University (under A.R.D.A. administration) provided both moral and financial support. In Victoria, I would l i k e to acknowledge the prompt assistance provided by Dr. W.H. Mackie and his staff at Gonzales Observatory; Mr. D. Pearson of the Geographical Division, Department of Lands and Forests for his friendly 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 i v . LIST OF ILLUSTRATIONS v i . Chapter 1 INTRODUCTION . . . 1 South Central B r i t i s h Columbia Review of Literature Outline of Thesis 2. AN ANALYSIS OF PRECIPITATION PATTERNS *3 Analysis of Synoptic Weather Patterns Analysis of Rainfall Probabilities Summary 3. STATISTICAL ANALYSIS OF ¥ET AND DRY SPELLS . . . . . . . 26 The Persistency Model The Markov Chain Model Summary k. AN ANALYSIS OF TEMPERATURE AND HUMIDITY PATTERNS . . . . 4? Analysis of Temperature Frequencies Analysis of Relative Humidity Frequencies Combination of Weather-Type Frequencies Summary 5. THE FREQUENCY AND INTENSITY OF DROUGHT 6 5 Review of Literature Analysis of PE Frequencies / The Soil Moisture Budget 6. SUMMARY AND CONCLUSIONS . . . . . . 81 BIBLIOGRAPHY 8 5 - 8 9 APPENDICES I. Cumulated Frequencies of Wet and Dry Spells at Selected 90 Stations during the Growing Season 1935-1964. II. Additional Uses of the Markov Chain Model. 91 - 9 2 i v . LIST OP TABLES Table Page I. \> Average Dates of Beginning and End of Growing Season at Selected Stations . . . . . . 14 I I . Empir ical P robab i l i t i e s of Observing P rec i p i t a t i on Amounts (Inches) Less than or Equal to Specif ied Values at Selected Stations, 1945-1964 19 I I I . Empir ical P robab i l i t i e s of Observing Monthly P rec i p i t a t i on Amounts (Inches) Less than or Equal to Speci f ied Values at Selected Stat ions, 1945 - 1964 . 21 - 22 IV. The Average Number of Rain Days per Month during the Growing Season, 1945-1964 23 V. Relat ive Frequencies of Monthly R a i n f a l l per Rain Day at Selected Stat ions, 1945-1964 24 VI. Frequencies of Runs of Dry Days at Pr inceton, VI I. Frequencies of Runs of n or More Dry Days at Princeton, 1935-1964 . . 31 VII I . Frequencies of Runs of Exactly n Dry Days at Princeton, 1935-1964 . . . . 33 IX. Frequencies of Runs of Exact ly n Dry Days at Princeton, 1935-1964 34 X. Frequencies of Runs of Exact ly n Wet Days at Princeton, 1935-1964 35 XI. S ignif icance of Constant P robab i l i t i e s of Wet and Dry Days at Selected Stations during the Growing Season 35 XI I. Regression. Analysis of Dry and Wet Spe l l s during the Growing Season at Selected Stations 38 XI I I . I n i t i a l and Trans i t iona l P r obab i l i t i e s at Selected Stations 40 2 XIV. Observed Numbers for Computing X S t a t i s t i c s for the Month of A p r i l at Princeton . . . . . . . . . . . . 44 XV. Months during the Growing Season for which the Ch i -Squares were S ign i f i cant at the P = 5 per cent l e ve l • 45 L i s t of Tables - Continued Table Page XVI. Relat ive Frequencies of Dai ly Maximum Temperatures at Selected Stat ions, 1945-1964 . . . . 5 1 - 5 3 XVII. Relat ive Frequencies of Da i l y Minimum Relat ive 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 Stat ions, 1957-1964 58 - 60 XX. Accumulated Frequencies of Torr id Days per Month During the Growing Season 61 XXI. Duration of Torr id Days at Selected Stations 1957-1964. 63 XXII. Relative Frequencies of Monthly PE (Inches) at Selected Stations 69 XXIII. Empirical P r obab i l i t i e s of Seasonal Supplemental I r r i ga t i on Requirements (inches) at Selected Stations. 7 2 XXIV. Monthly Supplemental I r r i g a t i on Requirements at Selected Stations 7 6 - 8 0 v i . LIST OP FIGURES Figure Page 1. Location of the Region l a . 2. Summer Moisture De f i c i t (af ter Thornthwaite) . . 4a. 3. P r ec i p i t a t i on Regimes at Selected Stations . . . 15a. 4. Average May-September P rec i p i t a t i on . 17a. 5. Twenty Percent i le May-September P rec i p i t a t i on . 18a. 1. CHAPTER I INTRODUCTION This thes is attempts to analyse s t a t i s t i c a l l y the spa t i a l and temporal var ia t ion of the various c l imat i c elements that influence the supply and demand of ava i lab le s o i l moisture fo r crop growth i n the semi-arid plateau and va l l ey country i n the south central I n te r i o r of B r i t i s h Columbia. The resu l t s of these analyses enable an objective assessment of the amounts of i r r i g a t i o n water required by crops to maintain optimum growth throughout the growing season. Since successful agr icu l ture i n t h i s a r i d and semi-arid country i s almost en t i r e l y dependent upon i r r i g a t i o n , th i s information i s e s sent ia l f o r the design of storage reservo i r s and i r r i g a t i o n systems and fo 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 centra 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 tory of a g r i cu l t u r a l development, yet s t i l l contains considerable ag r i cu l t u r a l p o t en t i a l . The def ic iency of ava i lab le s o i l moisture for optimum crop development during the growing season i s one of the two major handicaps a f f ec t i n g p ro f i tab le agr icu l ture with in the region, the other being the high frequency of f r o s t s during the spr ing and autumn months. Although frost damage causes an annual loss of crops of varying i n ten s i t y , the inadequacy of the ra i n during the growing season i s a more un iversa l problem and consequently one more su i ted fo r geographical i n v e s t i -gation. The dif ference between the amount of moisture crops require and the amount they receive from natural p r ec i p i t a t i on i s known as the moisture balance. Figure 2 shows that the south cent ra l i n t e r i o r l i e s with in 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, exper-iencing the lowest recorded precipitation i n the whole of Canada. Upland precipitation 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 reflect the importance of terrain. Generally, average, temperatures drop with increasing altitude, thus the sheltered valleys 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 their part i n influencing temperature patterns. Vegetation The variety of climates resulting from these r e l i e f and aspect variations i s indicated by the different plant and s o i l types distributed throughout the region. Three major altitudinal zones of vegetation have been distinguished^. At elevations below 2,000 feet, the combination of summer heat and low precipitation has allowed natural grasslands to develop. An association of perennial bunch grasses is the main vegetation, though severe overgrazing has induced a mixed covering of sagebrush (Artemesia tridentata), rabbit brush (Chrysothamnus nauseosus) and other unpalatable shrubs and forbs. Between 2,000 and 4,000 feet this 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 vertical zonation i n B r i t i s h Columbia", Sci. A g r i c , vol. 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 menzeis i i ) , which climaxes above 2,500 feet . Local depressions and lakeshore locat ions support stands of Aspen (Populus tremuloides), Maple (Acer glabrum) and Mountain B i rch (Betula f o n t i n a l i s ) . Plateau ridges above 4,000 feet carry a sub-alpine vegetation dominated by Spruce (Picea engelmanni) and Balsam P i r (Abies las iocarpa). So i l s The s o i l types represented i n the area are c lo se l y connected to the c l imat i c and vegetational complexes. The Chernozemic (grassland) s o i l s , subdivided i n to Brown, Dark Brown and Black s o i l groups, are associated with the warm, dry s i te s of the va l l ey bottoms and lower slops up to about 2,500 feet . In the semi-arid va l l ey f l oo 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 sparc i ty of the vegetation there i s l i t t l e humus accumulation and the lack of leaching has allowed lime accumu-l a t i o n i n the upper horizons. Sal ine and a l k a l i ne s o i l s can be seen i n l o c a l drainage hollows. Where the moisture d e f i c i t s are les s (4 to 8 inches), 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 resu l t s from the decay of the greater density of grassland vegetation. This zone extends into 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 region. These appear on the upper grassland zones i n the south and more general ly i n the north-eastern section of the region, 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 nutr ients down the p r o f i l e . Increasing podzol izat ion occurs at the higher elevations as the moisture balance swings from a d e f i c i t to a surplus - a resu l t of the combination of increased p rec i p i t a t i on and lower 5. temperatures. Since most of the so i l s have a nutr ient base and structure suitable f o r agr i cu l ture , y ie ld s are high where moisture i s avai lable from e i ther p rec ip i t a t i on or i r r i g a t i o n . Agr iculture The region may be subdivided into three subregions - the Okanagan Val ley, the Upland Plateau ( inc luding the Thompson Val ley) and the Praser Watershed. The Okanagan Va l ley - In terms of farm cash income, the Okanagan Val ley i s the second most important ag r i cu l tu ra l region i n the province, ranking behind the Lower Praser Va l l ey . The t o t a l potent ia l arable acreage wi th in 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 lop ing va l l ey benches south of Vernon i n the Okanagan Va l l ey and south-east of Keremeos i n the Similkameen Va l ley. The combination of warmer summers and a longer f r o s t - f r ee season i n the southern part of the va l l e y (115 days at Armstrong and 151 days at Osoyoos^) favours soft f r u i t and apple orcharding, whereas the northern end of the va l l ey concentrates on apple orcharding and vegetable production. Outside t h i s f r u i t be l t the farming i s more extensive and the emphasis s h i f t s to gra in, hay and forage crops, i n conjunction with l i ves tock 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 ree days at Joe Rich Creek ) ru le out most of the plateau for c u l t i v a t i o n . However, the Grassland and Dry Forest vegetation have promoted beef ca t t l e and sheep ranching, which remains the only important A . J . Conner, The f ro s t - f ree season i n B r i t i s h Columbia. Met. Div. Dept. of Transport (Toronto, 1 9 4 9 ) . '. • 7 Ib id . 6. agricultural activity on , the plateau. Irrigated hay crops, which are grown in conjunction with the beef cattle and sheep enterprises, occupy a large portion of the cultivated land, situated mostly in 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 closely connected to the avai l a b i l i t y of water for irrigation, though natural precipitation i s s u f f i c -ient i n the Shuswap area and on the plateau south of Kamloops to allow dry-land farming. The Shuswap area i s an extension of the mixed livestock economy found i n the northern part of the Okanagan Valley around Armstrong and Enderby. Potentially cultivable land, which is widely scattered throughout the area, totals approximately 100,000 acres. The Fraser Watershed - This south-western section of the region has l i t t l e agricultural potential due to the rugged terrain of the Coast and Cascade Mountains. Agriculture i s restricted 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 is precipitation. However, the amount of water a crop demands to maintain maximum growth depends upon a number of external and internal factors within i t s environment. The external factors may be subdivided verti c a l l y into two groups, namely atmospheric or climatic, and edaphic. The atmosphere is 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 level 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 roots* 0. The internal or plant factors influencing 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 level. Above ground level the albedo** of the crop determines how much energy w i l l be absorbed by the plant surface. Since water i s lost through stomata on the leaf surface, the size of this surface and the density of these stomata are other factors determining crop water needs. Underground, the concentration and the vertical distribution of the root system of the plant affects the rate of water loss throughout the s o i l profile. An examination of the energy balance enables those climatic elements that influence the rate of evapotranspiration to be defined. The only direct source of radiation i s solar radiation, which i n turn determines directly and indirectly both the air 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 vertical 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 de 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 affecting the absorption of water", Plant and  Soil Water Relationships (McGraw-Hill. 1949) Ch. 9, p. 212. ** Albedo - proportion of incident radiation that i s reflected. 12 C.B. Tanner, "Energy Balance approach to the evapotranspiration from crops", Proceedings Soil Science Soc. America,Vol. 24 (i960) p. 1-9• 8 . 13 the surface . Therefore, the major meteorological elements affecting evapo-transpiration within the atmospheric environment of crops are solar radiation, a i r temperature, wind speed and vapour pressure d e f i c i t . Since the relative 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 correlation of observed water use with these variables i n the f i e l d . Fortuna-14 tely, such a study has been undertaken within the region. Wilcox , working at Summerland i n the Okanagan Valley, concluded that solar radiation and a i r temperature were the most important variables affecting evapotranspiration from lysimeters and evaporation from Bellani plate atmometers, though the best estimates required the use of a l l four elements. Pelton 1^, working in a similarly semi-arid climate at Swift Current, Saskatchewan, found that between 70 and 80 per cent of the variation i n evaporation could be accounted for by a linear combination of these four variables. ' These researchers and others 1^ have a l l verified s t a t i s t i c a l l y that better results are obtained when equating climatic variables to evapotrans-piration i f a l l four elements are used. However, earlier 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 evapo-ration", Proceedings Second Canadian Hydrology Symposium (Toronto, 1961), 8-26. 14 • J.C. Wilcox, "The effect of weather on evaporation from Bellani plates and evaporation from lysimeters", Can. Journ. Plant Science, Vol. 43 (1963), 1-11. 15 W.L. Pelton, "Evaporation from atmometers and pans",;; Can. Journ. Plant Science. Vol. 44 (1964), 397-404. 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 in irrigated areas from climatological and irrigation data"; U.S. Dept. of Agric. S.C.S. - TP-96 (Washington, D.C., 1950), 1-48. 18 Thornthwaite, loc. c i t . a i r temperature when deriving their empirical equations for estimating eva-potranspiration. 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, his equation produces the most accurate 20 results from observed meteorological data for most climates , and has therefore been used to estimate water loss i n this thesis. Agro-Climatological Studies i n the Region Until recently l i t t l e research has been undertaken into the applied 21 aspects of agricultural climatology in any part of the province. Kerr presented an exhaustive study of the variation in climatic elements across 22 the southern part of the province and Chapman followed this with a detailed study of the climate as a natural resource. The most detailed regional 23 climatology of part of the province to date was published by Walker , i n which.he attempted to improve the estimation of the mean annual r a i n f a l l 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 Agricultural 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 British Columbia", (unpublished Ph.D. dissertation, Dept. of Geog., University of Toronto 1950)« 22 J.D. Chapman, "The Climate of Br i t i s h Columbia", B.C. Nat. Res. Cpnf., No. 5 (Victoria, B.C., 1952), 8-37. 23 Walker, loc. c i t . 10. (A.R.D.A.). In each province agro-climatological committees have been set up to assess the climatic factors that affect agricultural production and to produce maps of climatic zones significant to crop production. Chapman 24 and Brown drew up a series of maps on a national scale, showing the d i s t r i -bution of several of these climatic elements, while on the provincial scale 25 Rheumer and O'Riordan prepared a more detailed set of maps showing quanti-tative distributions of derived climatic variables. 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 their geographical variation throughout the region. Outline of the Thesis It is the task of the climatologist to depict and explain the different climates that appear on a l l or part of the earth's surface. To accomplish this, he must possess knowledge of the causal relationships and conditions governing the occurrence of climatic elements in order that he may compare the climates as they vary from place to place. This theoretical and descriptive approach to climatology has been termined 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 application of these theoretical and descriptive understandings of the climates of a region for the benefit of man i s known as applied climatology. This thesis deals with this aspect of climatology. 24 L.J. Chapman and D.M. Brown, Climatic Maps of Agricultural Areas  of Canada, Ontario Research Foundation, Dept. of Physiography A^.R.D.A., 1964) 2 5 G. Rheumer and J. O'Riordan, Agro-climatic Maps of B r i t i s h  Columbia. (In print, Dept. of Agriculture, Victoria, B.C.). ~ 2 6 A. Court, "Climatology" Amer. Geog., Vol. 4? (l957;, 125-136. ^ . "Climatology" Complex,dynamic and synoptic". Am. 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 object i ve ly quantify the inf luence of the several c l imat ic elements that influence the supply and demand for water by growing crops. From these re su 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 sent ia l l y a geogra-phica l study i t emphasises the spa t i a l v a r i a t i on of these c l imat ic elements and the consequent va r i a t i on i n the supplemental water need from place to place throughout the reg ion. Since c l imat ic observations are by nature subject to considerable var ia t ions , a representative p icture of the p reva i l i n g c l imat 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 thes is r e l i e s e n t i r e l y upon data observed at the meteorological recording stations s ituated wi th in the areas under study and which have been observing continuously fo r at least twenty years. The da i l y weather data were ava i lab le i n the Monthly Cl imatic Summaries published by the Meteorological Branch of the Department of Transport i n Toronto and the monthly data were abstracted i n a publ icat ion issued f o r the province by the Department of Agr iculture i n V i c t o r i a (see data sources i n b ib l iography). Certain more deta i l ed weather observations were made ava i lab le to the wr i ter by the s t a f f of Gonzales Observatory i n V i c t o r i a . I t has been known for a long time that the^mean values of c l imat i c s t a t i s t i c s have l i t t l e value i n appl ied cl imatology, other than as a general guide to p reva i l i ng c l imat i c condit ions. Therefore, a l l observed data used i n the work are tabulated according to t he i r frequency of occurrence, from which selected empir ical p robab i l i t i e s of cer ta in spec i f ied values may be obtained. Frequency d i s t r i bu t ions of the ava i lab le c l ima t i c elements a f f e c t -i ng crop water supply and demand, namely p r ec i p i t a t i on , maximum da i l y 12. temperature, minimum da i l y r e l a t i v e humidity and monthly evapotranspiration (empir ica l ly derived) are presented. Since none of these var iables was normally d i s t r ibuted, i n each case an empir ical method of determining the selected p robab i l i t i e s was used i n order that a l l derived p robab i l i t i e s be r e a l i s t i c . As the only form of water supply fo r crops, the seasonal and monthly p rec i p i t a t i on patterns were examined f i r s t . Recently considerable attent ion has been directed towards the use of s t a t i s t i c a l techniques for estimating the p robab i l i t y of wet and dry s pe l l s . Since such spe l l s a l te rnate ly af fect 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 robab i l i t y of the i r occurrence at various points w i th in 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 s tat ions . The frequency d i s t r i bu t ions of the two ava i lab le c l imat ic elements a f fec t i ng 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 gn i f i c an t r o l e i n promoting water loss, the i r jo in t e f fect was also analysed. Prom the re su l t s of these comparative analyses and with the use of an empir ica l formula devised by Penman i t was possible to determine ob ject i ve l y the water requirements for optimum plant growth as they vary i n both time and space wi th in the region. 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 robab i l i t i e s of the add i t iona l water requirements necessary to sustain crop growth were tabulated at selected stat ions on a monthly and seasonal bas is . 13. CHAPTER 2 AN ANALYSIS OP PRECIPITATION PATTERNS The only important s ing le c l imat ic element a f fec t i ng the amount of moisture avai lable fo r crop growth and, therefore, the crop water supply of any region i s p rec i p i t a t i on . Because drought, i n i t s agrocl imatological sense, i s perennial i n the southern I n te 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 natural r a i n f a l l during the growing season. However, both the supply of water for 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 rec ip i t a t i on f a l l i n g wi th in the region from year to year and, therefore, var iat ions i n precipitation patterns i n both time and space are of c r i t i c a l importance to ag r i cu l tu re . There are th i r t y -e i gh t stations with a period of record extending over at least twenty years, most of them s i tuated i n the p r i n c i pa l va l l ey s . Out of these stations s i x were chosen for the more deta i led c l imat i c analyses, since they maintained da i l y observations of the various c l imat ic elements that a f fect water lo s s . These s i x stations are Hope, Lytton, Penticton, Pr inceton, 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 cross-sect ion of areal c l imat i c changes wi th in the more se t t led ag r i cu l t u r a l sections of the region. Since t h i s thesis analyses weather elements that af fect a g r i c u l t u r a l crop growth, only growing season p rec i p i t a t i on patterns w i l l be examined i n d e t a i l . 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 tat ions and ends i n la te October or ear ly November. In accordance with known ag r i cu l t u r a l pract ices wi th in the r eg i on 1 the growing season i s assumed to extend from A p r i l to September 1 R. K. Kreuger, "The physical basis of the orchard industry i n B r i t i s h Columbia", Geo. B u l l . , Vo l . 19 (1963), 5-38. 14. i n c l u s i ve . Table I - Average Dates of Beginning and End of the Growing Season at Selected Stat ions. (Based on 42 P Threshold Temperature) Stat ion Hope Lytton Penticton Princeton Vernon Kamloops Average F i r s t Day March 11th March 19th March 27th A p r i l 10th March 30th March 25th Average Last Day November 8th November 6th November 1st i October 22nd October 28th October 29th Analys is of Synoptic Weather Patterns The P a c i f i c anticyclone dominates the pressure patterns over the ent i re province during the six-month period, the mean Ju ly pos i t ion of i t s centre being 38°N and 1 5 0 ° ^ . A ridge extends up the coast to Alaska, sending a p reva i l i ng north-westerly a i r stream over the Central I n te r io r . This dry, subsiding a i r i s fu r ther s t a b i l i z e d by i t s descent of the coastal mountains i n t o the va l leys of the region, br ing ing the general ly c lear skies f o r which the region i s famed during the summer months. To the south a thermal trough extends from the Central Va l ley of Ca l i f o r n i a into the Intermontane Basin. This occasional ly establ ishes a flow of very warm, dry, t r o p i c a l cont inental a i r i n to the region, r e su l t i ng i n the hottest summer weather i n southern B.C. To the north, weather disturbances from the P a c i f i c gyrate around the ant icyc lon ic c e l l occasional ly br ing ing cloud and showers to the northern parts of the region, with greater amounts of p rec i p i t a t i on on the h i l l s as a re su l t of induced condit ional 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 Aleutians, marking Kerr, l oc . c i t . 15. the gradual return to winter conditions. The summer precipitation regimes (Figure 3) indicate a transition 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 precipitation totals are a result of moist Pacific air being funnelled up the Fraser Valley and forced to rise over the Cascades. The resulting precipitation on the mountains also f a l l s into the narrow valley floor - a phenomenon known as the "canyon effect 1! • By mid-summer, however, the establishment of the more stable anticyclonic circulation lowers precipitation totals generally over this southwestern corner of the region. A l l other interior stations show a marked warm season maximum i n June that deserves some comment. An analysis of the average latitude of the centre of the Pacific anticyclone over a period of twenty years indicates that i t maintains a position of about 34°N during May and June and then i n early o 3 July i t shifts abruptly northwards to about 40 N . While i t i s at i t s south-erly May-June location, a trough at the 500 mb level develops, inducing a flow of moist maritime air from the Pacific Ocean into the region. The short wet season of early summer is the result, but when the Pacific high suddenly shifts northwards and eastwards i n early July, the circulation pattern changes, the region coming under increasing anticyclonic control with i t s associated subsidence. This anticyclonic situation 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 of wet days. The actual precipitation during the growing season appears to be controlled by upper level disturbances rather than convectional influences. 7 G.T. Trewartha, Earth's Problem Climates (University of Wisconsin Press, 1962), p. 2?6. F i g . 3 PRECIPITATION REGIMES AT SELECTED STATIONS 10-" fi-l o HOPE 2-LYTTON PENTICTON 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 (A 0) PRINCETON 4 -2-VERNON KAMLOOPS 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 rc t i c are in jected into the upper atmosphere and, according to Walker , a ba roc 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 en s i f i ed 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 , br ing ing wet weather to h i l l s and va l leys a l i k e . Pincock^ found a cor re la t ion between such pressure systems and the height of the 500 mb surface, but no s i gn i f i can t cor re la t ion with the 1000 mb surface. Walker noted that the maximum frequency of such "co ld lows" occurred i n June (co in -c id ing with the p rec i p i t a t i on maximum);when, on average, four such disturbances may cross the southern i n t e r i o r . The increas ing s t a b i l i t y of the upper atmos-phere, coupled with the les s frequent outbreaks of cold a i r from the A r c t i c , reduces the probab 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 rec ip i t a t i on Since the large majority of the meteorological recording s tat ions are s ituated on the va l l e y f l oo r s , i t i s d i f f i c u l t to obtain a representative p icture of the growing season p rec i p i t a t i on amounts over the whole area from these sources alone. By inspect ion of the s t a t i on records, however, i t appeared that the r a i n f a l l tended to increase with e levat ion and l a t i t u d e , espec ia l l y i n the eastern sect ion of the area. Therefore, an estimation of r a i n f a l l on the plateau surface was obtained from an analys is of the regress ion of mean growing season p r e c i p i t a t i o n with l a t i tude and a l t i t u d e . Eighteen stat ions i n the Okanagan Val ley area were used i n the regression ana lys i s . The mult ip le coe f f i c ient of co r re l a t i on was 0.70 ( s i gn i f i can t at the 95$ confidence l i m i t ) and the regression equation, determined by the method of least squares, was: __ Walker, Loc. c i t . > 17. A -82.26 + 0.00095X1 + l . ? W 2 - 1.32 Y (1) where A Y estimate of mean growing season p rec i p i t a t i on i n inches, e levat ion i n f ee t . l a t i tude i n degrees. Since t h i s map considered plateau areas as wel 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 ve . necessary on the plateau areas. While almost the ent i re region receives less than 10 inches during the five-month period, there are three regions that on "~J~" average receive less than f i v e inches. These are the Thompson Va l ley sect ion, l y i n g between Lytton and Kamloops, the Mer r i t t Lowlands and the southern end of the Okanagan Va l ley and Lower Similkameen Val ley sect ions. Local topographic inf luences play the i r part fo 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 ef fects on the P a c i f i c a i r masses as they descend over the coasta l mountains. The Thompson dry be 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 va l l e y s . Apart from these areas, the map does ind icate a tendency for the r a i n f a l l to increase towards the north and east due to the increas ing frequency of weather disturbances i n the north and the "approach e f f e c t " of the Pu rce l l Mountains i n the east. A map of the mean growing season p rec i p i t a t i on was prepared for the area (Figure k), using th i s equation to estimate p rec i p i t a t i on tota l s where This equation i s e f fect i ve for elevations between 1,000 and 4,000 feet and la t i tudes between 49 N and 51 N. 18. Analysis of Ra i n f a l l P r obab i l i t i e s I t i s we l l known that mean values of p rec i p i t a t i on have l i t t l e value i n semi-arid regions, s ince the r a i n f a l l d i s t r i bu t ions are invariably-skewed from the normal. Although useful as a general summary of r a i n f a l l condit ions, they cannot be used to make statements about the p robab i l i t y that p rec i p i t a t i on of a cer ta in magnitude w i l l occur i n a given month or season. To make such statements an analys is of the p robab i l i t y d i s t r ibut ions i s required. Several techniques fo r making p robab i l i t y estimates were invest igated. One of the simplest, the logarithmic transformation, was found to be suitable to estimate certa in selected confidence i n te rva l s fo r a large number of s ta t ion 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 percent i le i s o l i ne s wi th in the region. This empir ical p robab i l i t y means that the stated amount of p r ec i p i t a t i on or less w i l l occur during two growing seasons i n ten. The map does show how meagre the r a i n f a l l can be during the five-month per iod, less than 5 inches occurr ing at a l l low elevat ions, but i t emphasises more strongly the increas ing 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 port ion of the region. To obtain more deta i led p robab i l i t y estimates for the s i x selected s tat ions , an empir ical method of data analys is fo l lowing Kanglesir and 7 Green was chosen. Each r a i n f a l l ser ies was arranged i n order of increas ing values, and the p robab i l i t y value assigned to each of the ordered observa-t ions 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 ser ies . Table I I shows the amounts of 7 P.C. Kangleser and C,R. Green, P r obab i l i t i e s of P rec i p i t a t i on at  Selected Points i n Arizona, Tech. Report No. 16, Inst. Atmos. Physics (TucsonJ Univers i ty of Arizona, 1965), 1-7• 8 E.J. Gumbel, S t a t i s t i c s of Extremes, (New York: Columbia Un ivers i ty Press, 1958) p.29. 19. r a i n f a l l to be expected during the s i x months growing season (Ap r i l to September) at various speci f ied p r obab i l i t i e s at each of the s ix synoptic stat ions wi th in the region. Table I I - Empir ical P robab i l i t i e s of Observing P rec i p i t a t i on Amounts (inches) Less than or Equal to Specif ied Values fo r the Growing Season at Selected Stations, (1943 - 1964).  Hope Lytton Penticton Princeton Vernon Kamloops 10 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 The table indicates that Hope and the Lower Praser Canyon area receive f a i r l y large amounts of p rec ip i t a t i on i n most years compared with the other s tat ions . I t also shows just how inadequate the natura l r a i n f a l l can be for agr icu l ture i n other parts of the region, less than 3" occurring at Lytton once a decade on average, while the increas ing r e l i a b i l i t y of r a i n f a l l east of Kamloops i s underlined by the f igures for Vernon (over 9" once i n four years). The effect iveness of p rec ip i t a t i on for crop growth depends both upon i t s absolute amount and the t iming of i t s occurrence during the growing season. Therefore monthly p robab i l i t i e s of p rec i p i t a t i on amounts were tabulated for each of the s i x months of the growing season at each of the selected stations (Table I I I ) . Exactly the same procedure was used to obtain the empir ical p robab i l i t i e s of these to ta l s as was out l ined e a r l i e r . The prominence of June as the only "wet" month at a l l stat ions can 20. be seen from an examination of the table, though Lytton s t i l l may receive less than hal f -an- inch once i n every four years. The p rec i p i t a t i on to ta l s of a l l other months are extremely unre l iab le, any one of them rece iv ing 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 tota l s at Hope (see Table I I ) , the increas ing dominance of the stable ant i cyc lon ic a i r masses over the area from May to August i s indicated 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 essent ia l i f f u l l crop growth i s to be maintained. Two other facts should be noted from th i s t ab le . F i r s t l y , the prominence of the June maximum appears to increase towards the north of the region, as indicated by the f igures f o r that month at Vernon and Kamloops and, to a lesser extent, at Lytton. This i s i n accord-ance with the paths of the "co ld low" weather disturbances, which migrate down from the north. Secondly, the highest maxima (95?^  p robab i l i t y ) do not always occur i n June but often 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 Specif ied L imits of P rec i p i t a t i on Increasing the d e t a i l of the analys i s of p rec i p i t a t i on patterns another step, the actual d i s t r i bu t i on of the r a i n f a l l throughout each month was also examined. P rec i p i t a t i on effectiveness for crop growth depends 9 upon t h i s fac to r and, therefore, the actual d i s t r i b u t i o n of the number of r a i n days* 0 per month during the growing season was analysed (Table IV). L. Curr ie, "The c l imat ic resources of intens ive grassland farming", Geog. Review, Vo l . 52 (1962), 174-194. * ° Rain day i s defined as a day when at least 0.01 inch of r a i n f e l l . 21. Table I I I - Empir ical P robab i l i t i e s of Observing Monthly P rec i p i t a t i on Amounts (inches) Less than or Equal to Specif ied Values at Selected Stations, (1945 - 1964). Hope M A p r i l May June Ju ly August September 10 1.46 0.79 0.66 0.48 0.51 0.76 2 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 Lytton SL'- A p r i l May June Ju l y 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 Penticton Ffo A p r i l May June July August September 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 A p r i l 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? Vernon p£ A p r i l May June Ju l y 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 iCamloops ? 1 A p r i l May June July August September 10 0.09 0.14 0.34 0.15 0.15 0.04 2 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 23. Table IV - The Average Number of Rain Days per Month During the Growing Season,(1945 - 1964). Stat ion . A_ _M J J A_ Total Hope 18 13 15 7. 10 11 74 Lytton 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 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 stat ions fo l lowing the i r own remarkably s imi la r pattern. However, the actual number of days per month i s subject to remarkable f luctuat ions from year to year; f o r example, at Kamloops 40% of the July 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 isp lay a tendency to be con-centrated into a few days, there does not appear to be a high convectional cha rac te r i s t i c about them. Tables showing the r e l a t i v e frequencies of selected amounts of r a i n f a l l per r a i n day (Table V) ind icate that at a l l the stat ions, apart from Hope, 60% or more of the t o t a l r a i n days measure 0.1" or less, and over 80% measure under 0 .25". With t h e i r low monthly t o ta l s one would expect p robab i l i t i e s of large amounts per r a i n day to be very low. Admittedly, the actua l time span of da i l y r a i n f a l l amounts was not considered (hourly i n t en s i t i e s were hot ava i lab le at any s t a t i on ) , but high frequencies of such low amounts are not general ly associated wi th semi-arid c l imat ic condi t ions . The tables do show a greater frequency of larger da i l y amounts during the mid-summer months at a l l stat ions apart from Hope, which again emphasises 'that'-this s ta t ion belongs to the maritime c l imat i c type rather than the i n t e r i o r type. * * Kerr, l o c . c i t . Table V - Relat ive Frequencies of Monthly R a i n f a l l per Rain Day at Selected Stations ,(1945 - 19,64).  Hope Percent Inches A p r i l May ' June Ju ly August September > 0.12 47.57 50.12 52.17 61.15 50.16 41.57 0.12 - 0.25 21.93 25.56 27.43 19.83 26.40 18.97 0.25 - 0.50 17.25 16.70 10.98 12.80 13-20 19.27 0 . 5 0 - 1 . 0 0 11.25 7.34 8.69 5.78 8.25 12.95 1.00 + • 2.00 0.05 0.60 0.50 1.93 7.22 Lytton . > 0.12 69.79 59.05 59.13 58.82 60.24 52.83 0.12 - 0.25 14.58 22.32 21.50 17.64 22.98 28.77 0.25 - 0.50 10.41 10.63 13.97 11.76 9.93 11.32 0.50 - 1.00 4.68 6.38 5.37 4.54 6.21 7.07 1.00 + 0.55 1.59 0.00 0.00 1.50 0.00 Penticton > 0.12 74.14 63.63 62.42 58.06 69.16 69.13 0.12 - 0.25 13.26 23.05 23.96 23.11 15.85 19.13 0.25 - 0.50 9.18 8.44 6.21 12.90 11.89 8.69 0.50 - 1.00 3.06 4.22 7.10 4.83 3.08 3.04 1.00 + 0.33 0.66 0.33 1.07 0.00 0.00 Princeton ' >0.12 79.66 64.23 60.32 61.49 59.54 62.99 0.12 - 0.25 14.40 23.46 24.83 20.85 25.00 25.55 0.25 - 0.50 5-50 8.84 10.00 12.29 10.00 8.81 0.50 - 1.00 0.50 2.69 4.51 4.27 4.54 2.64 1.00 + 0.00 0.05 0.33 1.02 1.04 0.00 Vernon > 0.12 75.53 60.00 61.6? 60.20 59.32 61.94 0.12 - 0.25 16.90 23.57 23.65 19.89 23.30 23.48 0.25 - 0.50 6.83 12.14 8.98 13.77 12.28 11.33 0.50 - 1.00 0.30 3.92 4.79 6.12. 4.23 2.02 1.00 + 0.30 0,30 1.00 1.00 1.00 1.21 Kamloops > o . u 71.83 67.77 53-60 61.11 62.55 62.57 0.12 - 0.25 20.34 24.71 27.55 19.15 20.65 24.22 0.25 - 0.50 6.56 5.12 14.84 14.14 12.05 10.21 0.50 - 1.00 0.?1 2.40 3.91 4.68 4.37 2.80 1.00 + 0.76 0.00 0.00 0.92 0.48 0.00 25. Summary An analysis of p rec ip i t a t i on patterns during the growing season indicates that while r a i n f a l l amounts are general ly inadequate for vigorous crop growth throughout the lower parts of the area, the drought i n tens i t y var ies from place to place w i th in the region. The Thompson Val ley, Me r r i t t Lowlands and South Okanagan Val ley are notable dry spots while, i n comparison, the Horth Okanagan and Shuswap areas receive considerably more moisture, espec ia 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 for 12 e f fec t i ve r a i n f a l l s ( i . e . more than 0.1") to be concentrated in to a few days per month. This suggests that the r a i n f a l l i s less e f fec t i ve f o r plant growth than i t s absolute t o t a l s suggest. However, no general statements on p rec ip i t a t i on effectiveness 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 capacity and the root ing systems of the p lan t s . These larger amounts general ly al low moisture i n f i l t r a t i o n into the s o i l and subsequent absorption by the plant roots, whereas the smaller amounts are evaporated d i r e c t l y o f f the s o i l and plant surfaces. 26. CHAPTER 3 STATISTICAL ANALYSIS OP WET AND DRY SPELLS This chapter concentrates upon determining the probab i l i t y of the occurrence of wet (and dry) spe l l s during the growing season at the s i x selected stations i n the region. Not only does t h i s information amplify the material i n the previous chapter, but i t provides an objective method for assessing the duration of such spe l l s throughout the growing season. Wet spe l l s being periods of supply and dry spe l l s being periods of demand, t h i s chapter also acts as a natural bridge between the two sections of the the s i s . Problems invo l v ing the estimation of the p robab i l i t y d i s t r i bu t ions of lengths of wet and dry spe l l s have received an increasing amount of at tent ion recent ly. Several invest igators have set up and confirmed a number of hypotheses concerning such p robab i l i t i e s which, general ly speaking, conform to two mathematical models - a persistency model establ ished by Brooks and 1 2 Carruthers and the Markov Chain Model as presented by Gabriel 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 stat ions i n the region for the six-month period A p r i l to September i nc l u s i ve . The Persistency Model I t i s we l l known that the p robab i l i t y of a wet or dry day i s not independent of previous condit ions, i . e . there i s a greater p robab i l i t y that r a i n w i l l f a l l on a given day, 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. Gabr ie l and J . Neumann, "A Markov chain model for d a i l y r a i n f a l l occurrences at Tel Av iv " , Quart. Journ. Royal Met. S o c , Vo l . 88 (1962), 90-95. • 2 7 . 3 day was dry. Jorgensen , studying the persistency e f fect s of r a i n and non-ra i n days i n San Francisco, noted that the number of observed frequencies of wet and dry days did not agree with that ca lculated on the basis of constant p robab i l i t y , equal to the r a t i o of the number of wet (or dry) days divided by the t o t a l number of wet or dry days. 4 Williams applied the hypothesis that the longer the s p e l l has lasted, 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 series to h i s observations. Longley^ concluded from his study of wet and dry days i n various Canadian c i t i e s that the probab i l i t y of a wet day, the previous day being wet, was constant, no matter how long the spe l l l a s ted. However, he did notice a s l i gh t increase i n the p robab i l i t y of a dry day, with increas ing length of the dry s p e l l . Method of Investigation Since the same mathematical procedures were used at a l l s i x stat ions to test the persistency model, a deta i led analys i s of the data processing w i l l only be presented fo r one s ta t ion , v i z . Pr inceton, and the resu l t s of the other stations w i l l simply be tabulated. A wet day i s defined as a day when at least 0.01" r a i n f e l l , and a s pe l l i s taken to mean an unbroken succession of occurrences (or non-occurrences) of such days. The data were tabulated from the Monthly Cl imat ic Summaries published by the Meteorological Branch of the Department of Transport for the 30-year period 1935 - 1964. Since the dry spe l l s frequently overlapped from month to month, the data 3 D.L. Jorgensen, "Pers istency of r a i n and non-rain days in. San Francisco", Monthly Wea. Rev., Vo l . 77 (1949), 302-30?. 4 C.B. Wil l iams, "Sequences of wet and dry years considered i n r e l a t i o n to the logarithmic se r ie s " , Quart. Journ. Royal Met. S o c , Vo l . 78, (1952), 91-96. ^ R.W. Longley, "Lengths of wet and dry per iods " , Quart. Journ.  Royal Met. S o c . Vo l . 79 (1953), 91-98. 28. were cumulated over the t o t a l growing season, a l l s p e l l s being assumed to begin and end on A p r i l 1st and September 30th r e s p e c t i v e l y . Ho: No p e r s i s t e n c e e f f e c t between events. H i : P e r s i s t e n c e e f f e c t between events. 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 the p r o b a b i l i t y p_ that an event w i l l occur, and the p r o b a b i l i t y £ = 1 - p that the event w i l l not occur are independent of what has gone on before. At P r i n c e t o n , f o r dry days, p_ (the p r o b a b i l i t y of any day being dry) was 0.738. Since no p e r s i s t e n c e i s assumed, the chance that any day w i l l be wet i s q = 0.262. The chance of another day b e i n g dry i s a l s o equal t o p_ and, consequently, the p r o b a b i l i t y 2 of the occurrence of at l e a s t two dry days i s qp . S i m i l a r l y , the chance of 3 at l e a s t three consecutive dry days i s qp , and so on. I f the t o t a l number of days over a c e r t a i n p e r i o d i s N, the expected number of runs of at l e a s t one day, of at l e a s t two days, of at l e a s t three days over that p e r i o d are Nqp, 2 3 Nqp , Nqp ....... provided t h a t there i s no p e r s i s t e n c e . For P r i n c e t o n , p = 0.738, q = 0.262 and N = 5^90; thus Npq = 1061. These expected frequencies are shown i n the f i r s t column of Table VI. The d i f f e r e n c e s between successive values i n t h i s column give the expected number of runs of at l e a s t n days (n =1, 2, 3 ) and are shown i n the second column of the t a b l e . The observed frequencies are given f o r comparison i n the t h i r d column. The X f o r 18 degrees of freedom was not s i g n i f i c a n t at the 0.05 confidence l i m i t . I t i s obvious t h a t the short runs are much l e s s frequent, and the long runs much more frequent than would be expected on the hypothesis of independence, i . e . of no p e r s i s t e n c e . Therefore the hypothesis of no p e r s i s t e n c e between events 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 , that there i s p e r s i s t e n c e , i s accepted. 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 at the other f i v e s t a t i o n s . The observed runs of at l e a s t n days at P r i n c e t o n were then converted 29. Table VI - Frequencies of Runs of Dry Days at Princeton, (1935 - 1964). Observed Runs of n Expected runs runs of Observed -n days & more days of n days n days 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. into observed runs of n or more days to give a ser ies of cumulative frequencies shown i n Table VI I. The second column gives the r a t i o s between successive frequencies, I.e. i s the p robab i l i t y of a dry day when the k days immediately preceding i t were also dry. I t should be noted that a l l of these r a t i o s exceed the general p robab i l i t y (p = 0.738) of a dry day. In attempting to f i t a theoret i ca l persistence model to the dry (and wet) spe l l s at Princeton, three hypothese.s were considered: 1. Hj>: P robab i l i t y of a dry day fo l lowing a dry day i s constant for a l l values of k. 2. H>>: P robab i l i t y of a dry day after two dry days i s constant for a l l values of k greater than 1. 3. H3: P robab i l i t y of a dry day increases as length of s pe l l increases, i . e . p^ cont inual ly increases as k increases. Considering the f i r s t hypothesis, i f the p robab i l i t y of the occurrence of a dry day i s constant a f te r the f i r s t day, the frequencies of runs of 1, 2, . . . . n or more days are 68? ( l , p, » P]_' • • • • P-^  )• Prom the observed data, the number of dry days i s 4050. Therefore 687/(l - p^) = 4050, from which p 1 = 0.830. Using t h i s value fo r p^, the ca lcu lated ser ies of runs of •exaetlyn days are shown against t he i r observed frequencies i n 2 Table VI I I . The X test with 18 degrees of freedom showed that the expected resu l t s calculated on the bas i s of constant p robab i l i t y were s i gn ig i cant l y d i f fe rent from the observed frequencies at the 95f° l e ve l of confidence. Since the largest discrepancies are at low values for n, i t was thought that the second hypothesis, i . e . the p robab i l i t y of a dry day fo l lowing two dry days i s constant might f i t the observed d i s t r i bu t i on more c l o se l y . The frequencies of runs of 2, 3> n or more days are now 515 ( l , p 2 , Pg ....) (2 or more days) + (3 or more) + , then 515 ( l - P 2 ) = 3363, from which p_ = 0.847. A comparison between expected numbers of Table VII - Frequencies of Runs of n or more Dry Days at Princeton, (1935 - 1964). Runs of n or n days more days Ratio = p. 1 687 0.750 2 515 0.775 3 399 0.832 4 332 0.816 5 271 0.790 6 214 0.827 7 177 0.853 8 151 0.808 9 122 0.844 10 103 0.767 11 74 0.722 12 57 0.772 44 0.795 14 35 0.857 15 30 0.733 16 20 32. runs calculated on the basis of t h i s p robab i l i t y and the observed number of 2 runs i s shown i n Table IX. The X test fo r 17 degrees of freedom showed that the two d i s t r i bu t i on s were s t a t i s t i c a l l y the same at the 95$ l e ve 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 th i s value of X when allowance i s made for the decrease i n the number of degrees of freedom required for each add i t iona l assumption. The wet s pe l l frequency d i s t r i bu t ions were subjected to the same treatment. For the f i r s t hypothesis, i . e . p Q - the probab i l i ty of a wet day fo l lowing 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 ser ies was 298/(l - p Q) = 1440, from which p Q = 0.535. The X test (Table X) indicates a close cor re la t ion between observed and expected frequencies, which i s s i gn i f i can t at the 95$ l e ve l of confidence. Since the p robab i l i t y of accepting th i s f i r s t n u l l hypothesis was greater than the p robab i l i t y fo r accepting the second, i . e . the p robab i l i t y of a wet day fo l lowing 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 ibut ions of both wet and dry spe l l s at the other f i v e s tat ions . Table XI summarizes the r e s u l t s . The d r i e r stat ions at Lytton and Kamloops respect ive ly did not show a s i gn i f i cant constant p robab i l i t y i n t he i r dry s p e l l frequencies on th i s persistence model. Their observed frequencies showed a tendency for 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 th 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 on s may be maintained for long periods at these stat ions during the growing season - a 49 dry day spe l l occurr ing at Lytton i n 1940 and a 44 dry day s pe l l at Kamloops i n i960. Altogether there have been 10 dry spe l l s that have exceeded 30 days at Lytton over the.past t h i r t y years and 8 such spel l s at Kamloops, while over the same period of time there have been 6 spe l l s at Table VIII - Frequencies of Runs of Exactly n Dry Days at Princeton, (1935 - 1964 ). 1 Ho: p k " P l k 0 n days Obs. Exp. 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 13 . 9 12 3 0.75 14 5 9.9 4.9 2.42 15 • 8 8.5 0.5 0.03 16 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 x 2 = 49.18 N.'S. ' 34. Table IX - Frequencies of Runs of Exactly n Dry Days at . Princeton, (1935 - 1964).  (b) Ho: p k = p 2 for k ^ » 1 2 days Obs. Exp. Obs. - Exp. X 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 2 * X. = 20.28 * S ign i f i cant at the 95% confidence l e v e l 35. Table X - Frequencies of Runs of Exact ly n Wet Days at Princeton, (1935 - 1964). Ho: p k = P l = 0.535 k o days Obs. E x P « Obs. - Exp, • 2 X 1 298 ,311 13 0.543 2 174 16? 7 0.293 3 93 89 > 0.180 4 49 47 2 0.085 5 1 31 25 6 1.440 6. 8 13 5 1.923 7 8 5.3 2.7 1.371 8 6 4.0 2.0 1.000 9 2 2.1 x 2 • 0.1 = 6.836 * 0.001 Table XI -• S igni f icance of Constant P robab i l i t i e s of Wet and Dry Days at Selected Stations during the Growing Season Station Dry Spells P l P 2 Wet Spells 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 Note: p^ = p robab i l i t y of a dry (or wet) day fo l l ow ing a dry (or wet) day. P 2 = probab i l i t y of a dry (or wet) day fo l lowing 2 dry (or wet) days. NS = not s i gn i f i cant at 95$ l e v e l of confidence, s i gn i f i cant at 95$ l e ve l of confidence. 36. Penticton or Vernon respect ive ly , k spe l l s at Princeton and 3 at Hope. The p robab i l i t i e s of wet spe l l s during the growing season fo l low a more consistent pattern across the region, a l l s tat ions except Kamloops having a constant p robab i l i t y of a wet day, provided the previous day was wet. The cons istent ly shorter spe l l s of wet weather compared with dry weather at a l l stations might account f o r t h i s s imp l i f i ed constant p robab i l i t y . S imi lar re su l t s were obtained i n a study undertaken by the B r i t i s h Meteorological Off ice i n South East England^. The constant p robab 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 ions i n the moisture supply and demand by crops at selected points wi th in the region during the growing season. In the case of both wet and dry spe l l s , high p r obab i l i t i e s ind icate a tendency towards a greater duration of such spe l l s and, as expected, s tat ions with high p robab i l i t i e s of wet spe l l s have low p robab i l i t i e s of dry spe l l s and v ice-versa. Thus these f igures contrast the r e l a t i v e l y unfavourable moisture supply and demand pattern for crop growth i n the Thompson Val ley and at Princeton against the more favourable balance at Hope, Vernon and Pent icton. Since there appeared to be a constant p robab i l i t y of a dry (or wet) day fo l lowing a ce r t a i n number of dry (or wet) days at most s tat ions, i t was thought that there might be a re la t i onsh ip 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 test and the appropriate degrees of freedom, a l l the observed frequencies of both wet and dry spe l l s at a l l the s tat ions f i t t e d the negative binomial d i s t r i bu t i on r e l a t i v e l y w e l l . Accordingly, the frequency d i s t r i bu t ions were normalized by transforming the cumulative frequencies i n t o t he i r logarithmic Spells of Dry Weather i n Eastern England. Agro. Met. Branch (London: Met. Of f i ce , 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 spell (wet or dry) i n days. The various regression equations, standard errors of the estimate and correlation coefficients are summarized in Table XII. A l l regression analyses are highly significant at 18 and 8 degrees of freedom for the dry and wet spells respectively, i n a l l cases over 90$ of the variation in the spell frequencies being explained by their duration. It i s therefore thought that f a i r l y accurate forecasts of the recurrence intervals of wet and dry spells.of any length less than approximately a month could be made from these equations. The relevance of these equations to the study can be seen from an examination of the regression constants (the number followed by n in each equation), which indicate the slope of the regression l i n e . For both wet and dry.spells, the lower this figure,the greater i s the tendency for the spell to continue. These figures support the conclusions resulting from an analysis of the constant probabilities, namely that Lytton, Princeton and Kamloops tend to experience the longest dry spells during the six-month growing season, and that Hope is the only station that can expect wet spells of some considerable length. However, such results can only be applied for data covering lengthy time intervals which avoid the awkward overlapping of dry spells from month to month. The agriculturalist i s also concerned with the probabilities of wet and dry spells over shorter periods of time (say a monthly basis), which requires the use of the Markov Chain Model. Table XII - Regression Analysis on Dry and Wet Spel l s during the Growing Season at Selected Stat ions.  Stat ion Hope Ly t t on Penticton Princeton Vernon Kamloops Dry Spe l l s  Regression Equation S.E. R_ Wet Spel l s  Regression Equation S.E. log y = 2.909 - 0.112311 0.103 0.989 log y = 3.063 - 0.1702n 0.117 A A log y = 2.927 - 0.0956n 0.151 0.968 l og y a 3.099 - 0.3308n 0.070 A A l og y = 2.991 - 0.1076n 0.107 0.98? l o g y ~ 3.104 - 0.25l6n 0.027 log y = 2.960 - 0.1020n O.O65 0.995 log y - 3.186 - 0.2985n 0.099 A A log y = 3.027 - 0.1l45n 0.136 0.982 log y = 3.031 - 0.24l9n .0.091 A A l o g y = 2.983 - 0.1055n 0.168 O.967 l og y = 2.950 - 0.2534n 0.108 R 0.989 0.997 0.999 0.994 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 verified 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 for and (for some stations) against the use of a simple Markov Chain probability model, and to present the operational procedures necessary to estimate the i n i t i a l and transitional probabilities 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 this state i s dependent upon some previous condition. Any day can be either wet or dry, and i t has been verified 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 this outcome in any given sequence, given that the outcome q. appeared on the previous day. This quantity p.. is known as a transitional probability, since i t indicates the probability of moving from one state (wet or dry) to another or remaining in the same state as time passes. References dealing with the Markov Chain model. Gabriel and Neumann, loc. c i t . J.E. Caskey, "The Markov chain model for the probability of preci-pitation occurrence i n intervals of various lengths", Monthly Wea. Rev., Vol. 91 (1963), 298-301. L.L. Weiss, "Sequences of wet and dry days described by a Markov chain probability model", Monthly Wea. Rev., Vol. 92 (1964), 109-176. J.W. Hopkins and P. Robillard, "Some st a t i s t i c s of daily r a i n f a l l occurrence for Canadian Prairie Provinces", Journ. Applied Met., Vol. 3 (1964), 600-602. A.M. Feyerherm and L.D. Bark, "Statis t i c a l methods for persistent precipitation patterns", Journ. Applied Met., Vol. k (l96^)s 320-328. The transitional probabilities may be set up in a matrix form, from which the following formula may be derived, assuming that the transition probabilities depend only upon the previous day's weather. P <Xt> Xi»l hJ - P (V P< Xt +l/V P ( X t * n / X t + n - l > ' Where X = states (wet or dry). P(X X ,...) denotes the probability.that the sequence shown in in parenthesis w i l l occur. P(X t) i s the i n i t i a l probability of a wet or dry day. P(X t + 1/X^) i s a transitional probability, the sign (/) meaning "given that" i.e. P(W +^1/W ) i s the transitional probability of a wet day, the previous day being wet. Thus i t can be seen that the right-hand side of (l) is the product of an i n i t i a l probability and a set of transitional probabilities. Since the above model assumes that the probability 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 to estimate the probabilities of wet and dry spells of lengths n days, equation (l) may be simplified by assuming the transitional probabilities of the right hand side to be equal, i.e. Pw/w = Pw/w,w (in the case of vret spells). This assumption i s sometimes part of the definition 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. Feller, An Introduction to Probability Theory and i t s Applica-tions (2nd Ed.; New York! John Wiley and Sons, Inc., 1957), Vol. 1 41. The p robab i l i t y of a wet spe l l of length n days i s : (1 - Pw/v) Pw/w"1"1 . .(2) and the probabi l i ty of a dry s pe l l of length k days i s Pw/d (1 " Pw/d ) k _ 1 (3) Before th 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 fo r each of the s ix synoptic stations wi th in the region, the procedure f o r estimating the i n i t i a l and condit ional p robab i l i t i e s must be discussed. This i s best i l l u s -trated by means of a p robab i l i t y " t r e e " . where: Pw = p robab i l i t y of an i n i t i a l wet day on random se lec t ion . Pd = p robab i l i t y of an i n i t i a l dry day on random se lec t i on . Pw/d = p robab i l i t y of a wet day, the previous day being dry. Pw/w = p robab i l i t y of a wet day, the previous day being wet. Pw/d,w = p robab i l i t y of a wet day, the previous days being dry and wet respect ive ly . and -Pw/w,w = p robab i l i t y of a wet day, the two previous days being wet. 42. Using the appropriate branches of this tree, the probabilities of any consecu-tive combination of wet and dry days may be estimated. Since the sum of the probabilities on any two branches away from a single outcome i s 1 (e.g. Pw/w + Pw/d = l ) only the probabilities of wet days following the various combina-tions of wet and dry days were calculated (Table XIII). An analysis of the table underlines two points already noted i n earlier chapters. F i r s t l y , the various transitional probabilities vary by larger or smaller amounts, both from month to month and from place to place across the region. The lower probabilities of wet days are associated with the drier months and drier areas i n accordance with earlier results. Secondly, the persistence effects are immediately obvious from a comparison of the transitional probabilities for Pw/w against Pw or Pw/d. Generally speaking, Pw/w and Pw/d,w are the highest probabilities at most stations. It has already been mentioned that one of the conditions of the f i r s t order Markov Chain i s that the probability of a wet day i s constant, provided the previous day was wet, i.e. Pw/w = Pw/w,w, etc. An examination of the tables shows that this assumption i s remarkably consistent for most months at most places, though there appear to be a few exceptions. Therefore, i t was decided to test s t a t i s t i c a l l y whether the differences between these probabilities were significantly different or not. Sta 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 and, Feyerherm and Dean Bark^. In accordance with their results, the 2 x 2 contingency table for both wet and dry days respectively was used to test the null hypothesis s T.W. Anderson and L.A. Goodman, "Sta t i s t i c a l Inference about Markov Chains", Am. Math. Stat.. Vol. 28 (1957), 89-110. Feyerhern and Bark, loc. c i t . 43. Table XI I I - I n i t i a l and Trans i t iona l P robab i l i t i e s at Selected Stations Proba-b i l i t y . Stat ion A p r i l June Ju ly August September Pw Hope 0.553 0.384 0.418 0.271 0.313 0.363 Lytton 0.177 0.163 0.237 0.148 0.171 0.208 Penticton 0.230 0.266 ' 0.327 0.190 0.197 0.200 Princeton 0.205 0.255 0.312 0.213 0.232 0.217 Vernon 0.287 0.264 0.367 0.234 0.255 0.258 Kamloops 0.168 0.203 0.293 0.203 0.210 0.185 Pw/w Hope 0.684 0.647 0.606 0.536 0.547 0.628 Lytton 0.302 0.347 0.387 0.304 0.330 0.416 Penticton 0.391. 0.455 0.464 0.390 0.361 0.433 Princeton 0.293 0.462 0.428 0.455 0.444 0.413 Vernon 0.413 0.488 0.514 0.469 0.468 0.452 Kamloops 0.257 0.373 0.520 0.333 , 0.369 0.387 Pw/d Hope 0.391 0.220 0.284 0.173 0.211 0.212 Lytton 0.150 0.127 0.190 0.121 0.138 0.183 Penticton 0.182 0.198 0.260 0.143 0.157 0.142 Princeton 0.182 0.184 0.259 0.148 0.168 0.162 Vernon 0.236 0.184 0.282 0.161 0.182 0.191 Kamloops 0.130 0.160 0.204 0.170 0.167 0.139 Pw/w,w Hope 0.656 0.623 O.566 0.456 0.471 0.606 Lytton 0.250 0.343 0.400 0.179 0.371 0.269 Penticton 0.389 0.467 0.462 0.326 0.364 0.269 Princeton 0.306 0.452 0.375 0.483 0.454 0.370 Vernon 0.451 0.538 0.514 0.441 0.392 0.414 Kamloops 0.346 0.362 0.505 0.333 0.352 0.372 Pw/w,d Hope 0.390 0.274 0.333 0.256 0.233 0.284 Lytton 0.216 0.167 0.195 0.187 0.127 0.192 Penticton 0.156 0.267 0.352 0.153 0.244 0.162 Princeton 0;218 0.224 0.346 0.181 0.275 0.239 Vernon 0.254 0.190 0.364 0.169 0.190 0.247 Kamloops 0.138 0.266 0.163 0.250 0.195 0.206 Pw/d,w Hope 0.743. 0.690 0.666 0.628 0.611 0.66? Lytton 0.324 0.348 0.379 . 0.359 0.310 0.521 Pentict on 0.393 0.444 0.467' 0.431 0.359 0.559 Princeton 0.28? 0.470 0.467 0.431 0.413 0.44? Vernon 0.387 0.440 0.495 0.494 0.538 0.482 Kamloops 0.262 0.380 0.535 '0.333 0.378 0.397 Pw/d,d Hope 0.393 0.205 0.189 0.155 0.205 0.193 Lytton 0.138 0.119 0.177 0.112 0.140 0.147 Penticton 0.188 0.185 0.227 0.142 0.141 0.138 Princeton 0.177 0.176 0.229 0.142 0.146 0.14? Vernon 0.229 0.183 0.249 0.161 0.179 0.236 Kamloops 0.129 0.157 0.215 O.I54 0.162 0.128 44. Ho: P(X / I w , X t._ 2) = P(X A t T l ) against H i : P (X t / X t _ l f X t _ 2 ) = P ( X t / X t - 1 ) Again, data at Princeton 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. s t a t i s t i c . 2 Two X were computed, one fo r sequences i n which the middle day was dry and one for sequences i n which the middle day was wet. 2 Table XIV - Observed Numbers for Computing X. S t a t i s t i c s for the month of A p r i l at Pr inceton, (1945 - 1964). X t - i = D X t - 1 = w D V D w D 321 69 390 D 62 25 87 W 69 19 88 W 25 11 36 390 88 4?8 87 36 123 5C2D = 0.0010 * * >c2w = 0.0001 ** Using the 5% l e ve l of s ign i f i cance Ho would be accepted i n both instances i . e . the f i r s t order Markov Chain holds for both wet and dry spe l l s at Princeton during A p r i l . However, i t must be stated that accepting t h i s hypothesis does not prove that the data fo l low 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. 2 S imi lar X tests were run for each month of the growing season at 2 each of the s i x chosen stat ions. The months for which the X were 45. s i gn i f i cant at the 5% l e ve l are tabulated i n Table XV * * each month being denoted by a number. Table XV - Months during the Growing Season for which the Chi-Squares were S ign i f icant at the P = 5 per cent Level  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 to r a t i ona l i z e why the f i r s t order chain i s rejected fo r cer ta in months at the various stat ions, since no month i s cons istent ly rejected throughout the whole area and no two stat ions have the same monthly pattern of accepting and r e jec t i n g the n u l l hypothesis (except i n the case of dry s pe l l s at Penticton and Pr inceton). However, i n judging the re su l t s of Table XV, i t should be noted that there are 12 independent tests for each s ta t ion (2 conditions and 6 months). Thus i t would not be surpr i s ing t o f i n d one or two months per s ta t ion for which the n u l l hypothesis would be rejected. The resu l t s suggest that although the f i r s t order Markov Chain i s an imperfect model for pred ic t ing p rec i p i t a t i on patterns wi th in the region on a monthly bas is, i t does provide a r e l i a b l e approximation to the problem:. Con-sequently, the p robab i l i t i e s of wet and dry s pe l l s of any length may be obtained with a ce r ta in degree of v a l i d i t y from equations (2) and (3). It i s thought that f o r some months and at some stat ions th i s approximation might be improved by a second order Markov Chain, i . e . a day's weather depends on events occurring two days previous ly, though i t i s doubtful whether th i s improvement would be worth the add i t iona l computational e f f o r t . 1 1 Threshold of 0.01 inch was s t i l l used. I t was hoped that the 0.1 inch threshold could also be used, since such r a i n f a l l i s more useful for 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. ^ s t a t i s t i c s . Conditions  X t - l - D 46. Summary An analysis of the distribution of daily precipitation data at selected points within the region indicates that both the persistency model and the Markov Chain model may be used to estimate probabilities of wet and dry spells. Both hypotheses reject overwhelmingly the, hypothesis of independence i n daily r a i n f a l l occurrence. The frequencies of wet and dry spells over the entire length of the growing season appear to follow a con-sistent pattern, the probability of a dry day following two dry days and the probability of a wet day following a single wet day being relatively constant. From linear relationships between the cumulated frequencies of wet and dry spells and the lengths of these spells, probabilities of the occurrence of a spell (wet or dry) can be determined. However, the analysis of transitional probabilities on a monthly basis indicate that one must take into account variation i n the matrix of such probabilities with time. For short sequences, one might consider the i n i t i a l and transitional probabilities constant, without biasing f i n a l estimates, but aggregation over several months might produce severely biased results. The Markov chain technique i s a useful tool i n quantitative climatology, since through i t s application direct comparisons of precipitation patterns from place to place can be made. Furthermore, cumulative probabilities and expected return periods of both wet and dry spells can be forecast by using the formulae described i n Appendix II. 47. CHAPTER 4 AN ANALYSIS OP TEMPERATURE AND HUMIDITY PATTERNS Evaporation and t ransp i ra t ion, that i s the conversion of water i n l i q u i d form into a gaseous form, requires a considerable amount of heat energy (approximately 590 ca lo r ie s per gram of water at normal temperatures and pressures). Under f i e l d condit ions, t h i s ava i lable heat comes from two sources, namely d i rect so lar and sky rad ia t ion and that conveyed to the crop from the surrounding a i r by turbulent f low. By fa r the more important source of energy i s d i rec t solar radiation" ' ' . 2 Several invest igators have noted high corre lat ions between observed evapora-t ion and t ransp i rat ion from crop covers and the d i f ference i n water loss from the black and white Be l l an i atmometers. Since these instruments d i f f e r prim-a r i l y i n the i r rad ia t ion cha rac te r i s t i c s , i t would appear that evapotranspira-t i o n (the combined processes of d i rect evaporation from the s o i l plus t rans-p i r a t i on from the crop) and solar r ad ia t i on are highly cor re lated. S t r i c l y speaking, i t i s net r ad ia t i on rather than i n so l a t i on upon which evaporation 3 4 rates are la rge ly dependent.. However, i t has been shown by Shaw that solar • ^ U.S. Geological Survey. Water Loss Invest igat ions, Vo 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 for crops from c l imat ic data", H i l ga rd ia , Vo l . 24 (l955)s 207-233. R.M. Holmes and G.W. Robertson, "Conversion of latent evaporation to potent ia l evapotranspirat ion", Can. Journ. Plant Science, Vo 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, So 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 so la r rad ia t ion and net r ad i a t i o n " , B u l l . Amer. Met. S o c , Vo l . 37. (1956), 205-207. 48. rad ia t ion and daytime net rad iat ion over grass are p r a c t i c a l l y d i r e c t l y proport ional . As was mentioned e a r l i e r , the other source of heat energy i s the' turbulent flow of heat between the ground and the a i r . Mukammel and Bruce noted that on dry, windy days the observed water loss from Be l l an i P lates was four times as much as the water loss calculated from the net rad ia t i on energy supply alone. Examination of the heat balance equation explains th i s d i f ference^. . R = LE • +K + A . . . . . . . . . . . .; ( l ) where R i s the net r ad i a t i on , LE i s the latent 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 layers . Since the component A i s general ly neg l i g ib le when deal ing with evaporation from plant surfaces^, th i s turbulent advection of heat (K) i s the p r i n c i p a l add i t iona l component of energy other than net rad ia t i on a f fec t i ng the loss of water from moist surfaces. The importance of these two heat components vary from climate to 7 c l imate. Pelton working i n the semi-arid climate at Swift Current, Saskat-chewan estimated that only 50% of the Be l l an i Plate evaporation was due to net r ad i a t i on . Mukammel and Bruce, working with the same instrument, but i n the more humid cl imate at Ottawa, suggested that t h i s factor accounted for 80% of the evaporation (the lengths of the. records were not s im i l a r , but they were comparable). These resu l t s suggest that i n the d r i e r c l imat ic regions a larger ..proportion of Lthe t o t a l rad ia t ion balance f a l l s in to the sensible heat component and a lesser proportion into the latent heat component. 5 M.T. Budyko, The Heat Balance of the Ear th ' s Surface, Trans lat ion PB 131692 (Washington, D.C.: U.S. Dept. of Commerce, 1 9 5 5 ) . ~ ^ Mukammel and Bruce, loc . c i t . 7 Pelton, loc. c i t . 49. Should th i s be true, then a i r temperature should be more s i g n i f i c a n t l y corre-lated with evaporation i n dry areas than i n humid areas. At Swift Current, the co r re la t i on between Be l l a n i Plate evaporation and a i r temperature was 0.739 ( s i gn i f i cant at 95$ l eve 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 rad ia t i on recordings were only a v a i l -able at one s ta t ion w i th in the area (Summerland), but since t h i s thes i s emphasises the spa t i a l v a r i a t i on i n the c l imat ic parameters a f fect ing evapo-t ransp i rat ion, other re lated c l imat ic elements recorded at the s ix synoptic stat ions were used. Judging from the above re su l t s , a i r temperature i s the best s ingle element a f fec t i ng evapotranspiration i n t h i s dry area. Relat ive humidity patterns are also analysed since they are an expression of the saturation d e f i c i t of the a i r , which i s i n turn an ind icator of the a b i l i t y of the atmosphere to accept the evaporated moisture. Since by f a r the greater proportion of water lo s s from plant and s o i l surfaces occurs during the day than at night, i t was thought that the d a i l y maximum temperature and the da i l y minimum re l a t i ve humidity were the most representative c l imat ic "cond i t ions a f fec t i ng crop water losses. Although, as maxima and minima respect ive ly , they w i l l overemphasise the average con-d i t i on s p reva i l i ng throughout the dayl ight 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 reva i l i n g condit ions at ground l e v e l at any point i n time. Therefore, they are probably the most representative f igures of a l l the da i l y c l imat i c data commonly observed at synoptic recording stat ions fo r estimating evaporating condit ions. Analysis of Temperature Frequencies . As with p rec i p i t a t i on patterns, the frequency and p robab i l i t y d i s t r i bu t ions of maximum temperatures rather than the i r means are discussed. 50. I t i s bel ieved that much of the d i f f i c u l t y that i s experienced i n cor re lat ing f i e l d observations of c l imat ic parameters with evaporation l i e s i n the i n d i s -criminate use of d a i l y averages. Ba s i ca l l y the same procedure was fol lowed to obtain the p robab i l i t i e s of maximum temperatures as was used to determine the p robab i l i t i e s of p r e c i -p i t a t i o n . The da i l y maxima were tabulated i n 5°F classes for each of the s i x growing season months at each of the s i x synoptic s tat ions over the 20-year period 1945 - 1964. These 5°* ' frequencies were then cumulated from the lowest c lass , each of the cumulated frequencies being div ided by the to ta l monthly s ize sample plus one to y i e l d t he i r desired p robab i l i t i e s of occurrence. An analysis of the Table XVI shows that Lytton and Kamloops are notably warmer than the other stat ions for a l l months except A p r i l . This i s mainly due to t h e i r l ocat ion i n the rather confined Thompson Va l ley, yet these towns occupy s i te s representative of much of the potent ia l arable land i n the v a l l e y . Although the p robab i l i t i e s of cooler maxima (below 75°F) are lower at these stat ions from May onwards, the p robab i l i t i e s of the warmer maxima (80°F and above) are not noticeably greater u n t i l Ju l y . The unsett led, cloudy weather of June i n the In ter io r keeps the maxima on a par with Hope, but when the more se t t l ed ant icyc lon ic conditions p reva i l i n the In te r io 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 robab i l i t i e s at Kamloops, Penticton and Vernon quickly shows how the climate i s general ly cooler towards the north and east of the region. The differences i n height between the stat ions (Kamloops 1133 feet, Penticton 1140 feet, Vernon 1580 feet) would hardly account for these re su l t s , espec ia l l y as Princeton (2283 feet) pa ra l l e l s Vernon's p robab i l i t i e s i n a l l months except Ju ly , when i t i s considerably warmer. 51. Table XVI - Relative Frequencies of Dai ly Maximum Temperatures at Selected Stations, (1945-1964). Hope T V A p r i l May June Ju ly August Septembi 30 - 35 35 - 40 4 0 - 45 1.41 45 - 50 7.97 1.95 1.63 50 - 55 28.01 9.51 1.95 55 - 60 51.77 21.36 7.39 0.92 1.28 11.20 60 - 65 70.04 . 43.83 25.88 7.02 10.09 28.92 65 - 70 82.45 62.33 49.42 19-59 23.85 46.84 70 - 75 93.44 75-92 73.54 39-56 48.07 65.17 75 - 80 97.87 89.71 87.74 68.39 69.54 80.45 80 - 85 99.82 95-34 93.97 87.25 85.50 87-58 85 - 90 98.45 97.47 93.53 94.86 97.75 90 - 95 99.61 99.42 96.49 97.80 99.18 95 - 100 99.81 99.80 98.71 99.81 99.80 100 - 105 99.81 105 - 110 Lytton T°F A p r i l May June July August September 30 - 35 35 - 40 40 - 45 0.73 45 50 3.10 0.40 1.29 50 - 55 14.75 1.74 0.40 53 — 60 34.24 8.93 1.01 0.36 4.97 60 _ 65 59.39 20.24 8.45 0.90 2.25 17.49 65 70 77.05 39.28 21.13 5.61 7.30 31.86 70 75 89.98 56.75 46.68 17.36 23.97 50.28 75 — 80 95.45 72.82 64.78 34.54 42.88 65.01 80 — 85 99.63 85.91 81.29 51.36 56.93 79.37 85 — 90 99.81 93.25 90.54 67.09 73.97 91.53 90 - 95 99-60 96.37 82.64 86.70 99.08 95 — 100 99.80 98.79 92.77 97.94 99.81 100 - 105 99.59 98.37 99.81 105 - 110 99.80 99.45 110 - 115 99.82 • I. I 52. Table XVI - Continued Penticton t l A p r i l May June July. August Septeml 30 - 35 35 - 40 40 - 45 0.82 45 50 5.77 0.36 50 - 55 21.07 2.?2 1.18 55 - '• 60 44.93 10.31 1.07 0.34 4.74 60 - 65 73.76 27.72 8.21 1.04 3.40 18.38 65 - 70 96.66 46.38 21.07 4.58 9.17 34.78 70 - 75 99.01 68.12 46.25 11.85 21.56 59.68 75 - 80 99.81 86.96 68.39 29.83 44.14 83.40 80 - 85 95.65 87-86 52.20 71.64 97.23 85 - 90 99.82 95.71 78.20 89.13 99.41 90 - 95 99.46 94.07 97-79 99-81 95 - 100 99.82 99.23 99.82 100 - 105 99.61 105 - 110 99.81 Princeton T°F A p r i l May June July August Septeml 30 35 35 - 40 0.54 40 - 45 4.75 0.37 45 - 50 17.55 2.21 0.36 0.57 50 - 55 40.76 10.11 0.72 0.17 0.37 4.92 •'55 - 60 64.17 26.47 6.32 0.87 1.31 16.48 60 - 65 80.26 43.75 24.19 5.05 7.68 31.44 65 - 70 89,76 59.38 42.96 12.19 18.73 43.75 70 - 75 95.98 76.10 64.26 26.83 39.33 57.76 75 - 80 98.53 87-50 82.31 43.21 56.55 73.86 80 - 85 99.45 95.04 91.52 62.72 73.60 89.01 85 — 90 99.82 98.71 97.11 82.93 87.45 97-35 90 - 95 99.81 99.10 94.25 96.44 99.81 95 — 100 99.82 98.95 99.62 100 - 105 99.48 99.81 105 - 110 99.82 53. Table XVI - Continued Vernon A p r i l May June Ju ly August Septeml 30 - 35 35 - 40 0.37 4o - 45 1.69 45 - 50 7.50 0.90 0.53 50 - 55 22.51 3.81 0.19 4.27 55 - 60 50.09 27.77 1.69 0.41 0.53 12.10 60 - 65 74.48 48.64 8.60 1.64 2.81 26.33 65 - 70 88.55 69.87 25-98 6.78 11.78 44.84 70 - 75 97.18 86.75 48.60 36.75 29.17 65.30 75 - 80 99.80 93.10 73.46 59.34 53.60 87.19 80 - 85 98.91 87.29 80.29 . 73.46 96.44 85 - 90 99.82 96.82 94.04 88.93 99.81 90 - 95 99.44 98.97 98.77 95 - 100 99.82 99.80 99.81 100 - 105 105 - 110 Kamloops T°F A p r i l May June Ju ly August Septemb< 30 - 35 35 - 40 40 - 45 2.29 45 - 50 6.11 0.37 0.56 50 - 55 16.41 2.40 0.19 2.10 55 - 60 38.55 9.59 2.06 0.54 6.50 60 - 65 66.22 24.1? 7.88 1,25 1.43 19-85 65 - 70 82.82 37.82 19-70 6.26 6.44 35-95 70 - 75 92.75 57-74 39.96 14.13 21.65 49.06 75 - 80 98.28 78.41 62.85 29.52 43.47 66.29 80 - 85 99.81 89.48 82.18 49.91 65.12 86.70 85 - 90 95.94 91.18 68.69 81.75 95.88 90 - 95 99.45 98.50 86.68 95.52 99.61 95 - 100 99.82 99-62 96.24 99.81 99-80 100 - 105 99.82 99.10 105 - 110 99.82 Rote: The p robab i l i t i e s are tabulated i n percentages and represent the empir ical p robab i l i t y of obtaining maximum temperatures i n the stated range or l e s s . 54. Analysis of Relative Humidity Frequencies According to the mass t ransfer process, evaporation i s a funct ion 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 effectiveness of turbulent mixing above the surface. E » . f (u) (e - e ) .(2) o o a where E q i s the evaporation, f (u) i s a funct ion of the wind speed at some height 2 above the ground and e and e are vapour pressures at the surface o a 8 and height 2 respect ive ly . 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 re l a t i ve humidities are analysed i n Table XVII. As can be seen from the table, da i l y observations of r e l a t i v e humidity were only ava i lable 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 table shows that both Lytton and Princeton experience considerably d r ie r atmospheric conditions than Penticton during the growing season. For example, at Lytton 33.5$ and 45.2$ of the days during June and July respect ive ly 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 humidit ies, while at Penticton such conditions only p reva 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 exper-ienced a l l along the lake shores were most of the p r i nc i pa l orchards are s i tuated. However, the general r e l a t i v e humidity f igures are so low that i t i s doubtful whether t h i s d i f ference would s i g n i f i c a n t l y affect J . Leighly, "A note on evaporation", Ecology, Vo l . 18 (1937), 180-198. 55. Table XVII - Relat ive Frequencies of Dai ly Minimum Relat ive Humidities at Selected Stations i n the In ter io r , (1937-1964.).  Lytton R.H. fo A p r i l May June Ju ly August September 5 - 10 0.80 1.05 2.15 0.81 10 - 15 2.46 6.37 6.28 13.44 7.29 15 - 20 10.66 28.84 18.85 30.11 18.62 5-85 20 - 25 21.31 44.28 33.51 45.16 36.84 16.45 25 - 30 34.25 63-75 50.79 55.38 48.99 32.91 30 - 3 5 J 52.46 77.29 65.45 69.35 62.35 49.39 35 - 40 68,44 88.84 84.29 81.72 74.49 62.04 4 0 - 4 5 82.79 91.24 92.67 88.71 83.80 71-31 45 - 50 90.57 96.41 97.38 94.62 90.69 83 .34 5 0 - 5 5 94.67 98.00 98.95 97.85 94.33 88.61 5 5 - 6 0 97.54 99.20 99.48 99.40 97-57 96.20 60 - 65 98.36 99.60 97.89 65 - 70 98.36 99.50 70 - 75 99.59 7 5 - 8 0 Penticton R.H. ,4 i° A p r i l May June 5 - 10 10 - 15 0.42 15 - 20 2.09 1.60 3.78 20 - 25 9.62 14.00 13.03 25 - 30 24.25 33.20 38.66 30 - 35 44.75 52.00 56.30 35 - 40 64.44 • 67.20 74.37 40 - 45 77.59 80.40 86.13 45 - 50 82.88 86.80 91.18 50 - 55 94.56 92.40 94.96 55 - 60 97.07 95.20 97.48 60 - 65 98.33 96.40 99-16 65 - 70 99.50 98.40 99.50 70 - 75 98.80 75 - 80 99.60 80 - 85 Ju ly August September 0.81 6.85 2.09 0.37 18 .55 10.88 10.78 47.18 28.45 33.47 68.15 51.05 46.10 81.85 69.26 64.31 90.73 84 .02 79-18 93.95 94.26 86.25 96.77 96.31 90.71 98.39 97-54 95.17 99.60 99-18 97-40 99.60 98.88 99.26 99.60 56. Table XVII - Continued Princeton R.H. fo A p r i l May June July August September 5 _ 10 0.41 2.04 4.45 1.27 10 - 15 1.25 5-75 3.32 10.61 19.03 10.55 15 - 20 8.75 15-70 14.94 28.98 35.63 18.99 20 25 17.50 25.67 32.37 48.16 49.80 38.40 25 - 30 33.33 42.15 46.89 59.59 61.54 50.21 30 - 35 49-58 60.15 62.66 ' 71.49 70.45 63.29 35 - 40 70.41 75.48 73.03 82.45 83.81 76.37 40 - 45 84.16 83.14 82.16 88.57 89.07 85.23 '+5 - 50 90.83 88.89 89.63 93.47 93.93 90.30 50 - 55 93.33 91-57 92.53 96.33 97.17 96.62 55 - 60 94.58 95.01 95.02 98.38 98.79 97.89 60 - 65 95-83 96.55 97.93 99.68 99.63 99-58 65 - 70 99-16 98.08 98.76 70 - 75 99.60 98.85 99.65 75 - 80 99.65 Rote: P robab i l i t i e s are tabulated i n percentages and represent the empir ical p robab i l i t y of obtaining minimum r e l a t i v e humidities i n the stated range or le s s . 57. t ransp i rat ion losses along the lake shore. Combination of Weather-Type Frequencies Since evaporation i s known to be affected by at least four c l imat i c elements, v i z . temperature, humidity, wind and net rad ia t i on , i t was thought that a more r e a l i s t i c representation of the evaporating conditions i n the Inter ior 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 avai lable for only two of the four weather elements, v i z . temperature and humidity. Frequency tables were tabulated at the three stat ions for the 8 years when both da i l y minimum humidity and d a i l y maximum temperature observa-t ions were avai lable (Table XIX). The c l a s s i f i c a t i o n system used i n the tables f o r each of the two elements i s presented i n Table XVIII. Table XVIII - C l a s s i f i c a t i o n of Weather Elements used i n Table XIX Da i ly Maximum Temperature  Class Number Range 1 2 3 4 5 6 7 below 50 F 51 - 60°F 61 - 70°F 71 - 80°F 81 - 90°F 91 - 100°F above 100°F Dai ly Minimum Relative Humidity  Class Number Range 1 2 3 4 5 6 7 0 - 10% 11 - 20% 21 - 30% 31 - 40% 41 - 50% 51 - 60% above 60% The diagonal patterns apparent i n Table XIX indicate that there i s a pronounced negative co r re la t ion between the two weather elements - the higher the maximum temperature, the lower the minimum re l a t i ve humidity. A l l other factors being equal, these conditions would combine to i n tens i f y the rates of evaporation loss and, accordingly, the greater the frequency of occurrences towards the right-hand top corners of the tab les , the greater w i l l be the evaporation ra te . 58. Table XIX - Temperature-Humidity Combinations at Selected Stations, (1957-1964) 1. LYTTON A p r i l Temperature - P • H Tl •H j - P • r l Tj • H - P • H ' d • H 1 2 3 4 5. 6 7 1 4 2 2 5 '24 14 1 3 31 32 13 4 40 31 4 5 5 17 7 1 8 7 1 1 June Temperature 1 2 3 .4 5 6 7 1 1 4 9 2 2 12 38 18 2 3 8 48 21 4 1 7 . 32 1 5 15 4 6 4 7 1 August Temperature 1 2 3 4 5 6 7 1 2 7 8 2 5 23 40 6 3 2 25 23 8 4 7 35 10 5" 8 18 6 7 5 7 2 • H • H May 1 2 3 4 5 6 7 June -p • H • r l Temperature 1 2 3 4 5 6 7 3 5 7 1 3 10 20 18- 4 13 34 31 11 9 x? 6 8 10 1 4 2 1 Temperature >5 - P • H • H 1 2 3 4 5 6 7 1 1 17 18 2 1 24 49 11 3 3 23 28 12 1 4 3 25 10 5 6 9 3 6 3 7 September Temperature 1 2 3 4 5 6 7 1 2. 2 15 21 3 3 17 48 15 3 4 2 19 29 4 1 5 9 25 7 6 4 16 7 3 59-Table XIX - Continued 2. PENTICTON • H Temperature 1 2 3 4. 5 6 7 1 2 7 13 2 1 3 29 41 14 1 40 33 1 5 1 20 8 6 1 14 1 7 3 1 May Temperature 1 2 3 4 5 6 • H • H June • H • H 1 2 3 4 5 6 7 3 4 5 6 1 7 1 12 3 43 46 11 16 37 18 13 8 1 6 4 1 July- Temperature •p • H •rt w 1 2 , 3 4 5 6 7 1 2 2 2 15 25 2 3 18 61 44 1 4 1 28 26 2 5 4 10 1 6 2 5 7 August Temperature >M1 • P • H T J • H 1 2 3 4 5 6 7 1 2 3 11 11 3 25 50 22 4 9 40 32 2 5 5 15 11 6 2 5 7 September Temperature 1 2 3 4 5 t>3| - P • H • H 2 5 4 6 5 1 5 22 40 9 37 35 14 34 20 16 2 4 60. Table XIX - Continued 3. PRINCETON A p r i l >» •p • r l m •p • r l • r l Temperature 1 2 3 4 5 6 7 1 1 1 2 9 23 8 3 12 41 18 6 16 61 6 1 5 4 13 5 6 4 1 7 7 3 June Temperature 1 2 3 4 5 6 7 1 2 3 3 2 4 27 31 7 3 1 25 35 11 4 24 19 5 2 20 4 6 8 1 7 1 w -P • r l • H May Temperature 1 2 3 4 5 6 7 1 2 3 4 4 2 3 9 18 4 1 3 1 31 37 18 2 4 3 25 14 3 5 1 13 1 2 6 2 7 3 7 2 2 1 Ju ly Temperature 1 2 3 4 5 6 7 1 7 18 1 2 9 52 31 3 6 28 20 5 4 13 24 5 5 1 13 5 6 2 5 2 7 August Temperature f»4 -P • r l 1 2 3 4 5 6 7 1 1 9 1 2 13 43 23 3 5 31 37 1 4 23 24 4 5 2 18 5 6 4 1 1 7 2 September Temperature • r l • r l 1 2 3 4 5 6 7 1 2 1 2 1 4 21 15 1 3 4 27 30 13 4 1 10 31 19 1 5 12 17 4 6 8 6 7 7 61. At a l l stat ions, such frquencies increase sharply during July 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 with low humidities deserve c loser scrut iny. An Analysis of Tor r id Day Frequencies The hot, sunny day with low re la t i ve humidity and a gentle breeze i s known to extract the greatest amounts of moisture from a crop cover. Such a day i s ca l led 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 re l a t i ve humidity 30% or l e s s . 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 so la ted 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 imat ic elements, the frequencies of t o r r i d days and spe l l s are analysed i n terms of t he i r monthly, seasonal and geographical va r ia t ions . The actual number of t o r r i d days, accumulated over the 8-year period 1957-1964, are tabulated for each of the months of the growing season at each of the three s tat ions. (Table XX) Table XX - Accumulated Frequencies of Torr id Days per Month During the Growing Seasons, 1957 - 1964. Stat ion A p r i l May June July Aug. Sep. Season Lytton - 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 tat ion i n the Inter ior i s again emphasised, but the i n te re s t ing fact 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 va l ley (213), that i s approximately 28 days per season at Princeton against 27 per season at Penticton. By comparison, Lytton averages % days per season. However, the year to year va r i a t i on i n the frequency of t o r r i d days at the i nd i v i dua l s tat ions i s so great as to make the statement for the seasonal averages fo r each s tat ion v i r t u a l l y meaningless. Lytton had a range from 20 to 57 days per season; Penticton 9 to 43 and Princeton 6 to 44. This va r i a t i on resulted from the fac t that, while during the e a r l i e r months, t o r r i d days occurred as s ingle events, by f a r the larger number occurred i n associat ion with 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 spe l l s tended to be concentrated into a few seasons, other seasons only exper-ienc ing short spe 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 stat ions. An analysis of these t o r r i d spe l l frequencies shows that, as wi th t o r r i d days, t o r r i d spe l l s are most frequent at Lytton, (Table XXI). They also tend to be longer at t h i s s ta t ion - 2.3 days over the season on average against 1.8 days and 1.7 days at Penticton and Princeton respect ive ly . Thus, although Princeton experienced more t o r r i d days per growing season than Penticton, the l a t t e r s tat ion tended to have the greater frequency and the greater proportion of longer s pe l l s , e spec ia l l y during Ju l y and August. At a l l s tat ions , t o r r i d spe l l s are more frequent and l a s t longer during the month of Ju ly , which i s i n keeping with the high incidence of ant icyc lon ic weather during th i s period of the growing season. In f ac t , Lytton experienced more than ha l f of i t s t o r r i d days i n July during spe l l s l a s t i n g fo 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 cooler springs on the plateau. 63. Table XXI - Duration of Torr id Days at Selected Stations, (1957 - 1964) Duration of Torr id Spel l s (Days) Tota l No. Average of spe l l s Duration  Stat ion 1 2 3 4 5 6 7 8 9  Lytton May 9 3 2 14 1.5 June 14 10 5 3 1 1 - - - 34 1.9 July 10 6 4 5 3 3 2 2 1 36 3.5 August 10 5 2 3 - 1 - - - 21 2.1 September 5 10 1 1 17 1.9 Season 122 2.31 Penticton May 6 2 8 1.2 June 16 7 4 1 - - - - - 28 1.6 July- 20 11 9 4 1 1 1 47 2.2 August 15 10 6 1 32 1.4 September 3 1 4 1.1 Season 119 Princeton May 5 2 7 1.3 June 6 1 1 16 1.7 Ju ly 25 14 11 2 - 1 - - - 54 2.0 August 20 16 2 1 _ - - _ - 39 1.6 September 9 2 11 1.2 1.79 Season 127 1.73 6k. Summary The analys is of temperature and humidity frequency patterns at selected points with in the region tends to emphasize the area l differences i n crop water requirements suggested from an; analysis of p rec ip i t a t i on patterns. The d r i e r areas are generally warmer and less humid than the moister areas and experience more frequent and longer t o r r i d spe 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 ie r areas than the study of p rec ip i t a t i on p r obab i l i t i e s alone would suggest. However, th i s s i t ua t i on i s not en t i r e l y true throughout the area, since the tempering ef fects of the Okanagan Lake are re f lec ted 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 tat ions . I t remains to be seen i n the next chapter whether th i s microcl imatic influence s i g n i f i c a n t l y a f fec t s crop water requ i re-ments. 65. CHAPTER 5 THE FREQUENCY AND INTENSITY OF DROUGHT The term "drought" can have several meanings^". In th i s chapter i t i s defined as a s o i l moisture concept, a drought occurring when there i s no longer su f f i c i en t moisture i n the s o i l to sustain vigorous plant growth. Obviously any analysis of drought frequency and i n tens i t y so defined w i l l require some measure of the s o i l moisture content and the var iat ions i n the s o i l moisture content i n both time and place w i th in the region. Although procedures f o r measuring s o i l moisture have improved recent ly and new ones have been made ava i lab le, a l l commonly used techniques have i n -herent shortcomings and require considerable c a l i b r a t i on and r ep l i c a t i on to provide representative s o i l moisture data. Furthermore, since the d i r ec t measurements of s o i l moisture wi th in the area only provide point readings, they do not integrate 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 rec t s o i l moisture measurements, various methods have been developed f o r ca lcu lat ing t h i s water loss from meteorological data. Most of these techniques make use of the w e l l -known concept of potent ia l evapotranspiration (PE) as an indicator of the maximum loss of water from a s o i l (a combination of both evaporation and transpi rat ion) 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 so le ly by meteorological factors , 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. Prof. Paper'372!A (1962;. Thornthwaite, l oc . c i t . 66. Review of Literature Early workers based their calculations of PE on a few selected 3 climatic elements. Hedke suggested a method from a study of available heat expressed in degree days, the base temperature depending upon the minimum 4 growing temperature of each crop. Lowry and Johnston undertook a broader study which indicated a linear relationship between consumptive use and o 5 accumulated maximum temperatures above 32 P. Blaney and Criddle expressed monthly PE as proportional to the product of the mean monthly temperature and the monthly percentage of daylight hours in the year. The proportionality constant took different values for different crop types. Also using mean monthly temperatures, Thornthwaite^ developed his formula which included a correction factor for latitude. These methods that use mean monthly tempera-7 tures have been subjected to some criticism since the irregular lag of air temperature behind solar radiation 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 transfer of water vapour into the atmosphere. However, he simplified his technique so that PE could be calculated from commonly recorded meteorological observations - air temperature, relative 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 of water for agriculture", Amer. Soc. C i v i l Eng., Vol. 107 (1942), 1243-1302. ^ Blaney and Criddle, loc. c i t . 6 ' Thornthwaite, loc. c i t . 7 W.R. van V/ijk and D.A. de Vries, "Evapotranspiration", Neth. Journ. Agric. Science, Vol. 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 result of pract ical experi-ments that Penman's method provides the most accurate estimation of crop Q water requirements on a monthly basis . Since this method also combines the effects of the climatic elements already analysed in previous chapters, i t 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 a l l 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 a l l stations as were the other frequency tables. The minimum period of continuous record thought necessary to produce results 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 probabil i t ies of monthly PE (Table XXII) were tabulated in identical manner as those for the maximum temperature occurrences. As expected from the analysis of temperature and humidity frequencies, PE rates 8 W.O. Pru i t t , "Relation of consumptive use for water to climate", Trans. Amer. Soc. Agric. Eng., Vo l . 3 (i960), 9-17. W.C. Munsen, "Method for estimating consumptive use of water for agriculture", Amer. Soc. C i v i l Eng. , Vol . 127 0-962), 200-212. K. Smith,"A long-term assessment of the Penman and Thornthwaite potential evapotranspiration formulae", Journ. Hydrol . , 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. Criddle , "Methods for computing consumptive use of water", Proc. Amer. Soc. C i v i l Eng. ( irr igat ion and Drainage), V o l . 84 (1958}, 1-27 68. are highest at Lytton and Kamloops. However, values are relatively high at Hope during June, July and August which, coupled with i t s notable summer mini-mum i n r a i n f a l l , would suggest that s o i l moisture conditions at this station may be limiting i n most years by the end of July. The table also indicates that PE rates at Penticton are definitely greater than rates at Princeton, verifying earlier r e s u l t s * 0 that a i r temperature is a more important element affecting water loss than the relative humidity. However, the differences are generally less than PE rates estimated from Thomthwaite's formula, but not reported here. The Soil Moisture Budget The components necessary for the computation of the s o i l moisture budget have now been analysed. This budget for cropped soils under irr 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 irrigation. The bookkeeping procedure for estimating s o i l moisture and for scheduling the time of irrigation 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 in 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 definition, they w i l l lose water at PE rates. It is not 12 easy to define exactly what is meant by adequate s o i l moisture. Penman *° Wilcox, loc. c i t . ** O.W. Thomthwaite and J.R. Mather, The Water Budget and i t s Use  in Irrigation, U.S. Dept. of Agriculture Yearbook (Washington, D.C., 1955), 3 -358. c.H.M. van Bavel, "A drought criterion and i t s application in evaluating drought incidence and hazard", Agron. Journ. sVol. 45 (1953), 167-172 12 H.L. Penman, Vegetation and Hydrology, Tech. Comm. No. 53 (Harpenden, England: Commonwealth Agricultural Bureau, 1963). 69. Table XXII - Relat ive Frequencies of Monthly PE (inches) at Selected Stations. HOPE - Period of Record 1945-1964 P.E. (Inches) A p r i l May June Ju ly August Sept ember 1.0 - 1.5 1.5 - 2.0 8.33 4.16 2.0 - 2.5 33.30 20.83 2.5 - 3.0 72.00 4.16 4.00 58.33 3.0 - 3.5 96.00 16.67 4.00 12.00 87-50 3.5 - 4.0 37.50 28.00 20.00 95.83 4.0 - 4.5 62.50 44.00 12.50 36.00 4.5 - 5.0 83.33 72.00 25.00 60.00 5.0 - 5-5 95-83 84.00 41.66 80.00 5.5 - 6.0 88.00 62.50 92.00 6.0 - 6.5 96.00 75.00 96.00 6.5 - 7.0 83.33 7.0 - 7.5 91.66 7.5 - 8.0 95.83 8.0 - 8.5 8.5 - 9.0 LYTTON - Period of Record 1946-1964 P.E. (Inches) A p r i l May June Ju ly August September 1.0 - 1-5 1.5 - 2.0 2.0 - 2 . 5 2.5 - 3 . 0 4.76 3.0 - 3.5 20.00 23.81 3.5 - 4.0 50.00 61.90 4.0 - 4.5 70.00 90.47 4.5 - 5-0 95.00 8.30 4.75 10.00 95.23 5.0 - 5-5 23.80 9.52 25.00 5.5 - 6.0 47.62 14.29 40.00 6.0 - 6.5 80.95 38.10 10.00 65.00 6.5 - 7.0 90.48 57.11 30.00 75.00 7.0 - 7.5 71.42 35.00 95.00 7.5 - 8.0 76.19 75-00 8.0 - 8.5 90.47 80.00 8.5 - 9.0 95-24 95.00 The p robab i l i t i e s are tabulated i n percentages and represent the empir ical p robab i l i t i e s of obtaining PE of the stated amount or l e s s . 70. Table XXII - Continued PENTICTON - Period of Record 1946-1964 P.E. (inches) A p r i l May June August 1.0 - 1.5 1.5 - 2.0 2.0 - 2.5 2.5 - 3.0 3.0 - 3.5 3.5 - 4.0 4.0 - 4.5 4.5 - 5.0 5.0 - 5.5 5-5 - 6.0 6.0 - 6.5 6.5 - 7.0 7.0 - 7.5 7.5 - 8.0 8.0 - 8.5 8.5 - 9.0 16.67 45.83 79.17 95-83 17.39 52.17 60.87 91.30 95.65 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) A n r i l May June July August September 1.0 - 1.5 1.5 - 2.0 2.0 - 2.5 23.07 4.00 2.5 - 3.0 61.54 24.00 3.0 - 3.5 92.31 4.00 68.00 3.5 - 4.0 96.15 20.00 4.00 4.00 88.00 4.0 - 4.5 52.00 24.00 16.00 96.00 4.5 - 5.0 84.00 52.00 8.00 48.00 5.0 - 5.5 92.00 80.00 32.00 68.00 5-5 - 6.0 96.00 92.00 60.00 . 92.00 6.0 - 6.5 96.00 72.00 96.00 6.5 - 7.0 92.00 7.0 - 7.5 96.00 7.5 - 8.0 KAMLOOPS - Period of Record 1954-1964 P.E. (Inches) A p r i l May June Ju ly August 1.0 - 1.5 1.5 - 2.0 2.0 - 2.5 2.5 - 3.0 5.88 3.0 - 3.5 11.76 3.5 - 4.0 41.18 4.0 - 4 . 5 76.47 4.5 - 5.0 94.11 11.76 25.00 5.0 - 5.5 29.41 17.65 31.25 5.5 - 6.0 52.94 29-41 12.50 37.50 6.0 - 6.5 82.33 47.06 25.00 81.25 6.5 - 7.0 94.11 79.59 43.75 93-75 7.0 - ?o 88.24 56.25 7.5 - 8.0 94.11 75.00 8.0 - 8.6 93.75 8.5 - 9.0 September 5.88 23.52 35.29 82.33 88.24 94.11 71. i n reviewing extensive literature pertaining to moisture loss under conditions of non-limiting water supply noted that some investigators considered the water supply to be limiting as soon as i t dropped below f i e l d capacity (i.e. the T O amount the s o i l can hold against gravity), while others showed^tKat'^crops can continue to transpire at PE rates almost throughout the range from f i e l d capa-city to permanent wilting point. Moisture available for a plant depends upon both the vertical root distribution of the plant and the porosity of the s o i l within the root zone. Adequate water for a shallow-rooted crop on a sandy s o i l may be very much different from that for a deep-rooted crop on a clay loam s o i l , for the 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 total s o i l water avail-able to the crop. The second assumption i n connection with the use of soil moisture budget i s that PE rates under the above conditions are independent of plant and s o i l factors and are solely a function of the climate. Therefore, fluctuations in PE rates should vary directly with the fluctuations in the climatic elements affecting evapotranspiration. Thus, the required amount of irrigation to maintain maximum crop growth within the area will be the difference between that amount of water available to the crop from s o i l 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 irrigation", Can. Journ. Plant Science, Vol. 44 (1964), 439-445. 72. Table XXIII - Empirical Probabilities of Seasonal Supplemental Irrigation Requirements (Inches) at Selected Stations (assuming no s o i l storage capacity). Hope Lytton Penticton Princeton Kamloops 90 9.3 24.5 18.1 14.8 24.2 75 10.2 27.6 21.1 18.2 27.2 50 11.1 29.2 24.1 19.3 28.9 25 15.1 . 33.6 25.7 20.9 32.0 10 17.9 35.5 30.2 25.1 34.2 The general tendency for water income (rainfall) to decrease in areas where the expenditure (PE) is greatest is emphasized i n Table XXIII. Here are shown the supplemental water requirements cumulated over the entire growing season, as calculated by the s o i l moisture budget method at various probability levels. The risk (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 irrigation water req-uired w i l l exceed 17.9 inches only once i n 10 years, or 10 percent of the time. It i s important to note that the above table does not include s o i l moisture capacities. Once these are known (see results of soil surveys), the 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 irrigation required once a decade would be 9«9 inches. Even i n this dry region few crops require irrigation throughout the growing season, beginning i n Apr i l , thus when estimating the amounts of supplemental irrigation for short season crops such as hay i t would be advantageous to use Table XXIV, which shows the probabilities of monthly supplemental water requirements for crops at various s o i l moisture storage capacities. 73. The fact 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 factors a f f e c t i n g i t vary great ly throughout the region, a range of possible s o i l moisture capacit ies has been 15 used i n th i s tab le . According to Wilcox these capac i t ies cover most of the range represented by the ag r i cu l t u r a l l y productive s o i l s with in the region. However, remembering that PE rates only continue as long as 50 per cent or more of the ava i lab le moisture remains i n the s o i l , and that t h i s table has been calculated assuming-loss at PE rates, the s o i l moisture storage capacit ies indicated i n the table w i l l only equal approximately ha l f of the t o t a l amount of water ava i lable 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 point. For example, the s o i l with a 2 inch s o i l moisture storage capacity w i l l , i n fac t , contain 4 inches of ava i lab le moisture. An analysis of Table XXIV 1 6 indicates that there are considerable spa t i a l var iat ions i n the timing and the amount of supplemental i r r i g a t i o n requirements wi th in the reg ion. Because A p r i l and May are cool months at most i n t e r i o r locations (see Table XVI), and because the summer maximum r a i n f a l l accompanied by periods of coo 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 for the heavy s o i l s at most stat ions apart from Lytton and Kamloops u n t i l Ju l y . At Hope the high frequency of wet spe 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 capacity u n t i l early-June. However, the incidence of prolonged dry spe l l s i n June and Ju ly , as noted i n Chapter 3, allows considerable water d e f i c i t s to be b u i l t up by la te Ju ly i n most s o i l s , with the resu l t that i n order to maintain maximum J.C...,,.Wile ox, " Ind i rect determination .of f i e l d capacity, fo r moisture", S c i e n t i f i c Agr icu l ture, Vo l . 29 (19^9), 563-578. 1 6 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. 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 te 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 ce r ta in l y require 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 th i s t o t a l amount and the various p robab 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 for the appropriate p robab i l -i t y leve l s at Penticton. Although the appropriate f igures were not ava i lab le for Vernon, the combination of a higher incidence of p rec i p i t a t i on 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 imat ic factors reduce the i r r i g a t i o n requirements at Princeton, the only s tat ion studied which represents conditions i n the plateau. Unfortunately, the advantage of smaller i r r i g a t i o n amounts i s of fset 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 ava i lab le water with in 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 iming of the water d e f i c i t to be delayed u n t i l Ju ly and August, al lowing a system of transhumansce to enable ca t t l e to feed on fresh pastures u n t i l the middle of summer. I t was hoped that the empir ical resu l t s expressed i n Table XXIV could be compared with f igures for the actual use of i r r i g a t i o n water i n the region. Unfortunately, detai led information of th i s nature was not ava i lab le 17 Spilsbury and Tisdale, l o c . c i t . 75. for these s tat ions. However, the Water Resources Service i n V i c t o r i a issue water l icences for each i r r i g a t o r i n the province and, although th i s i s usual ly a f i xed amount from year to year (and therefore not v iable f o r comparative purposes), the empir ical resu l t s generally agree with the Water Resource Services estimates. Since such deta i led information i s lack ing, i t i s thought that these empir ical resu 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 region. 76. Table XXIV - Monthly Supplemental I r r i g a t i on Requirements at Selected Stat ions. HOPE (a) (b) (c) (a) (e) 1" S o i l Moisture Storage Capacity n A p r i l May June Ju ly August September 90 _ _ — 2.2 0.8 -75 1.2 2.8 2.1 — 50 0.9 1.6 3.9 2.4 — 25 1.9 2.7 5.0 3.7 0.1 10 0.6 3.9 4.2 6.6 4.3 1.7 2" S o i l Moisture Storage Capacity A p r i l May June Ju ly August September 90 mm *m mm 2.2 0.8 -75 0.2 2.8 2.1 — 50 1.3 3.9 2.4 — 25 0.9 2.7 5.0 3-7 0.1 10 2.9 4.2 6.6 4.3 1.7 4" S o i l Moisture Storage Capacity Ffo A p r i l May June Ju ly August September 90 _ _ — 1.2 0.8 - . 75 2.2 2.1 -50 0.8 3.5 2.4 — 25 1.2 4.8 3.7 0.1 10 3.3 6.2 4.3 1.7 8" S o i l Moisture Storage Capacity ._Pji A p r i l May June July August September 90 - — - - 0.2 -75 _ — — - 1.2 50 - 0.3 2.2 -25 — — — 1.3 3.5 0.1 10 - 5.1 4.0 1.7 12' " S o i l Moisture Storage Capacity A p r i l May June Ju ly August September 77. Table XXIV - Continued LYTTON (a) l w S o i l Moisture Storage Capacity (b) (c) (e) p%_ A p r i l May June July August September 90 1.4 4.2 3.6 5.2 3.3 1.3 75 1.6 4.6 4.8 6.3 4.3 2.1 50 2.3 5.0 5.9 7.0 5.8 2.7 25 2.5 5.8 6.9 7.6 6.1 3.6 10 3.2 6.5 7.7 8.7 6.8 3.8 2" S o i l Moisture Storage Capacity P%_ A p r i l May June July August September 90 0.4 4.2 3.6 5.2 3.3 1.3 75 0.6 4.6 4.8 6.3 4.3 2.1 50 1.3 5.0 5-9 7.0 5.8 2.7 25 1.5 5.8 6.9 7.6 6.1 3.6 10 2.2 6.5 7.7 8.7 6.8 3.8 S o i l Moisture Storage Capacity A p r i l May June Ju ly August September 90 3.2 3.6 5.2 3.3 1.3 75 - 4.1 4.8 6.3 4.3 2.1 50 - 4.4 5.9 7.0 5.8 2.7 25 - 4.9 6.9 7.6 6.1 3.6 10 0.3 6.1 7.7 8.7 6.8 3.8 8" S o i l Moisture Storage Capacity Si A p r i l May June July August Sept ember 90 _ — 3.4 5.2 5-3 1.3 75 - - 4.4 6.3 4.3 2.1 50 - 0.6 5.9 7.0 5.8 2.7 25 - 1.0 6.9 7.6 6.1 3.6 10 — 2.3 7.7 8.7 6.8 3.8 12' • S o i l Moisture Storage Capacity P% A p r i l May June July August September 90 • — 0.4 5.2 3.3 1.3 75 - - 1.8 6.0 4.3 2.1 50 - 2.7 6.9 5.8 . 2.7 25 - - 4.7 7.5 6.1 3.6 10 - - 6.4 8.7 6.8 3.8 78. Table XXIV - Continued PENTICTON (a) 1" S o i l Moisture Storage Capacity (c) (d) (e) p £ A p r i l May June July August September 90 1.8 2.7 4.2 3.4 1.3 75 0.7 3.0 3.2 5.0 4.0 2.3 50 1.6 4.0 4.0 5.4 4.4 2.9 25 2.1 4.2 4.6 5-9 5.5 3.4 10 2.7 5.4 6.2 7.5 6.0 4.1 2 n S o i l Moisture Storage Capacity Si A p r i l May June Ju ly August September 90 - 1.8 2.7 4.2 3.4 1.3 75 3.0 3.2 5.0 4.0 2.3 50 0.6 4.0 4.0 5.4 4.4 2.9 25 1.1 4.2 4.6 5.9 5.5 3.4 10 1.7 5-4 6.2 7.5 6.0 4.1 4" S o i l Moisture Storage Capacity . 5 A p r i l May June Ju ly August September 90 _ _ 1.6 4.. 2 3.4 1.3 75 1.6 3.2 5.0 4.0 2.3 50 2.4 4.0 5.4 4.4 2.9 25 3.1 4.6 5.9 5.3 3.4 10 - 4.4 6.2 7.5 6.0 4.1 8" So i l Moisture Storage Capacity A p r i l May June Ju ly August Septembei 90 _ 3.6 3.4 1.3 75 - - , 0.9 4.6 4.0 2.3 50 - - 2.9 5.2 4.4 2.9 25 - 3.8 5.9 5.3 3.4 10 0.5 6.0 7.5 6.0 4.1 12" S o i l Moisture Storage Capacity A p r i l May June July August Septembe] 90 _ 0.2 3.4 1.3 75 - - - 2.0 4.0 2.3 50 - - 4.2 4.4 2.9 25 - - 0.3 5.1 5.3 3.4 10 - 2.2 6.1 6.0 4.1 79. Table XXIV - Continued PRINCETON (a) 1" S o i l Moisture Storage Capacity (b) (c) (d) (e) P£ A p r i l May June 90 1.2 2.2 75 0.2 1.8 3.1 50 0.7 2.6 3.7 25 1.3 3.7 4.1 10 1.7 4.7 5.0 2" S o i l Moisture Storage Capacity A p r i l May June 90 1.2 2.2 75 - 1.8 3.1 50 2.6 3.7 25 0.3 3.7 4.1 10 0.7 4.7 5.0 4" S o i l Moisture Storage Capacity *L A p r i l May June 90 2.1 75 - 2.4 50 0.9 3.6 25 2.0 4.0 10 3.2 4.7 8" S o i l Moisture Storage Capacity Si A p r i l May June 90 - - — 75 - - . 50 - 1.0 25 - 2.1 10 3.5 12" S o i l Moisture Storage Capacity 2L A p r i l May- June 90 75 50 25 10 Ju ly August September 2.7 2.0 0.6 4.0 3.1 1.4 4.6 3.9 2.1 5-5 4.6 2.5 6.5 5.6 3.0 July August September 2.7 2.0 0.6 4,.0 3.1 1.4 4.6 3.9 2.1 5-5 4.6 2.5 6.5 5.6 3.0 Ju ly August September 2.7 2.0 0.6 4.0 3.1 1.4 4.6 3-9 2.1 5.5 4.6 2.5 6.5. V 5.6 3.0 July August September 2.4 2.0 0.6 3.4 3.1 1.4 4.2 3-9 2.1 5.^ 4.6 2.5 6.2 5-6 3.0 July August September 0.6 0.1 - 3.1 1.3 1.6 3-7 2.1 2.5 4.6 2.5 5.6 5.6 3.0 80« Table XXIV - Continued KAMLOOPS (a) 1" S o i l Moisture Storage Capacity ffo A p r i l May June July August September (b) (c) (d) (e) 90 2.2 4.3 4.0 5.1 3.2 1.4 75 2.5 4.7 4.7 5.2 4.4 2.5 50 2.6 5.1 5.8 5.7 5.0 3.2 25 3.2 6.2 6.4 7.6 5-9 4.0 10 3.8 6.8 6.8 8.1 6.5 4.6 2" S o i l Moisture Storage Capacity H A p r i l May June Ju ly August September 90 1.1 4.3 4.0 5.1 3.2 1.4 75 1.5 4.7 4.7 5.2 4.4 2.5 50 1.6 5.1 5-8 5.7 5.0 3.2 25 2.2 6.2 6.4 7.6 5-9 4.0 10 2.8 6.8 6.8 8.1 6.5 4.6 4" So i l Moisture Storage Capacity \± A p r i l May June Ju ly August September 90 4.3 4.0 5.1 3.2 1.4 75 4.7 4.7 5.2 4.4 2.5 50 4.9 5.8 5.7 5.0 3.2 25 0.3 5.5 6.4 7.6 5-9 4.0 10 0.9 6.5 6.8 8.1 6.5 4.6 8" S o i l Moisture Storage Capacity P$ A p r i l May June July August September 90 0.7 4.0 5.1 3.2 1.4 75 0.9 4.7 5.2 4.4 2.5 50 1.2 5.8 5-7 5.0 3.2 25 1.7 6.4 7.6 5.9 4.0 10 2.5 6.8 8.1 6.5 4.6 12' 1 S o i l Moisture Storage Capacity A p r i l May June July August September 90 0.9 5.1 3.2 1.4 75 - 1.6 5.2 4.4 2.5 50 - 2.6 5.7 5-0 3-2 25 3.5 7.6 5.9 4.0 10 - 4.7 8.1 6.5 4.6 81. CHAPTER 6 SUMMARY AND CONCLUSIONS The temporal and geographical var ia t ions i n the frequency, i n ten s i t y and duration of some of the meteorological phenomena a f f ec t i ng the supply and demand of water by growing crops have been analysed at selected stat ions i n the south-central Inter ior of B r i t i s h Columbia. The analysis 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 ea r l i e r ha l f of the growing season at most stat ions, the month of June experiencing a def in i te maximum. P robab i l i t i e s of wet and dry spe l l s supported th i s f a c t , the highest frequency of wet spel l s occurring i n June, while the lower p robab i l i t i e s of wet days i n Ju ly and August indicated an increase i n the length of dry spe l l s during the second ha l f of the growing season. The re su l t s of the analyses of the two weather elements promoting water loss, 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 pattern. 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 te r which i t increased sharply as these two elements combined i n such a manner that they i n ten s i f i ed evaporation lo s s . This conspiracy was i l l u s t r a t e d when t h e i r jo in t da i l y observations were combined i n a frequency table, both Ju ly and August experiencing the 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 humidit ies) . 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 stat ions, by estimating potent ia l evapotrans-p i r a t i on rates from Penman's empir ical formula and using the s o i l moisture * Evaporative power - the dynamic capacity or power of the surrounding a i r to permit or promote the evaporation of water. 82. budget technique. At a l l s tat ions except Lytton, l i t t l e i r r i g a t i o n was req-uired i n most years u n t i l the beginning of Ju ly, unless the s o i l s had low moisture storage capac i t ie s , but from Ju ly to September the required i r r i g a t i o n amounts were high, a fact that was due both to the increased dryness of the atmosphere and to the previous depletion of the read i l y ava i lab le 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 on scheduling and to the var iat ions of such amounts i n both time and space. For s o i l s of s im i l a r moisture storage capac i t ies , there are considerable va r i a t i on s i n water need from place to place throughout the region, the dry areas of the Thompson Valley and South Okanagan requ i r ing 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 mul t i -var ia te system rather than a mere sum of averaged c l imat ic data. Each ind iv idua l element of the overa l l complex of elements that i s known c o l l e c t i v e l y as the weather var ies independently to f i t i n to a general equi l ibr ium that forms a weather 2 type or natural period, 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 rates can be explained through the va r i a t i on of chosen c l imat i c var iab les , i f such co r re la t i on ana-lyses are conducted only during natural weather periods, rather than calendar periods. For example, Drinkwater and Jones noted a s i g n i f i c an t l y better co r re l a t i on between maximum da i ly temperature, so lar rad ia t ion and the dura-t i on of sunshine with atmometer and lysimeter evaporation when the analys is was only conducted during dry periods than when the same analysis wae W.O. Drinkwater and B.E. Jones, "Relat ion of potent ia l evapo-t ransp i rat ion to environment and kind of p l an t " , Trans. Amer. Geoph. Union, Vo l . 38 (1957), 524-528. 83. conducted over a 7-day period. I t would appear that the various meteorological elements that af fect evaporation adjust themselves to produce a pa r t i cu la r evaporation rate, and that a change i n one of these elements i s not accompanied by an immediate corresponding change i n evaporation rates , but rather a r e -adjustment of the other re lated var iables and the subsequent adoption of a new energy balance, that i n turn induces a d i f f e ren t rate of evaporation. Obviously the type of data recorded at the meteorological stat ions i s so general that i t obscures such deta i led f luc tuat ions . However, i t i s thought that the data are su itable to produce re su l t s i n keeping with the scale 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 luctuat ions i n the energy balance on the rates of evaporation, however, and have suggested that more detai led c l ima-to l og i ca l invest igations should be made to quantify t h e i r e f fec t . Such information most cer ta in 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 reservo i r capacit ies and i r r i g a t i o n layout. Undoubt-edly future growth i n the ag r i cu l t u ra l economy w i l l be c lo se l y re lated 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, either by pumping from the main r i v e r s or through large scale upland water d ivers ion. Consequently more e f f i c i en t use of such water w i l l al low a greater proportion of the po ten t i a l l y cu l t i va tab le land to be u t i l i z e d fo r p ro f i tab le agr i cu l tu re . Furthermore, the increased de t a i l of the estimates would allow the possible maximum da i l y rates of water loss to be ascertained. These would be invaluable to the i r r i g a t o r who wishes to know how quickly he must complete one cycle, 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 his cycle before h i s crops begin to Wilcox and Korven, l oc . c i t . 84. suf fer from water deficiency'. U n t i l such studies are carr ied out, the knowledge of the physical processes of the atmosphere a f fec t i ng the demand of water by plants w i l l be too incomplete to enable an evaluation of evaporation rates on theore t i ca l considerations alone. 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"Method for estimating consumptive use of water for agriculture", Amer. Soc. C i v i l Eng., Vol. 127 (1962), 200-212. Pelton, W.L. "Evaporation from atmometers and pans", Can. Journ. Plant  Science, Vol. 44 (1964), 397-404. Penman, H.L. "Natural evaporation from open water, base s o i l and grass", Proc. Royal Soc. (London), Sect. A., Vol. 193 (1948), 120-145. Penman, H.L. "Estimating evaporation", Trans. Amer. Geoph. Union, Vol. 37 (1956), 43-50. Pincock, G.L. "Correlations of weather conditions during the summer in British Columbia with the height of the 500 mb. surface", Amer. Met.  Soc. Vol. 28 (1947), 423-424.. Pruitt, W.O. "Relation of consumptive use of water to climate", Trans. Amer. Soc. A g r i c Eng., Vol. 3 (i960), 9-17. Robertson, G.W., and Holmes, R.M. "Estimating irrigation water requirements from meteorological data", Can. Dept. of A g r i c , Exp. Farms Service, Publ. 1054 (Ottawa, 1956). Robertson, G.W. "Evaporation measurements at research branch stations", Can. • Dept. of A g r i c , Research Branch, Publ. 1210 (Ottawa, 1964). Sanderson, M. "An experiment to measure potential evapotranspiration", Can. Journ. Res., Sect. C , Vol. 26 (1948), 445-454. Smith, K. "A long-period assessment of the Penman and Thornthwaite potential evapotranspiration formulae", Journ. Hydro1., Vol. 2 (1964), 277-290. Spilsbury, R.H., and Tisdale, E.W. "Soil plant relationships and vertical zonation in British Columbia", Sci. A g r i c . Vol. 24 (1944), 395-435. Tanner, C.B., and Pelton, W.L. "Potential evapotranspiration estimates by the approximate energy method of Penman", Journ. Geoph. Res., Vol. 65 (i960), 3391-3413. Tanner, C.B. "Energy balance approach to evapotranspiration from crops", Proc Soil Science Soc. Amer., Vol. 24 (i960), 1-9. Thornthwaite, C.W. "An approach toward a rational classification of climate", Geog. Review, Vol. 38 (1946), 55-94. Veihmeyer, F.J., and Hendrickson, A.H. 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Penman, H. L. Vegetation and Hydrology. Tech. Comm. No. 53, Commonwealth Agricultural Bureau, England, 1963. Quartermaster Research and Engineering Centre. Winter Weather Type Frequencies  in the Northern Great Plains. U.S. Army Tech. Report, EP-64. Natick, Mass., 1957. Rheumer, G. and O'Riordan. J. Agro-Climatic Maps of Br i t i s h Columbia. (in preparation). Dept. of Agriculture, Victoria, B. C. 1966. Thomthwaite, C.W. and Mather, J.R. The Water Budget and i t s Use in Irrigation. 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 Inst, of Technology, No. 8, Centerton, New Jersey, 1955• U.S. Navy Electronics Laboratory. Water Loss Investigationst a Review of  Evaporation Theory and Development of Instrumentation. U.S. Navy Electronics Laboratory Report No. 159, pp. 71 > 1950. U.S. Geological Survey. Water Loss Invest igat ions: Lake Hefner Studies. U.S.G.S. C i r . 229, 1952. 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 . A r c t i c Met. Research Group, McG i l l Univers i ty, Montrel, 1961. D. Data Sources B r i t i s h Columbia, Department of Agr icu l ture. Climate of B r i t i s h Columbia, V i c t o r i a , B. C. Canada, Department of 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", New Mexico State Engineers Of f i ce , 1924 (unpublished). Kerr, D.P. "Regional Climatology of Southern B r i t i s h Columbia", Unpublished Ph.D. d i s se r ta t ion , Univers i ty of Toronto, 1950. Wilcox, J.C. "Comparative Monthly I r r i ga t i on Requirements i n Southern B r i t i s h Columbia",. S o i l s 5, Summerland, B.C., 1963. (mimeographed). 9 0 . APPENDIX I Cumulated Frequencies of Wet and Dry Spel l s at Selected Stations 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 - 13 10 6 13 - 12 4 21 - 24 5 19 - 26 11 5 12 - 20 21 - 22 - 14 - 11 12 8 10 - 14 - 12 - 13 10 - 14 13 6 11 10 - 11 - 9 5 - 8 14 - 5 - 16 4 - 5 - 13 - 6 15 2 5 7 8 - 8 7 - 10 16 - - 7 7 - 3 2 - 12 17 1 3 8 6 - 4 7 - 6 18 - 4 3 1 - 5 5 - •4 19 - 4 - 10 6 - 5 3 - 6 20 - 2 3 3 - 5 2 - 2 91. APPENDIX II Addit ional Uses of the Markov Chain Model 1. Cumulative d i s t r i bu t i on of wet spe l l s through n i s : 1 - Pw^w and for dry spe l l s i s : where Pw/w = P (wet day / the previous day wet). Pw/d = P (wet day / the previous day dry) . 2. Formulae for computing the lengths of dry and wet spe l l s (n days) at selected cumulative p r o b a b i l i t i e s * . Wet Spel ls Dry Spel ls 98 -1.698? -1.6987 log 10 Pw/w log 10 (1 - Pw/d) 90 -1.0000 -1.0000 log 10 Pw/w log 10 ( l - Pw/d) 50 -0.3010 -0.3010 log 10 Pw/w log 10 ( l - Pw/d) 10 -0.0458 -0.0458 log 10 Pw/w log 10 (1 - Pw/d) 3. P robab i l i t i e s expressed as return periods. The p robab i l i t i e s of dry and wet s pe l l s may also be expressed i n terms of an average recurrence in te rva 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 Spe l l s : T = 1 - Pw/w + Pw/d  Sp w/d ( l - Pw/w)(l - Pw/d) n The p robab i l i t i e s are tabulated i n percentages and represent the empir ica l p robab i l i t y of obtaining the computed length of s pe l l i n days or le s s . 92. Appendix I I - Continued Wet Spe l l s : T = 1 - Pw/w + Pw/d Sp w/d ( l - Pw/w) Pw/wn 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• Addit ional References A. H. Eichmeter and W.D. Baton, " R a i n f a l l p r obab i l i t i e s during the crop season i n lower Southern Michigan", Monthly Wea. Rev.. Vo l . 90 (1962J, 277-281. A.G. Top i l , " P r ec i p i t a t i on p robab i l i t y i n Denver re lated to month of per iod" , Monthly Wea. Rev., Vo l . 91 (1963), 293-297. 

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