American Society of Agricultural Engineers PAPER NO PRAIRIE RAINFALL,CHARACTERISTICS

Transcription

1 - PAPER NO PRAIRIE RAINFALL,CHARACTERISTICS G.E. Dyck an D.M. Gray Research Engineer an Chairman Division of Hyrology University of Saskatchewan Saskatoon, Saskatchewan, Canaa For presentation at the 1979 Summer Meeting of ASAE an CSAE University of Manitoba Winnipeg, Canaa -.. June 24-27, 1979 SUMMARY: The paper provies information on the spatial character of rainfall over small areas on the Canaian Prairies. Curves showing rainfall variance as a function of net- ' work ensity are provie to ai the esign an evaluation of rainfall networks. American Society of Agricultural Engineers Papers presente before this meeting are consiere to be the property of the Societies. In general, the Societies reserve the right of first publication of such papers, in complete form. However, there is no objection to publication, in conense form with creit to this meeting an theauthor. The Socleties are not responsible for statements or opinlons avance in papers or iscussions at this meeting. Papers have not been subjecte to the revlew process by ASAE or CSAE eitorial committees; therefore, are not to be consiere as referee.

2 PRAIRIE RAINFALL CHARACTERISTICS G.E. Dyck an D.M. Gray Hyrological stuies often require reliable estimates of the mean epth an spatial variability of rainfall on a watershe. The accuracy of these estimates epen in part on the number of gauges use to sample a given event an their spatial arrangement. In the absence of absolute measurements of precipitation at a large number of points within a watershe the error associate with estimates of ifferent rainfall characteristics, for example the areal mean rainfall, cannot be evaluate. The paper reports the results of a stuy conucte in the semi ari region of west central Saskatchewan, Canaa in which the stanar error of the mean was use to establish the relative precision with which networks of ifferent gauge ensity measure mean storm rainfall over a Prairie watershe. Data from 180 storms which occurre uring the perio on a 42 square mile "Dense Precipitation Network" were groupe to three mean epth (a) classes: a in; 0.51 in a in an > 1.00 in. The results are presente as a series of envelope curves in which the stanar error of the mean is plotte against gauge ensity. It is shown, as woul be expecte, that the stanar error ecreases exponentially with increasing gauge ensity inepenent of the mean epth of rain over the area although the ecrease is more pronounce with the larger epths. In aition, the ata for the three storm epth classes suggest that network ensities greater than 0.78 gauges/mile woul not necessarily increase the precision of measuring mean areal rainfall. Within the perio of measurement the preominant storm activity was associate with low intensity, small rainfall events which exhibite wie spatial variability. Examples of the spatial istribution of storms having approximately equal means but varying spatial variability are presente. The statistic, the coefficient of variation (CV), was use as a measure of the spatial variation. These values were foun to range in magnitue from 6.52 to 100 percent; the larger values of CV were generally associate with storms exhibiting a low network mean. Approximately 53 percent of the total number of storms (180) that covere the entire network ha CV L 30%. These storms prouce 71.9% of the total rain at a centrally-locate network gauge uring the stuy perio. The results have practical application as they may be use in combination with stanar statistical techniques to assist in the esign an evaluation of raingauge networks on the Canaian Prairies or similar climatic environments. 2. INTRODUCTION Data on the spatial an temporal istribution of rainfall epths fin application in the solution of many problems concerne with hyrologic esign. For example, these ata combine with estimates of intensities an epths an their frequency of occurrence are use to etermine water yiel, surface runoff rates an seiment prouction. In aition these ata are use by meteorologists for many purposes which inclue, the esign an selection of precipitation gauges an the esign an evaluation of precipitation networks. The egree of accuracy of these ata require in the solution of particular problems influence

3 the number an spatial arrangement of gauges in a network an the length of recor (time) require to establish (stable) frequency istributions. Whenever etaile information of rainstorm characteristics are require, the network gauge ensity must be sufficient to provie an "absolute estimate" of the spatial variability of rainfall within esire confience limits. In this paper rainfall ata are presente showing the spatial variability of storm epths associate with Prairie rainfall events. Curves showing the rainfall variances as a function of network ensity are provie to ai the esign an evaluation of rainfall networks for the region. 3. BASIC DATA The ata use in the stuy were obtaine uring the 10-year perio; 1968 through 1977, from a "ense precipitation network" on the IHD Representative Basin - the Ba Lake Watershe - locate approximately 25 miles southwest of Rosetown in west central Saskatchewan, Canaa, Latitue 51 18'N, Longitue 108"W. During the 8-year perio; the "ense" precipitation network consiste of 41 recoring precipitation gauges (32 MSC tipping bucket raingauges an 9 Fischer-Porter precipitation gauges) an 41 MSC stanar gauges place on a one square mile gri. (Note: the MSC stanar gauges were place ajacent to the recoring gauges.) Dyck (1977) evaluate the aequacy of a network for etermining the spatial character of rainfall events on the Prairies base on inter-gauge correlations. He foun, assuming a correlation coefficient (r) equal to or greater than 0.90 between the total epths of rain from iniviual storms measure by the gauges as an acceptable level of association, that the network was aequate for etermining the storm characteristics over the area as all gauges in the network woul be encompasse by at least one iso-correlation line having a value of r = Herschfiel (1965) an Huff an Shipp (1969) in their stuies in the USA concerne with the spacing of raingauges have also use the value of r = 0.90 as a limit of acceptability of a network. Using this criterion Dyck (1977) foun that the "ense precipitation network" on the Ba Lake Watershe, which initially consiste of 41 gauges, coul be reuce to a network of 15 gauges which woul provie acceptable estimates of the spatial character of storm rainfall over the 42 square mile area. In 1976, the "ense precipitation network" on the watershe was reuce to 15 MSC stanar rain gauges an 15 tipping bucket rain gauges locate essentially on a 2-mile square gri an hence, a network ensity of 0.36 gauges/mile2. At stations having both a tipping bucket gauge an a stanar gauge, the reaing from the stanar gauge was use to verify the measurement from the recoring gauge an to ajust its storm total to the stanar catch. 4. TEMPORAL VARIABILITY OF PRAIRIE PRECIPITATION To illustrate the temporal character of precipitation at Ba Lake, the average monthly precipitation epths measure uring the 10-year perio; , at the climatological station are liste in Table 1. These values were obtaine using measurements from a MSC stanar gauge for rain an a Nipher gauge for snow water equivalent. On review of the ata it is evient that: 1. During the perio of measurement, the mean annual precipitation epth was inches. This value compares favourably with the 30-year

4 Table 1. Mean Monthly Precipitation Amounts in inches of Water Recore at the Climatological Station, Ba Lake Watershe; Average Average Precipitation Total Precipitation Coefficient of Month (inches) rain + snow Variation rain snow (inches) % January February March April May June July August September October November December Average Yearly Totals 0.01 Trace mean precipitation of 12 inches for this area reporte by McKay (1970). 2. On the average, 31.6 percent of the total annual precipitation occurre as snow. In the 10-year perio, precipitation uring the 5-months; May through September average 7.98 inches (63.2%). This compares to 8 inches (66.8%); the long term mean reporte by Longley (1972) for this area. 3. The fact that the mean precipitation statistics obtaine in the stuy perio are in general agreement with the long-term mean for the area (items 1 an 2) gives creence to the assumption that the character of the rainfall in the 10-year perio was representative. 4. The precipitation amounts occurring in a particular month vary wiely from year to year. This is evience by the large values of the coefficient of variation (CV); the ratio of the stanar eviation of precipitation epths to the mean epth, expresse as a percentage. 5. It is evient that the major accumulations of snow occur in January an December. Similarly, June an July ten to receive the highest rainfall amounts. 5. SPATIAL CHARACTER OF PRAIRIE RAINFALL Whenever rainfall amounts are measure an recore over fixe perios of time, such as a ay, the ata may inclue the integrate 'contributions of more than one "unique" storm event. In this stuy, in orer to elineate a unique rain event, a storm was efine as a rain perio which was separate from preceing an succeeing rains or measurable rainfall amounts by a perio of six or more hours. Any storm proucing a measurable epth of rain at any network raingauge was inclue in the stuy. A similar efinition of a storm has been use by Huff (1966) an Huff an Shipp (1969) in stuies of rainfall characteristics in Illinois. Partitioning the rainfall ata into storms accoring to

5 this efinition resulte in the elineation of 670 storms occurring over the network uring the 10-year perio; These storms were stratifie into eight rainfall epth classes, base on the value of the maximum rainfall epth recore by any gauge in the network in any given storm. The epths an epth increments use to efine the classes were: 0.01, , , , , , an greater than 2.00 inches. These ata are liste in Table 2. On review of these ata it can be observe that: 1. The maximum epth of precipitation of 429 storms (64.0%) was less than 0.11 inches. 2. Twenty-eight storms or 4.2% of the total number prouce a maximum point rainfall greater than 1.0 inch. 3. Only five storms prouce a maximum point rainfall amount greater than 2.0 inches. Table 2. Number of Storms Falling Within Different Maximum Depth Classes; May-September, Maximum Depth Class (inches) No. of Storms Total 670 The ata in Table 2 inicate that within the perio of recor no intense heavy rainfall activity occurre over the network. Therefore, the iscussion of Prairie rainfall character in this paper is limite to small, low intensity rainfall events. It shoul be recognize however that rains of this character are those most frequently experience in the region. The smaller storms, in most instances storms proucing rainfall epths of less than 0.25 inches (79.3% of the total), will contribute little water by infiltration to the soil moisture reserve nor will they prouce irect runoff. Their importance to surface runoff, if any, woul be as they effect anteceent moisture conitions. Conversely, these events may be important to agricultural prouction by satisfying some of the evapotranspiration emans. As well uring the occurrence of these storms evapotranspiration emans are reuce. Of the 670 storms which occurre on the network only 245 (36.6%) prouce measurable rainfall at all gauges; no storm in which the maximum recore rainfall amount was 0.01 inches at a particular gauge prouce measurable rain over the entire area (see Table 3). By comparing the ata given in Table 2 an Table 3 it can be observe that only those storms which prouce a maximum point precipitation total greater than 1.50 inch resulte in measurable rainfall amounts at all gauges. Approximately 90% of the storms having a maximum point

6 Table 3. Number of Storms Proucing Measurable Rain Over Entire Network; May-September Maximum Depth Class (inches) No. of Storms - 5 Total 245 rainfall between 0.25 an 1.50 inches resulte in rain over the entire network, whereas only 36% of the storms proucing a maximum point rainfall between 0.02 an 0.25 inches resulte in rain over the entire network. It shoul be recognize that ata from a precipitation network whose location is fixe in space monitors only that portion of a storm which passes over it. It is possible that some rainfall events which i not prouce rainfall at all gauge locations were associate with storms (of unefine areal extent) whose eges passe over a portion of the network. The ata (Table 3) suggests however, that the probability that rain will occur over the entire watershe increases, with an increase in point rainfall recore. 5.1 Spatial Distribution of Rainfall The total amount of rainfall occurring uring any given year over a particular area represents the contributions of many iniviual rainfall events, each having varying temporal an spatial characteristics. It is generally assume that rainfall measurements at each gauge in a network represent the temporal variation an mean epth of rainfall over an ajacent area. For esign one must know the relationship between point an areal measurements. The area that a gauge represents is a function of the natural spatial variability of the rain event, its physical extent an its uration. In esigning precipitation networks that will provie etaile information of rain storm characteristics one must initially establish that a given "ense" network will provie acceptable estimates of the spatial variability of rainfall over the network area. Creence for a reuction in gauge ensity of the network may be establishe if it can be shown that the estimate of the "true" spatial character of precipitation as measure by a reuce network is not significantly ifferent from those measure by the "ense" network. That is, one must establish that the network mean an variance, for iniviual storm events as measure by the "ense" network an the "reuce" network are not significantly ifferent. Dyck (1977) foun that the major limiting factor for obtaining an estimate of the "true" spatial character of rain events from "reuce" networks was ifferences in the rainfall epth variance. It shoul be recognize that although the mean epth of rainfall prouce by ifferent storms may be similar, the storms may iffer wiely in spatial

7 character. Figures 1 an 2 show the total epth of rainfall for storm /I179 (June, 1971) an storm #241 (June, 1972) for the ifferent gauges plotte as a percentage of the mean network rainfall. The mean network totals for these storms were 1.33 inches an 1.49 inches respecti~ely. As shown by the figures the spatial istributions in rainfall for these two storms iffer wiely in character. Figure 1 (storm ij179) shows rainfall graients increasing graually in an easterly irection to within approximately two miles of the eastern borer of the network. Steep rainfall graients occur in the southeastern corner; the maximum graient being 0.67 inches per mile. Point measurements over the network range from 66% to 182% of the mean network rainfall. Conversely, Figure 2 (storm ij241) shows a more complex yet relatively uniform spatial istribution in rainfall epths in which the rainfall graients exhibit little visible irectional tenency. The maximum rainfall graient was 0.47 inches per mile an occurre in the north-western corner of the network. The range in point rainfall amounts for this storm was consierably less than for storm /!I79 (Figure I), ranging from 80% to 129% of the mean network rainfall. Similarly the coefficients of variation (CV) for the two storms were 26.7% an 11.4% respectively. A commonly-use measure of the spatial variability of precipitaion is the statistic, the coefficient of variation (Longley, 1952; Kenall et al., 1956). Values of the coefficient of variation (CV) were calculate for 180 storms that prouce measurable rainfall amounts at all gauges in the network uring the 7- year perio; These values, groupe accoring to mean storm rainfall epth classes are liste in Table 4. It is evient from these ata by the wie range of values of CV that storms falling within any particular mean storm epth class exhibit wie variations in their spatial variability of rainfall. In other wors, the spatial character of these low intensity, small rainfall amounts are highly variable..however, the ata also inicate a tren for the spatial variability to ecrease as the mean network rainfall increases; all but one storm in which the mean rainfall epth was greater than 1.00 inch ha values of CV 5 30%. In total, 96 storms ha values of CV 5 30%. Table 4. Spatial Variability of Rainfall, Ba Lake Watershe; Mean Storm Rainfall (in) < >2.00 Number of Rain Storm Events Having Specifie Variability Coefficient of Variation (%) >

8 LEGEND Raingauge SCALE = I mile a Figure 1. Percent of Mean Network Rainfall (5 = 1.33 in). Storm 8179 (June, 1971), Ba Lake Watershe.

9 LEGEND Raingauge SCALE = I mile Figure 2. Percent of Mean Network Rainfall (i = 1.49 in). Storm /I241 (June, 1972), Ba Lake Watershe.

10 The proportionate amount of monthly rainfall totals prouce by two storm groups covering the entire network; those with values of CV 30% an those with values of CV > 30%, are liste in Table 5. These ata suggest that the longterm average contributions by storms having CV values 30% an > 30% to the total catch varies monthly. For May, June an July over 70% of the monthly total is prouce from storms having CV 5 30%, whereas in August or September these storms only contribute between 54% to 61% of the monthly totals. On the average 71.9% of the total seasonal (May-September) rainfall can be associate with storms having CV L 30%. The long term contribution by storms having CV 1 30% uring the months May, June, July an September is relatively constant, varying from 15.0% to 24.6%. However, uring the month of August, 43.1% of the total rainfall can be associate with storms having CV > 30%. Table 5. Percent of Total Monthly Rainfall (May-September) Occurring From Storms Having Specifie Variability (Coefficient of Variation) at Climatological Station, Ba Lake Watershe, Months ALL Storms Coefficient of Variation % (inches) 130% >30% May June July August September Total (in) Average (%I MEASUREMENT PRECISION OF RAINGAUGE NETWORKS In effort to establish the relative precision with which networks of ifferent gauge ensity measure mean storm rainfall over the 42 square mile Ba Lake Watershe "Dense Precipitation Network" area values of the stanar error of the mean, Sa, calculate using measurements obtaine from iniviual storms an networks having ifferent gauge ensities were compare. The stanar error of the mean is given by the expression, where S- = stanar error of the mean, S = stanar eviation of the precipitation epth of an iniviual storm, an n = number of gauges. The ata use in the analysis were from 180 storms which prouce measurable rainfall at all gauges in the network. Of these 180 storms, 118 occurre uring the 5-year perio; , uring which the network consiste of 32 tipping bucket gauges. The remaining 62 storms occurre in 1976 an 1977 when the 11 ense" network ha been reuce to 15 gauges. Storms were separate to fall

11 into three groups base on the magnitue of the network mean rainfall; L 0.50 in, in, a,n > 1.00 in; the number in each group were 156, 15 an 9 respectively. The stanar errors of the mean were calculate for each storm assuming 14 networks of ifferent gauge ensity. These networks inclue: 32, 28, 24, 18, 16, 15, 14, 12, 10, 8, 6, 4 an 2 gauges which correspon to network gauge ensities (gauges/mile2) of 0.76, 0.67, 0.57, 0.48, 0.43, 0.38, 0.36, 0.33, 0.29, 0.24, 0.19, 0.14, 0.10 an 0.05 respectively. It shoul be note that for network ensities (gauges/mile2) greater than 0.38, the values of S-, were obtaine using only storm ata collecte uring the 5-year perio; In subsequent iscussions the network containing 32 gauges, all of which are Tipping Bucket Rain Gauges is referre to as the "ense" network. The gauges inclue in each of the 13 "reuce" networks were selecte such that their spatial arrangement provie approximately a uniform gri over the area. To inicate the relative precision with which the networks of ifferent gauge ensity measure the mean network rainfall, the maximum value of S- for each of the 14 networks, from the three storm epth groups, were plotte as a function of gauge ensity (see Figures 3, 4 an 5). In each figure, two curves have been rawn, one to envelope the maximum values of S-, an, the other enveloping the values of the mean value of S- It is evient from the figures that the ' ' relationship between S- an gauge ensity is curvilinear with S- increasing with a ecrease in gauge ensity. Also it is reaily apparent that the "ense" network provies the best precision in measuring mean network rainfall. The ata in the figures inicate: (a) the maximum value of S- for a particular storm - having a network mean L 0.50 inches on the "ense" network was 0.04 inches with Sa = 0.01 inches, (b) the maximum value of Sa for a particular storm having a network mean in the range inches was 0.06 inches with = 0.03 inches an (c) the maximum value of S- for a particular storm havlng a network - mean > 1.00 inches was 0.07 inches with S- = 0.05 inches. As the "envelope" curves for the three epth groups inicate that S- approaches a constant value for gauge ensities greater than 0.76 gauges/nile2, (the gauge ensity of the "ense" network), suggests that an increase in ensity beyon this point will not greatly increase the precision in measurement of the mean network rainfall. It shoul be recognize that for a particular gauge ensity, the ifferences in the magnitue of the maximum values of S- an S- for storms in the three network epth classes represent ifferences in tfle magnitue of the stanar eviation. The magnitue of the stanar eviation for a given gauge ensity is affecte by such factors as the gauge configuration (location an istribution), the natural spatial variability of the rain event over an area, microtopographic effects, the "catch" characteristics of the gauges an others. As the "envelope" curves shown in the figures inicate the precision with which networks of ifferent gauge ensities measure the mean network rainfall they may be use as general guies in esign or evaluation of precipitation networks in the semi-ari regions of the Canaian Prairies. Base on the experience gaine in this stuy it is postulate that the "envelope" curves for storms having network means inches are well efine to reflect the population statistics for this epth class because they were evelope from a large sample (n = 156). The analysis of the rainfall ata collecte on the network have shown that the rain-proucing storms measure since 1968 can not be associate with either severe convective activity or with major frontal systems (Dyck, 1977). Thus, the network requirements necessary to evaluate the spatial character of rainfall from these intense vigorous systems remains unknown.

12 STORM CLASS: 7 s 0.50in. n = 156 GAUGE DENSITY (cjauge/mile2) - ENVE LOPE CURVE ENVE LOPE CURVE DENSE NETWORK (MAX. Figure 3. Range of Values for Stanar Error of Mean; sz, for Networks of Varying Gauge Density. Storm Class p L 0.50 in. I STORM CLASS : 0.51 in. s s 1.00in. CURVE CURVE (MAX. S - (s) Figure 4. Range of Values for Stanar Error of Mean; ~a, for Networks of Varying Gauge Density. Storm Class 0.51 in ( p 1.00 in.

13 STORM CLASS: az-i.ooin. n = 9 ENVELOPE CURVE (MAX. ~ a ) ENVELOPE - CURVE (~a) 0-1 I I I I I , GAUGE DENSITY (gouge/rnile2) DENSE NETWORK Figure 5. Range of Values for Stanar Error of Mean; sz, for Networks of Varying Gauge Density. Storm Class 2 l. 00 in.

14 7. SUMMARY The paper presents the results of a stuy concerne with the spatial character of rainfall on the Canaian Prairies, which was conucte uring the ten year perio; (inclusive) on the Ba Lake Watershe ense precipitation network; Latitue 51 18'N, Longtiue 108'~. Design curves are presente showing the variation in rainfall as a function of network ensity for storms groupe to three mean epth (a) classes: a 0.50 in; 0.51 in 5 a in an a > 1.00 in. It is shown that the stanar error ecreases exponentially with increasing gauge ensity inepenent of the mean epth of rain although the ecrease is more pronounce with the larger epths. Examples of the spatial istribution of storms having approximately the same mean rainfall but varying spatial variability are presente. The statistic, the coefficient of variation (CV), was use as a measure of the spatial variation; values range in magnitiue from 6.52 to 100 percent. In general it was foun that the lower values of CV were associate with those storms proucing the larger mean epth. 8. ACKNOWLEDGEMENTS The authors gratefully ackaowlege the loan of equipment an financial assistance given to this stuy by: Water Resources Support Program, Water Research Incentives Office, IWD~DOE, Ottawa, Ontario an Hyrometeorological Research Division, Atmospheric Environment Service, Environment Canaa, Downsview, Ontario. 9. REFERENCES Dyck, G.E., Areal precipitation estimates from point measurements. Unpublishe M.Sc. Thesis, University of Saskatchewan, Saskatoon, 174p. Herschfiel, D.M., On the spacing of raingages. IASH & WMO Symposium. on Design of Hyrometeorological Networks. Quebec City. 7p. Huff, F.A., The effect of natural rainfall variability in verification of rain moification experiments. Water Resources Research, Vo1.2, No.4, pp Huff, F.A. an W.L. Shipp, Spatial correlation of storm, monthly an seasonal precipitation. Journal of Applie Meteorology, Vo1.8, pp Kenall, R.G. an M.K. Thomas, Some characteristics of precipitation in the Canaian Prairies. Separata De Miscelanea Geofisica Luana. Longley, R.W., Measures of the variability of precipitation. Monthly Weather Review. 80:7: , July. Longley, Richmon W., The climate of the Prairie Provinces. Climatological Stuies No.13, Environment Canaa, Atmospheric Environment, Toronto, UDC: ( ). McKay, G.A., Precipitation. Section 11. Hanbook on the Principles of Hyrology. D.M. Gray, Eitor-in-chief. Secretariat CNC/IHD, Place Vincent Massey, Hull, P.Q. pp