A GENERAL OVERVIEW OF HYDROLOGY AND THE ANALYSIS OF RAINFALL DATA Dy Henry H. Smith, Ph.D. Introduction Hydrology can be detined in general terms as the science which deals with the waters of the earth, their distribution on the surtace, underground and the cycle involving evapora- tion, precipitation and flow to the seas. All components of this cycle are of equal importance. The linkages between subsystems in the hydrologic cycle are illustrated in Figure 1 while the hydrologic cycle and asscciated water quality parameters are illustrated in Figure 2. The hydrologic cycle is perhaps the best vehicie to use in a general discussion on hydrology. However, it is erroneous to give the impression that water moves at a constant rate through this cycle. It is instead, an erratic movement, both temporally and spatially. Furthermore, it 1s important to have more than a qualitative understanding of the cycle and knowledge of how to measure quantities of water at various stages in the cycle. It is necessary to be able to deal quantitatively with the iterations between the various fac~ —j- ATMOSPHERE / / f NS A « rey wy OY Wo ra oy en ey we VR & we 2, Q ey Xe, f L linfiltration = _ SURFACE pn) SOIL WATER i WATER SUBSYSTEM SUBSYSTEM a “ *, “Al ace coon Pad aS) Pa Rs "oO, Ta, ND WP 5) os No Oy . a a “oy P — a! OQ, ye Ne”. g Q" “3 RD ‘ ‘ ‘, Pi ef * OQ, Se \ Ne . of rd “aN GROUND SS) WATER N SUBSYSTEM Linkages Between Subsystems in the Hydrologic Cycle Figure l. (From: McWorther and Sunada, 1981) (O861 ‘Saepueg iwoig) Slajyaneieg ARTTeNY Asem pPpaqersdossy pue aTo9AH BDIsoOToOApAY su] *7 sansry 1 - uoIsns0doAz WwDEHS SPOS peajossig ‘eprion, 4s ‘aseunBbuoyw ‘ wos] ‘ @o9 ‘sseupsoy 1ajOM pUNoID JID PY PHOS ‘eobjy ‘iawipes ‘ piuejopg Ja;JOW papuedsns (27) ‘Q ' spioy '%o f ly 10°7OrS ‘sjusinnN ' Gog (JeUDW pasjossiq {1} 19D. FIDpANS DIVIOD “pouspoW AojD ‘ysAG “SeIDinoy4dg (¢) SED LH PO * 20S ° 19 [DteyOW pasrjossig (2) "ay7p UaBO HY JO SApIXG "*N" O05 f09 ‘SH '*Q lsasspg paajossig (1) JOJDM jOIbojosoayaw Fo siaydsouiy ager JsloM punoig a4 07 ¢ \ ) } +” UCHDIOIad UdHDIOUDAR ~—— jyouny go0png UOMOAL EU] ; vorjosuidsuory {933 MOUS *UIDY }. i i “OND YGINe8sd | | (DIJO; paaossiq sossny SOON IDN PNT.) M4 ae MN . 7 tors in order to make assumptions on the intluence of man- made works on the relations. It is necessary to be familiar with methods tor evaluating the frequency of various extermes ot the cycle. The final section of this discussion will examine some of the methods relevant to us. Of the average annual rainfall in the Virgin Islands, (38- 45 inches), it has been estimated that 87% returns directly to the atmosphere as evapotranspiration, 5% goes to groundwa-— ter recharge and 8% occurs as runoff. in Figure 3 the move- ment ot water through the hydrologic cycle for an average year in the Virgin Islands is illustrated. It is indeed a challenge then with our high slopes, cooling ever-present tradewinds and limited tlat areas, to intercept for use a5 needed, the maximum possible amount ot water that can be teasibly withdrawn from each source, Rain Water Harvesting When atmospheric water vapor condenses, hydrometeors are formed. These hydrometeors include damp haze, fog, ice fog, snow, frost, drizzle and rain. For purposes of clarifica- tion, drizzle consists of tiny liquid water droplets, usually with diameters between 0.004 and 0.02 inches, with such siow settling rates that they often appear to float. Drizzle rarely exceeds 0.04 inches/hour. Rain on the other hand consists of liquid water drops mostly larger than 0.2 inches in diameter. Raintall may be measured conveniently by any open recept-— acle with vertical sides. The standard gage of the JU. 5. f ) ioe tr ' I f ‘ b ge qt fr : | . ; F) t + * F ef, ee aera Bag eh } q 4 Ciauds a cu ew . or a. 4 an ad . . MAS arene ‘ \ A 4 * Rain Qo oF: Gn a Ns at “r ( g ey a we KL FE LAND Hischarge and - < Ong fom is a rr 7 ¥ ao wor . ,; Setns OPP Ery ae she Se 1 a ae ait oe ee oe ne ne ii a ee bre Level ee Fras Water iy ice en Ny Aauiter . SOIL fda Uf: Salt Water Wedge —} . o oT eee —- =1 SLA a - 1 oa be acy - * ee - oo - WRAG ? ap? 7 Figure 3. The Virgin Islands Hydrologic Cycle (From: Peebles, 1979) National Weather Service consists of a collector which passes the collected rain into a cylindrical measuring tube which stands in an overflow can. The cross-sectional area of the measuring tube is one-tenth that of the collector. In this way, 9.1 inch of rain fills the tube to a depth of 1.0 inch. This makes it possible to measure rainfall to an accuracy of 0.01 inch with the calibrated measuring stick. Other types of raingages in common use are the tipping bucket, the weighing type, and the float recording gages. These gages are all best suited for particular applications and, for the most part, used where a continuous record is desirable. The preferable network density of rain gages in an area is highly dependent on the use to which the data will be put. The density recommended by the World Meteorological Organiza- tion for small mountainous islands with irregular precipita-~- tion is one station for each 10 square miles. Rain water harvesting has been the traditional source of water in tne Virgin Islands and still is the preterred source of water for most residents. On each of the islands the greatest annual rainfall occurs in the northwest and the least on the southeastern coasts. AS can be seen from Figure 4, which shows average rainfall data for a location in St. Croix, February and March are the driest months and September is the wettest. Almost half of the average annual rainfall occurs between August and November. Generally, rainfall occurs as brief intense showers of less than a few tenths of an inch. ef RAINFALL, IN INCHES 2b.8@2 INCHES ANNUAL, 42.18 20.36 [RHCHES INCHES Figure 4. Mean Monthly Rainfall at Anna's 1920 ~ 1967) Hope, ot. Croix, r (From: Jordan, 1975) oA tht 4 morning Gamer th+ A oh | L P Bi, M3 % 5 4 el eu] I rae | 1 Pcp Key R-F-P i Buy coutth alan 1 Su Pasa ct uz P. AAW rq t- 3 HEAL Pele) Pavel {AAs bUDG iw clu : any CHIE 1400 | ' see! Bohs . rattle Ben 4 BOO ol Fides: uf SCJ boc 14 tA 40 fag 400 Gu BOO SUCKS : Mauty ,. eon i ! sou 600 a8 ¢ FU . 400 eu SUNG Psa S00 fu *, . a 54 GH Cah cy}. LI Tages cn Ea cz EEE - 3th}: digi} Ba aks es i Sats " q . st ad he) Ca v: ire 17th F . a: 3 Kee wn } a 40) 400 ™ E: = 1 tt u ca =" Ho! chia? . Tat . Zt, c ‘, ° e108 -_ : ret “oe i * i i . w fu : \, x 4 we PU Ad he re etal] - ay a aF all 3 : € fy ; : Hi He) = Py i : ‘ . - 1s Bui ies : IG ; a Be x md) ay bell : . Wij { aCe ; = 3 fo vo) | re a f Ms a : on ~ , = sah 44} - | 1b o J a) 3 "4 Pal ar ob: 4 = ro iy . - Pas) aan Lm) : u 4G aut a 4] 30 rs #0 30F 5a5 if ai : ae . 329 O4 ad 4 EC 1r- ZU vue ; Pao t EEE nae I my Figure 35. Nomograph of Rainfall and Runoff from Catchments (From: Cosner, 1972) Methods utilized to determine the amount of rainfall that may be harvested from a purpose built catchment use essentially the same approach as those to determine runoft from other surfaces (Explained further below). Results. ob- tained are often expressed in nomographs (Figure 5) or design curves (Figure 6). Cisterns are required by law in the Virgin Islands and sizing requirements are presented in the table below. Table 1. Cistern Sizing Requirements in the Virgin Islands ¥* Type of Structure Required Cistern $1ize Single story dwelling 10 Multi-story dwelling 15 Churches and warehouses 4.5 Other buildings Exempted * gallons per square foot of roof area In St. Thomas, rainfall harvesting satisfies 20% of the daily potable water demands and in St. Croix and St. Jonn 13% and 75% of the respective demands are satisfied by rain- fall harvesting. | Surface Water During a rainfall event, certain abstractions occur before there is any direct runoff from the ground surface. These initial abstractions include interception storage by the covering vegetation and depression storage due to surface unevenness. A schematic representation of this pro- cess is presented in Figure 7. Because of the mountainous relief and high evaporation rates, surface water in the Virgin Islands is very limited. Streams are for the most | 1050 1000 950 900 850 800 700 REQUIRED CISTERN STORAGE (Gals./Ft. 2 of Roof area) % RELIABILTY Figure 6. Cistern Sizing Curves for Sprat Hole, St. Croix , (From Smith, 1981) Oe ak ewes Pee ta Lor hh ae aa a fh Payee ee a ee as 4 te A a hing! 1 infer - Pore spaces partially . mediate filled with woter q = belt ta) . es _ Capillary fC : “Capillary rise > Ground weoter Lane Figure 8: Subsurface Distribution of Water Johnson Division, UOP Inc., 1982) (From: ~1 6 Table 1. Estimated Yeild of Virgin Islands Aquifers * Aquifer Characteristics Potential Yield Thin sand and gravel bed 10 - 30 Solution cavities 20 — 60 Fractured rock 2~ 5 * gallons per minute Tt is useful to examine the detinition ot several of the terms most commonly used in discussions of groundwater. The porosity of a soil is the proportion of its volume not oc- cupied by solid material. An aquifer is a water saturated geologic unit that will yield water to wells or Springs at a sufficient rate so that the wells or springs can serve as practical sources of water supply. While porosity represents the amount of water an aquifer will hold, it does not indi- cate how much water the porous material will yield. The specific yield of a soil is the quantity of water that a unit volume of the material will give up when drained by gravity, while the corresponding volume retained is its specific reo tention. The capacity of a porous medium for. transmitting water is its permeability. The rate at which water may be withdrawn from an aquifer without depleting the supply to such an extent that withdrawal at this rate is no longer feasible is the safe yieid. In their initial development, welis are tested by pumping under controlled and well monitored conditions to determine the productive capacity of the completed well and to provide data on which the selection of the pumping equip- ment to be used can be based (Refer to Figure 9). The -|7- ij Deoth to static woter we! , Crawdown ~ N \ Pumping \ Pal “ a Drowdows? | ieyer or dynamic water ‘eyel / re Le | aceutee ePFP eb pea Well screen .o = cn a oe a Oe i i a a ee | 1 Pe ee . v . 1 \ . wa r . 7 Te “oe oo. oa pore i L . ata sat ohy7t anos . a oa i a i es ere rt - . pen a - - at r "=. 7 oboe =-_4 0" . mae! re a Batoat . ™ sak ee satya a Fy oy L "=a a . - 7 a ot a wete aytlere : r corey : ute aaa ee rou wate may * ~ Teta an - cate ano? ut . W reales toa tee . eeu, “aor . "oe Poet 1a r eee et tar, a tata ty t a Sie a -. . wee *. i ee Tae atte vate! ae et i ee ee otha re 7 He ; tes - rhe rae re a : fe ae Ls Veena erate ay "Y a cee ye Fe, a " ee a er ee Satyr Ee bowa 7 er cr ar tale tte +, re Cr Tye ; i re ee he te a ee a oe ee grb ’ uy ee Tt tee ae ea tae ay 1 ra I a i a re a i i i ee i i i | i ee "aa . ah ead te . i ee eee ee . a TE a 2, a Ce .. - . rs . F ; ah asl wea -_ oo. re er or cs i a oe on . “ 4 7: . 5 . . ‘i = a'F * . rh 1 Lo r 1 a ee (cai I A | _. Mpervieus stratum 2000 0 LESS —_— Figure 9. Measurements Related to Well Performance and Pumping Tests of Wells and Aquifers (From: Johnson Division, UOP Inc., 1982) ~]18— Observation Production Piezometer | Wel! Weil | | piezometnic 1 _—— surface f Bal a ( _ water ! _table~, v | tei eee tightly pe seated | x STURN RG confining forat ; ‘ S stratum pertoragHons fF aa sealed S ee" OF SCTEENS f S | nie {| RSS - gravel pack confined aquifer Figure 10. Common Facilities for Observing Water Levels in Aquifers (From: McWorther and Sunada, 1981) 1 9- static level of the well is the level at which water stands in the well when no water is being removed from the aquifer. This level is normally expressed as the distance from the ground surface to the water level in the well. The pumping dynamic level is the level at which water stands in the well when pumping iS in progress. When pumping stops, water in a well rises and approaches the static »rter level. At any particular time during this recovery period, the distance at which the water level is found is the residual drawdown. The volume of water per unit of time discharged from a well is the well yield. The yield of a well per unit of drawdown is known as the well's specific capacity. Groundwater levels are commonly monitored by piezometers, observation wells and production wells. These are shown in Figure 10. A piezometer consists of a casing, perforated near the terminal point only, that is installed in such a way that the casing fits tightly against tne geologic formation. The height to which water rises in the piezometer is the water-pressure head at the terminal point of the piezometer. The observation well is a perforated casing simply placed in a bore hole with no attempt to provide a seal in the aquifer. In installing the observation well, care is taken not to penetrate the underlying confined aquifer in order that the observation well properly indicates the position of the water table. The production well may penetrate any confined layers present and indicates an average water-pressure head. —-?Q— Elementary Statistics in Hydrology In hydrology a hydrologic variable is defined to be any variable which measures or defines the magnitude or quantity of some element in the hydrologic cycle, The mean is an estimate of the most likely observed value, the average. It is a measure of central tendency as are the median, mode and the weighted mean, The middle value > a set of observed values arranged in order of magnitude is the median while the mode is the value which occurs most commonly. , The weighted mean is derived based on the association of weighting factors to the observed vaiues. The mean (Xx) is computed as 4 } | . Am = zx /N where N is the number of observations. The standard deviation (S,) 1s a measure of the dispersior of various values about the mean. [It i:. computed as Sy = \2 Cain Ka) /N Since the mean was used in the equation above we would have a biased estimate of the standard deviation. When there are only a few observations or when there is a great variability in the values, the effect of this bias is great. The un- biased standard deviation is preferred and is talculatec as 52 [EO ~?j- Multiplication of the biased estimate by the ratio N / (N - 1) will produce the unbiased standard deviation. The coefficient of variation (C,) is measure of the dis- persion of a variable about the mean expressed in dimension- less units. ft is calculated as It is often desirable in hydrology to determine if there is some change (trend) in the value of observations over a period of time (time series). This may be difficult to observe because commonly there is a high variability and 4a large scale random variation about the mean vaiue in most hydrologic time series. Variations may be seasonal or diur- nal resulting in cyclic components in the long term record. Stationarity in a hydrologic time series occurs when the statistical parameters (mean and variance) do not change with respect to the origin. Nonstationarity occurs when a trend or cyclic component is present. Nonstationarity also results when there is a sudden change in the hydrologic eco-system or in the method of observation or reduction of the data ({nonho- mogeneity or inconsistency). One way to determine trends is by plotting the data on a scatter diagram as well] as the mean of the full time record and observing if there any obvious trends. It a trend is suspected the data should be divided into two or three seg- ments of equal length and the mean for each segment computed. 2? The moving mean is another method of determining trends. The mean is calculated for periods of consecutive data of equal length but with successively different starting points. While periods of different length may be used, in the analy- Sis of precipitation records the five-year moving mean is usually satisfactory in damping out the effects of random variation. Use of the moving mean method to examine 80 years of annual precipitation data for the British Virgin Islands is illustrated in Figure ll. Probability analysis may be used to determine the probab- ility that an event may be equaled Or exceeded in any year. The return period or recurrence interval is used to signify the average number of years within which a given event will be equaled or exceeded. The return period and the exceedence probability are reciprocals. To determine the return period the data is first ranked according to magnitude and assigned . an Order number (Table 3). The plotting position of the data is determined using a chosen plotting position -formula. The one most commonly used is Weibull's n=m/ (n + 1) where nis the number of years of record and m is the rank. The data and the corresponding exceedence probabilities may then be plotted on probability paper (Figure 12). 3 3- Won X iy WSSU Se 4 b Ga =o qd} {3 fo 4 ic: en | &* ry by 0 ay fy Q@ 0 ee ord oq 43 = 4 : G* OD be fs La tm 43 ‘a “4 @ cd us Ri ue Lynd a Ph =F ty BS yet wt Ju bet oy TD Pe = we q) oh (S34 200) IIMS -~2h~ Table 3. Determination of Return Periods and Exceedence Probabilities for the British Virgin Islands YR RALN RET. ORDER PX. 1933 94.26 Gl 1.23 1932 88.52 40.5 2.4/ L931 75,03 2/ 344 1960 41.52 20.25 4.94 19Q9 70.64 lo.2 6.17 1916 609.05 13.5 7,41 1969 67.11 Il .5/ G.64 1936 05,505 IG.13 9.8/7 LO2/ 63.63 9 ii.ll 1952 63.14 10 Sed 12,35 L915 63 O4 1] 7.36 13.59 1942 O2 G2 12 6.75 14.61 1979 62 if 6 23 16 O05 1970 52 O2 14 5 79 lL? 2/7 1956 Og Cris m? © 15 3 di 18 92 - rc ra 19350 one O& 16 0 GO 19 7 rw 1905 59 28 1? fy 706 At oO] L9OL 29 O° iJ A 3 22 22 are 19 & 20 2 “y ad 1949 96 1902 Qf 69 20 & 7 fom 24 69 L951] 56 2d 1 -) O 6 25 91 193¢ 59 ae , on 22 3 = 20 3 Af i? 25 23 3 32 ZO 4] 1937 56 1975 56 Ll 2 & 3 39 29 59 1974 22 41 22 — 3 24 _ -, QO ) O 6 197 23 G2 26 3 i? 32 O05 55 Od Zf 3 33 33 1924 O 1947 23 99 Z i 2 2 OF 34 T9111 23 35 29 2 79 35 ~34 1909 33 GO 30 2 7 3/ » O4 Z 61 38 31 19035 23 S/ 34 a) 1903 53 2 32 he 53 39 223 1934 52 35 2 hy 2 E 40 82 19]s i + 34 2 230 4.2 O2 52 Aa 2 43 1923 5 2 3 4 31 29 19653 32 36 2 0 22 4 4 44 10354 i c " 4 / 2 o 19 45 66 LG44 = re) 3 } 2ei3 Af 95 38 4 {_} O08 L950 3] Oy 39 2,06 LG4s ome OZ iQ 2,03 49 26 ~25— (Table 3 Continued ) ge en, rata — Se ti RAL RET. PER. ur 1 ar. E x . a L922 50.72 & I] 98 50.51 SU 54 42 93 591.81 1904 1919 5G 306 43 & 393.19 1930 49 D2 dy dy B34 35 1943 4% 93 ra a” Cc & 53 2) { 6 46 7 56 82 1935 1985 3% 4] V2 56 14 19/7 O/ AS 69 59 1/ 1962 é7 Q “ 5 AQ 65 60 61 mn 73 1953 A] 71 a) tT tad 62 61 Lola A6 ere a) l 39 62 89 193¢ 46 5 Poa OQ t c 56 64 1 1912 41 > 4 Fae =f ~4 2 23 LG4v dy 1 } 54 2) 66 67 1o2i A, 95 35 47 68 Q3 L946 45 93 56 AS 68 97 45 23 a/ 42 ras 4.72 1950 1945 ad 5% fs 74 43 1955 ty / oh 37 f2 99 LSS 43 26 60 35 7 & 0? Oi 33 75 19 L929 43 25 LO7f é 3 Cf 62 34 76 34 - 1963 i? 0 > L Th 29 fi 7 2 LY10 oh yt &y OG D3 27 74 2.) BO 1920 42 Ll 65 ad 1961 ta DO 23 8] 1923 1 + 67 24 L976 30 i # c OS 1% 84 O03 ia 85 4/7 Lol? 3U w? } 9 1/ 1925 36 rae 16 36 21 1907 ua 26 ai 14 72 3/ f 72 13 WO ofa 1O59% a ” LOS/ — 7 a Jl 90 O9 19S 36 V7 wad 7é O9 91 74 G72 3 ™ Th 50 7 2») co OS 92 a9 4 / 76 ii / 93.406 1o4] 1367 34 2 if i OS 95,24 1964 5 10 i O4 90,15 1925 Ol / C 1.03 97.09 e 9.01 30 OD oe 1.Q1 ee oR Se Lor ERP De ae eS AS MEA 51.41 DEV. 11.81] ee ee ee ess 8 RAINFALL: EAR Fa IL el CY SSS oe Tee Se Sad ata a, ke fale eg ~26 a ee er ere 12.083 iaee © La 66°66 666 3°66 a OE 66 86 4 | l ' . 1 ! - 0 I A so alia toed : 1 . i + f . ES ue. x t . . : Lo | leila alah elle iota i ' ' B-—--4- lend ! : , 0 G th ie en ‘ — “ >.oaoftotft OE I a r -- : ' ee A ! : . _ ; i | : ed : teil : Lo Do. — CH] = . . a tobe ' \ | 1 i recgecerring ied : : ia a ae weed Hid le | L . ' + ' I eo t —_—— 1 a . " trees vim - . 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