MAY 1986 MARK L. MORRISSEY 931A Statistical Analysis of the Relationships among Rainfall, Outgoing Longwave Radiation and the Moisture Budget during January-March 1979' MARK L. MORRISSEY Department of Meteorology, University of HawaiL Honolulu, HI 96822 (Manuscript received 27 July 1985, in final form 5 November 1985) An analysis of the statistical relationships among observed daily rainfall, oulgoing longwave radiation (OLR)and the moisture budget (precipitation minus evaporation or P - E), obtained from three independent datasources during January through March, 1979, indicates that on a daily basis P - E and OLR correlate significantlybetter with each other than they do with observed rainfall over open-ocean regions where the spatial density ofrainfall observing stations is low. A spatial correlation over the Pacific Ocean indicates that P - E and OLRcorrelate well in most--but not all--highly convective regions where both variables have moderate to highvariances, and are uncorrelated in dry regions. Low correlations are obtained in regions of shallow convectionand in areas of weak moisture convergence with firms at upper levels. It is demonstrated that OLR, P - E, or observed rainfall alone cannot properly define the areal extent oflarge scale convective activity. A technique is developed in which P - E is used in conjunction with OLR tobetter establish the intensity and spatial bounds of large-scale convective activity.1. Introduction Researchers often use rainfall, outgoing longwaveradiation (OLR) and the moisture budget (calculatedprecipitation minus evaporation or P- E) as indicatorsof convection, particularly for the investigation oftemporal and spatial characteristics of large-scale (>500km) deep convective activity (hereafter referred to asLSCA) (Murakami, 1980; Yanai et al., 1973; Zangvil,1975). In order to properly define the time and spacescales of LSCA using observed rainfall, OLR, or P- E, it is nceess~ry to understand the physical relationships among these variables and to identify theirassociations with LSCA. Recently, several researchers compared data ohtained from satellite observations to observed openocean rainfall. Meisner and Arkin (1984) constructeda precipitation index which uses satellite infrared imagery to obtain rainfall estimates which are then correlated with observed station rainfall. Kilonsky andRamage (1976) developed a technique which relatesvisual satellite imagery to observed rainfall. Studiessuch as these use observed station rainfall as an accuratemeasure of convection, to which other con~cctive vailables are compared. This study will show, however,that open ocean observed rainfall, although a good indicator of localized convection, is not an accuratemeasure of LSCA, especially when considering synoptictime and spaee scales. This question is discussed furtherin section 5. The main objective of the present paper is to examine the physical relationships among rainfall, OLR, * Contribution Number 85-02 of the Dept. of Meteorology, University of Hawaii.and P - E using a detailed statistical analysis of dailydata obtained from three independent data sources overan extensive region of the central Pacific (37.5-N to37.5-S, and 120-E to 120-W). In section 3 a spatial comparison of three-monthtime-mean OLR and P - E is made and in section 4a time-space variance comparison of OLR and P - Eis performed. Due to the sporadic locations of rainfallobservation stations over the Pacific Ocean a spatialcomparison with rainfall was precluded. However, atemporal comparison of all three variables is done insection 5.2. Data and computational procedures This study utilizes daily (0000 GMT) values of u, v,qO, r, T at seven pressure levels (1000, 850, 700, 500,300, 200, 100 mb)for the period 1 January to 31 March1979. These data were extracted from the objectivelyanalyzed FGGE (First GARP Global Experiment) levelIIIb data set prepared by the European Centre for Medium Range Weather Forecasts (ECMWF) at a reducedresolution of 3.75- longitude-latitude intervals over aregion extending from 1200E to 120-W and 37.5-Nto 37.5-S. Twice daily OLR obtained from NOAA polar orbiting satellites are digitized on a 2.5- x 2.5- grid andresolution is reduced to 3.75- x 3.75- longitude-latitude intervals. Daily OLR was obtained by averagingthe twice daily values (0330 LST, 1530 LST). Daily rainfall data are extracted from FGGE IIc surface-based precipitation data sets for various Pacificarea rainfall stations and are time smoothed using ac 1986 American Meteorological Society932 MONTHLY WEATHER REVIEW VOLUME 114three-point weighted moving average in an effort toreduce small deviations in data recording times at eachstation. The horizontal u and v wind components and thegeopotential height (4) in the FGGE data set were thebasic objectively-analyzed fields. Temperature T wasdetermined from the initialization procedure; the initialized temperature is very sensitive to the numericalmodel used at ECMWF (Lubis and Murakami, 1984).A study by Murakami et al. (1984) showed that thenumerical model used to determine the temperaturehas questionable accuracy in certain regions and duringcertain periods and therefore affects the quality of themixing ratio estimates; this is also shown below. FGGE level IIb station moisture data provide thebasis of level IIIb moisture analyses. A simple successiveapproximation scheme (not an optimum interpolationscheme) was used at ECMWF for the analyses of layermean moisture. Since the moisture data in FGGE levelIIb observations are not significantly better than thoseavailable for the FGGE IIa data set, the resulting moisture analysis is biased towards the forecast model usedto provide the first guess. This is especially true for theperiod from December 1978 to April 1979. (A betterdescription of the problems associated with FGGEmoisture analyses is given in FGGE Newsletter No. I,1983). Therefore the FGGE level IIIb moisture analyseswere not well-handled and are of questionable accuracy, especially over data-void regions. The data-sparseareas of concern include the east-central and southeastPacific regions which are almost devoid of stations(FGGE Operations Report, 1980). A rather completeinvestigation of the accuracy of statistics calculatedfrom FGGE data is given by Lorenc and Swinbank(1984). It has also been noted in the literature that theECMWF FGGE moisture computations for the tropicsfor low levels are too dry by about 1-2 gm kg-l (Lambert, 1983). However, as will be shown in sections 3and 4, FGGE level IIIb moisture data appear to beadequate for describing the relative temporal and spatial fluctuations (i.e., comparing positive vs negativeregions and relative strengths of different spatial patterns) of the large scale (>500 km) moisture fields overmost of the tropical Pacific. Therefore the reader shouldkeep in mind the inaccuracies in the moisture data andshould concentrate on the qualitative rather thanquantitative results of this study. In the FGGE level IIIb data set, relative humidity isdetermined from the mean-layer water content andthe initialized temperature. The mixing ratio q is calculated from the temperature T and relative humidityr. The mixing, ratio at a given pressure level used inthe P - E calculations given here is given byq = 0.622r(es/p), (1)lnes = 21.6 - (5410/T),(2)where es and p represent the saturation vapor pressureand the pressure, respectively, at a given pressure level.Equation (2) is derived from the Clausius-Clapeyronequation with the latent heat of vaporization equal to2.500 x 106 J kg-~, the specific gas constant for watervapor of 461.7 J kg-~ and a saturation vapor pressureof6.11 mb at 273.155 K. P - E is calculated here by the following:P-E= -l/g(fe~f Oq/OtdP)- l/g(fl,~f v. qVdP) (A) (B) -1/g(Je~s Oqco/OPdP), (C)where Ps = surface 'pressure, Pry = 300 mb, V is thehorizontal velocity, co the vertical velocity in pressurecoordinates, g the gravitational acceleration (9.8 m s-2)and t time. Surface pressure is calculated from the geopotential height (q6) of 1000 mb using the hydrostaticequation. Due to the availability of q. and V only atdiscrete pressure levels, values of these variables at thesestandard levels (1000, 850, 700, 500 and 300 mb) represented layer-mean estimates (i.e., q at 850 mb represents the layer mean q from 925 to 775 mb). Theintegrals were evaluated using a trapezoidal rule fromPs to Pt~,. Term A represents the rate of change in thestorage of moisture and is important when consideringdaily time scales. Term B denotes the net horizontalmoisture convergence into a column of air, while termC is the net vertical convergence of moisture flux. TermC, which is neglected in the P - E calculation, integrates to zero over open-ocean regions (assuming vertical velocity is zero at the surface level), but could besignificant when considering mountainous terrain. Divergent wind fields for the tropics calculated fromECMWF IIIb u and v data have been reported to besuspect, especially on horizontal scales less than 1500km (Julian, 1984). Lubis and Murakami (1984), however, showed good agreement between the spatial patterns of integrated moisture divergence (using ECMWFIIIb data) and a convective index developed by Murakami (1983) over the Pacific Ocean from 1 December1978 to 3 February 1979. (The convective index incorporates, primarily, infrared (IR) imagery from satellites for its construction, and will be further discussedin section 8.) Julian (1984) compared spatial patternsof the divergent wind (calculated from the velocity potential) to OLR while considering OLR to be an absolute measure of the strength ofconvecfion. This studywill show that OLR is not necessarily an absolute measure of convection and its use must be carefully considered. Due to the difficulty of testing the accuracy ofthe divergent wind, the quality of the final P - E estimate, (a function of wind divergence) will be criticallyexamined in sections 3 and 4.MAY I986 MARK L. MORRISSEY 933 TO help compmensate for small inaccuracies in theFGGE wind data a divergence correction term, basedon the conservation of mass, is applied to the P - Ecalculations and is given byV' V-o,~.t~ = V' V~-u~at~ + ( f V' VdP) / (Ps - P~),where P~ = 100 rob. In addition, P - E is time and space smoothed (seethe Appendix for an explanation of the spatial smoothing function) over all grid points to eliminate unwantedsmall-scale fluctuations (noise) in the FGGE data. To help verify the reliability of the P - E estimates,four-times daily surface observations (0000, 0600, 1200and 1800 GMT, including plotted ship and land stationmodels) are utilized for the January to March, 1979period (hereafter referred to as the study period). Thesurface observations were plotted by National WeatherService personnel based in Honolulu, Hawaii. Surfaceobservations are used in this study to qualitativelyevaluate convective situations over selected areas ofthe Pacific by identifying cloud and precipitation type.Assessments of the convective situation for various regions are compared to those inferred from P - E andOLR values. (Refer to section 3.) Because of the qualitative nature of data extractedfrom the surface observations, the area represented byeach ship or island observing station varied with visibility. For instance, on a clear day a ship weather observer might report trade-wind cumulus with precipitation within sight and thus could be reporting for anarea of approximately 2000 km2 (assuming the observercan see 25 km in all directions). Since we were primarilyinterested in large-scale (>500 km) convective situations, all regions selected for investigation using thesurface observations were required to have, per day, atleast one observation for every 250 000 km2 of the region and the observations within the region have to besomewhat uniformly spatially distributed. (In this paper, exceptions were occasionally made to this criterion,based upon a subjective assessment of the synoptic situation.) This station density is the minimum necessaryfor the surface observations to adequately representthe large-scale convective situation within the selectedregion.3. Outgoing longwave radiation vs P - E: Time-mean relationship Time-mean charts of OLR and P - E for I Januaryto 31 March 1979 are presented in Figs. 1 and 2, respectively. (Note: all figures are for the time period 1January to 31 March 1979, except where indicated.)The following features are noted: 1) A large area of positive P- Eand low OLR (<240W m-2) values (which is the approximate radiationemitted by cold, high-level clouds) extend polewardfrom the equator to roughly 20-S and from 120-Eeastward to approximately 150-W. This area corresponds to a highly convective region associated withthe Southern Hemisphere summer monsoon and thesouthern Pacific Convergence Zone (SPCZ), which extends east and southeast from 170-E to 150-W (Vincent, 1982; Ramage, 1975; Davidson et al., 1984). A survey of the January to March surface observations was conducted for two subset areas of this region:Area A, encompassing an area of suspected strong convection within the monsoon region, extends from theequator to 15-S and from 150- to 170-E. Area B, encompassing another area of suspected strong convection, this time in the SPCZ region, extends from 155 oto 135-W and from 15-S to 30-S. Areas A and B wereselected because of the numerous ship and station observations in each area (>20 observations per day foreach region) and their proximity to actively convectiveregions [positive P - E and low OLR (<240 W m-2)]. During the study period, an average of 47 and 32%of the total observations per day included precipitationin areas A and B, respectively. Greater than half of theobservations reporting precipitation in both areas Aand B indicated heavy showers or thunderstorms. 2) Relatively poor association between OLR and P- E is observed over a region north of 25-N and extending eastward from 120-E to 120-W. Isolatedmoisture convergence and high level cirrus associatedwith midlatitude frontal systems, which travel eastwardthrough this area during January to March, are primarily responsible for this lack of agreement. 3) Low OLR (<240 W m-2) and negative P - Evalues over an area east of Hawaii extending from 140-to 120-W and from 30- to 15-N are the result of frequent large-scale cirrus surges accompanied by relatively dry lower levels associated with large-scale cloudintrusions from the tropics (Anderson and Oliver,1970). For this region (area C), an average of 12% ofthe surface observations per day reported precipitationduring the study period (from an average of 17 totalobservations per day). The precipitation reported wasprimarily light rain and drizzle. The most often reported cloud types were fair weather cumulus withscattered or dense cirrus, occasionally accompanied bymiddle cloud. Thus, the surface observations are in agreement with the assessment from the three-month P - E estimate that this region was dry and not highly convective dur ing the study period. The lack of association of P - E with OLR in thisregion illustrates the major difficulty with OLR whenused as an indicator of the intensity and spatial extentof LSCA. Outgoing longwave radiation cannot accurately distinguish cirrus directly overlying (and produced by) active, deep convection from large areas ofcirrus directly overlying nonconvective conditions. The averaged OLR values (see Fig. 1) in area C and in area B (mentioned in subsection 3a) are similar (be934 MONTHLY WEATHER REVIEW VOLUME 114OLR RVE JRN-MRB 1979INTEfiVRL= 20 W/M2 ]20E ]50E ]8;)s2ao" 1111]~~ 'llll]lHIlllllllllllililllilllhlHllllllHIIItlllfillllllllllt .... 3 TM ~~8' i ION / ~. ~ ~ I~1~ I~ll~n,~-' 105~ ~ ~1~ ~u~ I~bt lsbt 1~o 15FIG. 1. Time-mean chart of OLR from l Januar~ to 31 March, 1979. Shading indicates regions where OLR is less than 240 W m-:.tween 240 and 230 W m-e), but the convective situation is very different. The obtained values of 12 and32% of surface observations reporting precipitation perday for the present region and area B, respectively aresignificantly different at the 99% confidence limit, suggesting very different mean convective conditions inboth regions. This weakness in OLR for accurate evaluation ofconvective activity due to cirrus overlying nonconvecfive conditions will be referred to in this paper as "cirruscontamination" of OLR. 4) Near 10-N, 125-E, weak low-level moistureconvergence and wide spread shallow convection, associated with the low-level northeast monsoon flowthrough this region, are responsible for the positive P- E and high OLR values (>240 W m-2) (Flores andBalagot, 1969). The surface observations indicate primarily continuous light rain and drizzle for this region. 5) A large area of positive P - E values and highOLR (>240 W m-2) extends from 140- to 120-W andfrom 10-N south to 5-S. This region corresponds tothe climatological position of the Central Pacific NearEquatorial Convergence Zone (Ramage et al., 1981). Unfortunately, the convective situation during thestudy period (and thus the P- E values for the region)P-E RVE JRN-MRB 1979INTERVRL= 3 MM/DRYSOS. ~"" _'% ',~u'~ -"~]~;F-~,,,,,,,,,,'-~- ~ -'oT~ ~ .~ ~ , ':~ ~-d ~~ ~ ~ C~L ~ I~~~lll~ ~ ~~ I I~l~llll~ ~111~11~ Ill IIIII~ ~l~l~ I~ I~1~1~ ~ ~ ~~ ~lltl~ ~ I1_~ ~ ~ l~ 5E 30 161~ 12 ~G. 2. Time-mmn chin ofP - E ~m I Janu~ to )1 M~h, 1979. Sha~ng in~mtes r~ons where P - E is ~tcr ~ 0 mm d-L120# 90N SON ION EG 105 ~OS 305 )HMAY 1986 MARK L. MORRISSEY 935cannot be verified due to the scarcity of ship observations in this area; therefore, nothing more will besaid about this region. Thus, it is apparent from Figs. 1 and 2 that overmany regions OLR and P - E alone cannot satisfactorily define the nature and spatial extent of LSCA,and more importantly, it should not be assumed thatOLR is always inversely proportional to LSCA.4. P - E vs OLR: Time-space variance relationships It may ha~e been assumed that an estimate of thequality of P - E could be obtained from the strengthof its correlation with OLR. On the other hand, lowcorrelation values do not necessarily indicate the lowquality of the P - E estimate due to various physicalrelationships between clouds and convection. This wasdiscussed previously and is amplified further as follows. Figure 3 shows daily P - E correlated with dailyOLR at each grid point for January through March.Shaded areas indicate regions where the correlationcoefficient is less than -0.3. (A correlation coefficientof -0.3 is significantly different from a coefficient of0.0 at the 99% confidence limit.) A close examinationof this chart indicates that P - E correlates reasonablywell (< -0.3--that is, a linear relationship is establishedwith OLR) within the Southern Hemisphere summermonsoon region (10--20-S from 135- to 170-E) andthe SPCZ (roughly 25-S from 170-E to 135-W). Thecorrelation is also fairly strong southwest of Hawaiiwhere upper-level troughs occasionally induce low-levelconvergence-generating strong convection (Atkinson,1971). Thus the P - E estimate is apparently sufficientto describe the dally fluctuations in large-scale moistureconvergence at least over actively convective regionswhere the correlation coefficient is less than -0.3. Small positive correlation coefficients centered near25-N, 140-W again correspond to the region of largescale cirrus contamination as described in section 3. In dry, cloudless regions, where there is little precipitation, evaporation is not thought to correlate wellwith large values of OLR. (Outgoing longwave radiation is basically a measure of sea surface temperaturein cloudless oceanic regions.) This is because evaporation at the sea surface is a function of many dailyvarying factors other than sea surface temperature, suchas surface wind speed, moisture and air temperature(Gill, 1982). Thus P - E is not correlated well withOLR in areas such as 150-E, 20-N and 20-N, 170-Ewhich are regions of general subsidence and moisturedivergence (Atkinson, 1971) (hence P - E < 0 mmday-~ and OLR > 240 W m-2) where evaporation accounts for most of the variance in P - E. The spatial distribution of the standard deviationvalues for both OLR and P - E, calculated at eachgrid point for the study period, are shown in Figs. 4and 5, respectively. Comparing these figures with Fig.3, one can observe that in highly convective regionsboth OLR and P - E have large standard deviationsand correlate significantly well. This is illustrated bythe significant correlation (< -0.3) and large standarddeviation values (>32 W m-2 for OLR and >6 mmday-~ for P - E) of both variables along the monsoonregion (the upper-level trough region near Hawaii andthe SPCZ). An exception to this relationship betweenstandard deviation and correlation is discussed as follows. A curious area of low correlation values exist overNew Guinea which is a region that surface observationsOLR,P-E CORRELRTION JRN-HRR 1979:105~o, ~ - v"-/////~ ~ ~ -~ __ ../~'~ ~..~////////g :,o, ~~~ ,0.::,~ ~; ~/~,~/////////////////~ 7~A 7 ~/////~ ~/////~ ~ ~so[ ~o ~s ~. ~e ~o. 3. Spad~ ~s~budon of~e co.elation r ofP - E vs OLR ~c~at~ at eve~~d point. UnJ~ are r x 10. Sha~ng indi~tes re-ons where ~e co~elaQon is lessthan -0.3.936 MONTHLY WEATHER REVIEW VOLUME 114OLR $TRNDRRD DEVIRT]ON JRN-MRR 1979 (UNI T$=H/H~! 12OE JSOE 180 150H~QN 16 ' ~ '10N .~. ~~~~ ~ ~ ~ ~:, <.~, ,,. ,,, .;~ L ~G. 4. Spatiai ~stdbufion of the smn~rd deviations of OLR ~culat~ at eve~ ~d ~int.120H ~ON ~0N 10N E0 ~0S i~OS !aos ~-suggest is strongly convective (not shown). An examination of the spatial distribution of standard deviationsfor both variables (see Figs. 4 and 5) show relativelylow OLR standard deviation values (<32 W m-2) andmoderate P - E standard deviation values (>4 mmday-l) over this region. I suspect that the low correlation values over this region could be due to many orographically induced short-lived convective cellsembedded in a persistent cirrus deck (thus the low OLRand moderate P - E variances in this region). Thiscirrus deck is most likely created from the almost continuous vertical moisture transport from the numerouscumulonimbus clouds associated with the summermonsoon. Thus cirrus contamination of OLR can bea problem even in moist regions. Some-error might be introduced here by the neglectof term C in the P - E calculation (refer to section 2)which could become important when consideringmountainous terrain. Also, the moisture convergencedue to these short-lived convective cells must occuraround 0000 GMT to be measured by the once-dailyFGGE measurements used in the P - E calculations.Therefore, due to diurnal biases and questionable dataquality, care must be taken in assuming confidence inthese low correlation values. However, the physicalreasons suggested for these correlations are certainlyF'-E STRNDRRD DEVIRTION JRN-MRR 1979(ON] TS=MN/DI:IY) ~O. 5. As in FiB. 4 but for P - ~.MAY 1986 MARK L. MORRISSEY 937possible and should be considered when utilizing shortterm convective variables in the study of large scaleconvection.5. Time-variance comparison of open-ocean rainfall, P - E and OLR As was mentioned in the Introduction, due to thesporadic locations of rainfall stations in the central Pacific a general spatial comparison of observed rainfallwith P - E and OLR is precluded. However, a temporalcomparison of the three variables can be made oversome selected regions. A representative open-ocean area was chosen inwhich the enclosed daily observed rainfall, P - E, andOLR values were areally averaged and compared statistically for the period January through March, 1979.A correlation coefficient was calculated for each pairof variables. Each coefficient turned out to be statistically sign!ficant at the 99% level and, therefore, linearrelationships were established for each case. In conducting such a comparison a geographical areaencompassing a number of rainfall stations was selectedso that the station density was comparable to the P- E, OLR grid point density in that area. Only atollrainfall stations were chosen in order to minimize theorographic effect. Also, rainfall stations with missingdata during the study period were avoided and, to bemeaningful, the selected area was situated in an activelyconvective region. The region selected (hereafter referred to as studyregion I) contains the atoll rainfall stations Beru (l-S,175-E), Funafuti (8-S, 179-E), and Nanumea (5-S,176-E). This represents an area of 4.92 x 105 km2 (seeFig. 6) and is a region where OLR and P - E are wellcorrelated (Fig. 3).a. Rainfall vs P - E The rainfall vs P - E correlation coefficient obtainedfor study region I was 0.36. The variable-time plot ofthe observed rainfall vs P - E relationship is shown in~d?~')N01,4 -~lOS~'OS 150E 180~TUDY REGION I ~-~ ~, ~ , I t.~ ~.~10S 12 IE I$b- lit0 I~G. 6. Geographical location of the study regions I & II of islandrainfall stations. The regions are indicated by dashed lines. Stationlocations in study region I are indicated by heavy dots.'~ ?~o. ~0~ ~0~4 ~~ lOS ~OS 30515 114Fig. 7. Despite the statistically significant correlationcoefficient, poor agreement is often observed duringthe period, especially from days 45 to 80 when theareally averaged daily rainfall and P - E estimatesare low. Several factors which might influence the P - E vsobserved rainfall daily relationship are suggested: 1) Inaccuracies in daily rainfall values are certainlypossible, although this is extremely difficult to ascertain. As mentioned in section 2, the moisture and diver gent wind analyses for the FGGE IIIb data set is of questionable accuracy over data void regions. However, as mentioned above, P - E does correlate significantly well (< -0.3) with OLR in this region (Fig. 3). This indicates that P - E does, in fact, respond to changes in convective activity in this region and suggests that qualitative assessments of the P - E vs OLR rainfall relationships are of some value. 2) The spatial distribution of rainfall stations in thestudy area is quite uniform (see Fig. 6) and the stationdensity (number of stations per area) is equal to thatof the P - E grid point density (three-grid points inthe study area). Examination of daily rainfall values(not shown) shows large variations among stations. Dueto the nature of tropical LSCA, which consists of manyindividual convective cells with space and time scaleson the order of 10 km and a few hours respectively,observed rainfall at a given station is a measure of localized convection rather than a measure of large-scaleconvection. In order for observed rainfall to accuratelyrepresent LSCA, station density would have to be quitelarge. Thus, the validity of observed rainfall as a measure of LSCA is extremely sensitive to station density. P - E is derived from large-scale field variables (u,v, qO, T, r) and is therefore not as dependent on thenumber of observations per area. 3) In the tropics where the daily variances of humidity and, to a lesser degree, wind speed (Atkinson,1971), are small, fluctuations in evaporation rates arealso suspected to be fairly small. In highly convectiveareas, such as study region I, precipitation is believed'to account for most of the variance in P - E, althoughthis is difficult to verify. One estimation of the dailyfluctuations in evaporation rates can be made by observing that the standard deviation values of P - E(see Fig. 4) in dry regions (where P - E < 0 mm day-~in Fig. 2; i.e., 180-E, 20-N) are generally less than 4mm day-~. 4) As mentioned in section 4, there may also beconsiderable diurnal biases in the P - E estimates because the input parameters (u, v, T, qb, r) ofP - E aremeasured only once a day while rainfall measurements,on the other hand, are integrated daily values. b. P- E vs OLR The correlation coefficient obtained in this case is -0.67. Note that the correlation coefficient here rep938 MONTHLY WEATHER REVIEW VOLUME 114 ~ P-E V5 ~RINFRLL JRN-MRB,1979 ~ RR I N=SQU.R~E P-E=THIRNGLE 'il )- CI~m C3~~g " ~g 00 1~3 00 . 39.00 52.00 65.00 . '91.00DATFIG. 7. I January to 31 March plot of P - E vs observed rainfall for study region I.resents the areal averaged OLR and P - E estimateswithin study region I as opposed to the correlations atindividual grid points as in Fig. 3. The variable-timeplot is shown in Fig. 8: Factors which might influencethe P - E vs OLR relationship in the study area include 1) Moderately high variances of both P - E andOLR exist in this region during the' study period (seeFigs. 4 and 5). As demonstrated earlier, P - E usuallycorrelates well with OLR in areas where there are largevariations in strong convective activity. 2) Both OLR andP - E are averaged over the samegrid points. This is probably of minor importance dueto the relatively low spatial variance of OLR and P- E within this region;c. Rainfall vs OLR The correlation coefficient obtained is -0.52. Thevariable-time plot is shown in Fig. 9. Suggested factorswhich could influence this relationship are as follows: 1) The undetermined accuracy of the observed station rainfall estimates and low rainfall station densitywithin the study region (as discussed in subsection 5a)appear to severely limit the observed rainfalt's measurability of large-scale deep convection. 2) A scatter plot of OLR vs observed rainfall (notshown), shows a large amount of scatter throughoutthe range of both variables. This could reflect the effectsof cirrus contamination of OLR and the large amountof spatial variability in the observed rainfall data dueto local effects. Diurnal biases in the twice per day OLRmeasurements als0 contribute to this scatter.6. Testing the relationships The correlations between the variables were testedfor statistical significance using the standard normaltest of the null hypotheses H0: rt = r2, Ho: r2 = r3 andHo: r3 = r~ at the 95% confidence level where 1) q = 0.36; the P - E vs observed rainfall correlation coefficient. 2) r2 = 0.52; the absolute value of the observedrainfall vs OLR correlation coefficient. 3) r3 = 0.67; the absolute value of the P- E vs OLRcorrelation coefficient.The results of the test indicate that 1) Ho: r~ = r2 cannot be rejected. (Therefore r~ isnot significantly different than r2.) 2) H0: re = r3 is rejected. 3) Ho: r~ = r3 is rejected. Therefore, P - E and OLR correlate better with eachother than they do with rainfall during the study period.The major factor which may be responsible for this isP-E VS OLFIP-E=SQURREJAN-MAR, J979OLR=TR]ANGLEiJee ih.~ ~k.ee ' ' sk.~ ' ' - 39.0~ 52.00 78.00 91.00 DRY~G. 8. ! 3an~ to 31 M~ch plot ofP - E vs OLR for study ~on I. Dam are no~ by subbing ~e m~n and di~ding by ~e s~d deviation.OLR VS RAINFALL JAN-HAR, 1979RAIN=SQUARE OLR=TRIANGLEDRTFIG. 9. As in Fig. 8 but for OLR vs observed rainfall.940 MONTHLY WEATHER REVIEW VOLUME 114the low station density of rainfall observing stationswithin the study region. To investigate this further a second study region wasselected having the same total area and OLR and P- E grid point density as the original study region, butwith a greatly increased number of rainfall observingstations. Study region II is located over the highly convective region of northern Australia (see Fig. 6) andencompasses 298 stations. The correlation coefficientfor P - E and observed rainfall for this study regionfor the January to March period is 0.85. This value issignificantly greater than the P - E, observed rainfallcorrelation coefficient obtained for study region I(0.36). The P - E, OLR correlation is -0.65 and theOLR, observed rainfall correlation is -0.64, neither ofwhich is significantly different than their respectivecorrelations obtained for study region I. The P - E,observed rainfall correlation is significantly differentthan both the P - E, OLR and OLR, observed rainfallcorrelations. This indeed indicates that the low rainfallstation densities over open ocean precludes the use ofopen-ocean rainfall as an accurate measure of LSCAand helps to support the validity of P - E as a measurement of the large-scale fluctuations in precipitation(where data quality can be verified). Also, the strongcorrelation coefficient obtained for P - E, observedrainfall in study region II suggests that the error dueto diurnal biases in the P - E estimate becomes lesswhen considering large-scale moisture convergence.7. Spatial extent of cirrus contamination As the results of this study indicate, cirrus contamination of OLR can seriously limit the usefulness ofOLR as a measure of LSCA. Precipitation minus evaporation, although probably a better indicator of LSCA,cannot always accurately locate LSCA, as can seen fromthe time-mean chart ofP - E over the Philippine area(see Fig. 2), where there are high amounts of low-levelmoisture convergence and widespread shallow convection. The combination of daily OLR and P - E,however, helps to better define the intensity and spatialextent of LSCA, therefore isolating the spatial extentof cirrus contamination in OLR as well. The procedureis to identify moist (P - E > 0 mm day-~) and dry (P- E < 0 mm day-~) regions where OLR is less than240 W m-2. Either P - E or OLR can be contoured.The choice depends on the accuracy of the P - E estimate. As shown in sections 3 and 4, P - E appearsto be adequate for describing the relative temporal andspatial fluctuations of the largerscale moisture convergence fields. However, as mentioned in section 2, littleconfidence should be placed in the absolute accuracyof the P - E estimate derived from the FGGE dataset. Therefore, until better quality data can be utilized,OLR, not P - E, should be contoured, using OLR toestimate the intensity of convection. With OLR contoured, P - E is used only to identify dry and moistregions of low OLR. The threshold value of OLR (240W/m2) is used by many authors to delineate convectiveregions from nonconvective regions (Murakami, 1980;Lau and Chan, 1983). Lau and Chan (I 983) comparedthreshold OLR values with frequency distributions ofhighly convective clouds using a method developed byKilonsky and Ramage (1976). They found that theirresults were not very sensitive to the exact value of thethreshold used, provided it was in the 230-250 W m-2range. A sample output for the P - E, OLR methodwith P - E contoured is shown for 6 February 1979in Fig. 10. In Fig. 11, the method is again shown for 6February but with OLR contoured. Comparisons withvisual satellite imagery and radiosonde and surface datafor selected days and regions help validate this procedure for investigating convective vs nonconvectiveareas over the Pacific Ocean. As illustrated in Fig. 10, large areas of cirrus contamination in tropical regions are evident. By identifying (per day) what percentage of the area enclosedby OLR less than 240 W m-2 is also associated withnegative P - E values, and then averaging these percentages for the study period, we find a daily averageof approximately 34% of the area enclosed by OLRless than 240 W m-2 over the Pacific ocean is nonconvective. (Due to the uncertainty in the P - E estimatesand the diurnal biases in both OLR and P - E, thisvalue should be used as a qualitative estimate only.)Thus, cirrus contamination in the tropics should notbe ignored, especially on a daily basis.8. Concluding remarks Results of this study indicate that the tendency forobserved rainfall to be a measure of localized convection makes its usefulness as an indicator of LSCA verydependent on station density. Therefore, the very lowstation density, together with the sporadic locationsand varying data reporting times between rainfall stations over the central Pacific, suggest that observedrainfall may not be an accurate indicator of the time'and space scales of open ocean LSCA. Thus, carefulconsideration is required when utilizing observed dailyrainfall as a measure of LSCA. Physical explanations for the statistical relationships obtained suggest that OLR alone does not always ad equately describe convective conditions and that P - E combined with OLR helps to minimize the in adequacies of both variables for the identification of LSCA. The technique which combines P - E with OLR provides us with a descriptive tool with which to study LSCA. When moisture flux data become more reliable they will provide a better measure of convective inten sity. With the presently available FGGE data set, the technique can spatially isolate large-scale cirrus con tamination which is the major complaint with OLR over open ocean areas, especially on daily time scales.MAY 1986 MARK L. MORRISSEY 941OLR MOIST/DRY REGIONS FEB 6, 1979CONTOUR INTERVRL=I'~/-) 1B MM/DRTSHADING ANGLE: q5 DEG = P-E - 0 MM/DRT : 9~ BEG : P-E < 0 MM/DAT120E 150E 180 ]SON ]2DHEn~05son ~ ' ~'r~- ~ 'u, tllllllY~ IIIIIIIII17 I~'/////~ ['/1K ' so.20N ~ON ,: ,o, ~. ~ ~ ~lll ~ ,,~//~ ~o~ ~s ~ ~o ~so. ~ FiG. 10. Moist and dry regions of low OLR for 6 February 1979. Shading angled at45- indicates regions where OLR is less than 240 W m-2 and P - E is greater than 0mmd-'. Shading angled at 90- indicates regions where OLR is less than 240 Wand P - E is less than 0 mm d-L Data are contoured in units ofP - E (ram d-~).Other authors have attempted to deal with the problemof cirrus contamination of satellite obtained longwaveradiation. Murakami (1983) using irradiance (IR) dataobserved by GMS-1 geostationary satellite indicatedthat strong convection could be isolated by assumingthat regions with large temporal variances of IR correspond to regions of LSCA. As can be observed fromFig. 4, the standard deviation of OLR over the areasurrounding New Guinea during the study period israther low (<32 W m-2) and would thereby indicatean absence of strong convection using Murakami'smethod. Averaged P - E and OLR (see Figs. 1 and 2)together with the surface observations indicate strongconvection for the region. This discrepancy can be exOLR MOIST/DRY REGIONS FEB 6, 1979CONTOUR INTERVRL~ rio 14/M2SHADING ANGLE: ~5 DEG - P-E > ~ NI'~/ORT AND OLR < 2q0 N/H2~ 9g DEG = P-E < 0 Nil/DRY AND OLR < 2~S ~/~2EO305so~ t~ ' It'-- ~ ",1111t-I,S'11I-'//J1 IIIIIIIIII~F///////~II'IV ! ~o~ ~' ' ~ ~ '~- ..~71~~ '20# ! ~ONlON L ~ ~~ ION ~ ~ ~[ .,o, ,:: ~~. , ~ ~~OS ' ~ 20S~. ~'~,~ ~1 ~ ~ ~ ~ ~ ~ MtU ~//~ ~ ~ ~2)E ]S IE IB0 5 H ~2FiG. 11. As in Fig. 10 but data are contouredin units of OLR (Wm-:).plained by a large persistent cirrus canopy which possibly exists over this region (thus low IR standard deviation values) during the active phase of the SouthernHemisphere monsoon (January to March). As mentioned earlier, this cirrus canopy can be produced bycontinuous large-scale vertical moisture transport,which in turn is caused by the large number of convective "hot towers" inherent in the monsoon. Itwould, therefore, be very difficult to distinguish theareas of active convection in the high-level cirrus deckover this region using OLR exclusively. The P - E,OLR combination helps to overcome this difficulty byeffectively looking "below" the high-level cirrus cloudsand thus can better assess the convective situation. Acknowledgments. The author would like to thankDr. Takio Murakami for his help and advice, to Mrs.Dixie Zee for lending her computer expertise and Mr.Kelcy Chang for his help with the surface observations.Discussions with Dr. Colin Ramage, Dr. ThomasSchroeder, Mr. Mark Lander, Mr. Jose Maliekal, Mr.W. L. Sumathipala and Dr. Susan Postawko are gratefully acknowledged. This research was completed aspart of the author's dissertation. The author would liketo thank NOAA for funding this research under GrantNA 80 RAH 00002. APPENDIX Spatial Smoothing Function The spatial smoothing function for P - E consistsof a five-point weighted average and is given by942 MONTHLY WEATHER REVIEW VOLUME 114r(i,j) -- [r(i+ 1,j) + r(i- l,j) + r(i,j+ 1) + r(i,j - 1) + 4.0*r(i,j)]/8.0,r(i, j) - P - E estimate at grid point (i, j), i= 1,2,3 ... 33, j= 1,2,3, .-. 19. Index values (i,j) represent grid points 3.75- X 3.75-apart in the zonal and meridional directions, respectively. REFERENCESAnderson, R. K., and V. J. Oliver, 1970: Some examples of the use of synchronous satellite pictures for studying changes in tropical cloudiness. Ext. Abstracts: Syrup. Tropical Meteorology, Hono lulu, Amer. Meteor. Soc., EXIII-EXII6.Atkinson, G. D., 19;/I: Forecasters' Guide to Tropical Meteorology. Tech. Rep. 240, Air Weather Service, USAF, 240 pp.Davidson, N. E., J. L. McBride and B. J. McAvaney, 1984: Divergent circulations during the onset of the 1978-1979 Australian mon soon. Mon. Wen. Rev., 112, 1684-1696.Flores, J. F., and V. F. Balagot, 1969: Climate of the Philippines. World Climate Survey, 8, Elsevier, 159-213.FGGE Newsletter, 1983: No. 1, May, USC-GARP, JH 810, [Nat. Acad. Sci., 2101 Constitution Ave., Washington, IX2., 20418,] 33 pp.FGGE Operations Report, 1980: Observing System Operations, 1 December 1978-30 June 1979. The Global Weather Experiment, Vol. I. GARP Rep., ICSU and MO, [Nat. Acad. Sei., 2101 Con stitution Ave.,, Washington, DC., 20418,] 78 pp.Gill, A. E., 1982: Atmosphere-Ocean Dynamics. Academic Press, 661 19-38.Julian, P. R., 1984: Objective analysis in the tropics: A proposedscheme. Mon. Wea. Rev., 112, 1752-1767.Kilonsky, B. J., and C. S. Ramage, 1976: A technique for 9stimating tropical open-ocean rainfall from satellite observations. J. Appl. Meteor., 15, 972-975.Lambert, S. J., 1983: List of known or suspected problems with the ECMWF analyses of FGGE data. FGGE Newsletter No. 1, May 1983, USC-GARP, JH 810, Nat. Acad. Sci., 2101 Constitution Ave., Washington, DC., 20418.Lau, K., and P. H. Chart, 1983: Short-term variability and atmospheric teleconnections from satellite-observed outgoing longwave ra diation. Part I: Simultaneous relationships. Mon. Wea. Rev., 40, 2735-2750.Lorenc, A. C., and R. Swinbank, 1984: On the accuracy of generalcirculation statistics calculated from FGGE data--a coml~risonof results from two sets of analyses. Quart. J. Roy. Meteor. Soc.,110, 915-942.Lubis, S. M., and T. Murakami, 1984: Moisture budget during the 1978-79 Southern Hemisphere monsoon. J. Meteor. Japan, 62, 748-760.Meisner, B. N., and P. A. Arkin, 1984: The GOES precipitation index: Large scale tropical rainfall estimates using infrared data. Proc. 15th AMS Tech. Conf Hurricanes and Tropical Meteo rology, Miami, Amer. Meteor. Soc., 203-206.Murakami, T., 1980: Empirical orthogonal function analysis of sat ellite observed outgoing long-wave radiation during summer. Mort. Wea. Rev., 108, 205-222. ,1983: Analysis of the deep convective activity over the western Pacific and Southeast Asia, Part I: Diurnal variation. J. Meteor. Japan, 61, 60-75. , T. Iwashima and T. Nakazawa, 1984: Heat, moisture, and vorticity budget before and after the onset of the 1978-79 Southern Hemisphere Summer Monsoon. J. Meteor. Japan, 62, 69-87.Ramage, C. S., 1975: Monsoon Meteorology. Academic Press, 296 pP. , S. J. S. Khalsa and B. N. Meisner, 1981: The Central Pacific Near-Equatorial Convergence Zone. J. Geophys. Res., 86, 6580 6598.Vincent, D. G., 1982: Circulation features over the South Pacific during 10-18 January 1979. Mort. Wea. Rev., 110, 981-993.Yanai, M., S. Esbensen and J. Chu,. 1973: Determination of bulk properties of tropical cloud clusters from large-scale heat and moisture budgets. J. Atmos. Sci., 30, 611-627.Zangvil, A., 1975: Temporal and spatial behavior of large-scale dis turbances in tropical cloudiness deduced from satellite brightness data. Mon. Wea. Rev., 103, 904-920.