FEBRUARY 1992 SHEU AND CURRY 261Interactions between North Atlantic Clouds and the Large-Scale Environment RONGoSHYANG SHEU AND JUDITH A. CURRYDepartment of Meteorology, The Pennsylvania State University, University Park, Pennsylvania(Manuscript received 11 November 1990, in final form 10 June 1991)ABSTRACT This paper addresses the problem of understanding and predicting the presence of clouds and their effects onthe atmosphere in the midlatitudes of the North Atlantic Ocean. The European Centre for Medium RangeWeather Forecasting initialized analyses and the U.S. Air Force Three-Dimensional Nephanalysis are employedto construct a joint time series of gridpoint values of cloudiness and large-scale meteorological fields, includingheat and moisture budgets, for January 1979. Interpretation of cloud in the context of the large-scale flow isgiven for the monthly average situation, disturbed and undisturbed conditions, and a longitudinal cross sectionthrough a baroclinic wave. In general, middle clouds are formed primarily due to the benefit from large-scalethree-dimensional moisture convergence; and low cloud formation depends on surface moisture flux and thestatic stability. Upper-level moisture was deemed to be sufficiently unreliable so that no inferences regardinghigh clouds could be made. Comparison of the relative humidity field with cloud cover in a cross section of abaroclinic wave shows that peak cloud fractions are displaced approximately 3.5- latitude to the east of thepeak relative humidities. From concurrent examination of the residual heat and moisture sources, it is suggestedthat clouds do not respond instantaneously to the large-scale relative humidity field, but take a period of timeon the order of hours to adjust in terms of evaporation and condensation. The relationship of cloud fraction to the large-scale humidity field is examined, along with several diagnosticparameterizations of cloud fraction currently employed in general circulation models. The grid-scale thresholdrelative humidity below which cloud, on average, does not occur was determined to show a strong decreasewith height. It was shown that appropriate "tuning" of a diagnostic relative humidity-based parameterizationcan result in accurate parameterized mean monthly total cloud amount for the region, and layer cloud fractionsto within 5% of observed layer cloud fractions. However, this type of cloud fraction parameterization appearsto be unable to diagnose layer cloud fraction on the smaller time and space scales that are undoubtedly requiredfor obtaining the correct local cloud radiative and hydrological feedback with the dynamics.1. Introduction This paper focuses on the problem of understandingand predicting the presence of clouds and their effectson the atmosphere in one of the most persistentlycloudy regions of the Northern Hemisphere, namely,the midlatitudes of the North Atlantic Ocean. Therenow exists a great volume of literature confirming thevital role of cloudiness in both weather and climateprediction. The importance of clouds arises throughthe coupling of radiative, dynamical, and hydrologicalprocesses in the atmosphere through the reflection, absorption, and emission of radiation, the release of latentheat, and the redistribution of sensible and latent heatand momentum. While a substantial effort has beenspent in attempting to understand the interaction ofconvection, the planetary boundary layer, and the largescale flow in the tropics and subtropics, there has beenno comparable effort to understand the interactions of Corresponding author address: Prof. Judith A. Curry, Dept. ofMeteorology, 503 Walker Building, The Pennsylvania State University, University Park, PA 16802.cloudiness with the large-scale flow in midlatitudemaritime regions dominated by frontal systems. The role of clouds in climate is well understood interms of the albedo and greenhouse effects. Arking( 1991 ) has provided a useful review of research on theimpact of clouds on the earth's radiation balance. Allrecent estimates agree that the annual, global meaneffect of clouds on the net flux of radiation at the topof the atmosphere is cooling when compared with aclear-sky atmosphere (dominance of the albedo effect).Any long-term change in cloudiness that results in aglobal change of albedo and greenhouse warming caneventually lead to a global climate change. The sensitivity of atmospheric general circulation models(GCMs) to cloudiness has been shown by Manabe andStouffer (1980), Ramanathan et al. ( 1983 ), Roecknerand Schlese (1987), Wetherald and Manabe (1980),Cess et at. (1989), and Slingo (1990), among others. In addition to the importance of clouds in the earth'sradiation balance, diabatic processes associated withclouds substantially modify the baroclinic waves ofextratropical latitudes. The influence of clouds on shortterm weather patterns arises primarily from the effectof latent heat release on the development of synopticc 1992 American Meteorological Society262 MONTHLY WEATHER REVIEW VOLUME 120systems. In the climato..!ogical mean, latent heat releasedue to cloud formation over the North Atlantic duringwinter is about i --2-C day-~ (Geller and Avery 1978;Schubert and Herman 1981 ). For comparison, it isonly in the equatorial tropics that larger latent heatingrates are found. Clouds thus provide a strong sourceof mid- and upper-tropospheric latent heating over theNorth Atlantic cyclone tracks. Studies of extratropicalcyclones by Smith et al. (1984), Pauley and Smith(1988), and Zimmerman et al. (1989) show that latentheat release can have direct and indirect effects on theenhancement of mechanisms that lead to the furtherdevelopment of cyclones. Diagnostic studies (e.g.,Gyakum 1983) and numerical experiments (e.g.,Anthes et al. 1983; Kuo and Low-Nam 1990) point tolatent heat release as a key ingredient in "explosivemarine cyclogenesis." Hoskins (1980) has showntheoretically the mechanisms through which heatingcould enhance baroclinic development. It has also beensuggested that latent heating plays a role in the development of smaller-scale baroclinic systems (polarlows), which frequently develop to the south and eastof Greenland (e.g., Rasmussen 1979). An understanding of large-scale cloud diabatic processes and accurate representation ofdiabatic processesin GCMs is thus a prerequisite for accurate weatherand climate predictions. The proper formulation ofcloud properties and the hydrological cycle in GCMsunfortunately remains an unsolved problem. Difficultyin predicting cloud amount, height, and depth arisesfrom lack of knowledge of the processes resulting incloud formation and dissipation on the large scale.Since most clouds are either horizontally or verticallysubgrid scale, the complicated interactions betweenmoist convective turbulence, radiation, cloud microphysical processes, and the large-scale dynamics thatresult in cloud formation and dissipation must besomehow parameterized in terms of the grid-scalevariables. In this study the European Centre for MediumRange Weather Forecasts (ECMWF) initialized analyses and the U.S. Air Force 3D Nephanalysis(3DNEPH) are employed to construct a joint time series of gridpoint values of cloudiness and large-scalemeteorological fields for January 1979 in the NorthAtlantic. Heat and moisture budgets are determinedfollowing the techniques of Yanai et al. (1973). Thisdataset provides a basis for the phenomenological description of the cloudiness in terms of the atmosphericforcing parameters, thus elucidating the processes contributing to the formation, maintenance, and dissipation of the clouds, and also determining such fundamental diagnostics as the vertical distribution of latentheating. Interpretation of cloud in the context of thelarge-scale flow is given for the monthly average situation, disturbed and undisturbed conditions, and alongitudinal cross section of a baroclinic wave. Therelationship of cloud fraction to the large-scale humidity field is examined, along with several diagnostic pa.rameterizations of cloud fraction currently employedin GCMs.2. Data The time period under consideration is .January1979, corresponding to the First GARP Global Experiment (FGGE) Special Observing Period I. Thespecific area in the North Atlantic that is examinedextends from 40- to 60-N and from I0- to 50-W.Datasets employed in the analysis include the ECMWFFGGE IIIb dataset, 3DNEPH, the Nimbus-7 ScanningMultichannel Microwave Radiometer (SMMR) data,and the High-Resolution Infrared Sounder 2-Microwave Sounding Unit (HIRS2-MSU) radiances. Thesedata were averaged daily on a 1.875- latitude and1.875- longitude grid at 0000 and 1200 UTC, coincident with the ECMWF analyses. The region and period that we have chosen to examine has probably the best conventional data coverageof any oceanic region in the world (Bjorheim et al.1981 ). Analysis of the distribution of data used in theECMWF analyses gives an average for the region of82 and 100 surface ship observations at 0000 UTC and1200 UTC, respectively (Bjorheim et al. 1981 ). Aircraftreports (utilized in both the 3DNEPH and ECMWF)are abundant, but appear to vary with the day of theweek (Bjorheim et al. 1981 ). There are six radiosondesfrom stationary weather ships and from islands in thisregion.a. Atmospheric dynamic and thermodynamic data The ECMWF four-dimensional data assimilationscheme utilized in the "main" ( 1980/81 ) FGGE levelIIIb analyses is described by Bengtsson et al. (1982).It is an intermittent data assimilation system consistingof a multivariate optimum interpolation analysis, anonlinear normal-mode initialization, and a high-resolution model, which produces a first-guess forecastfor the subsequent analysis. The analysis consists oftwo parts: one for the simultaneous analysis of surfacepressure, geopotential height, and horizontal wind, andanother part for analysis of humidity. Hydrostatic balance is achieved through conversion of temperatureobservations into thicknesses prior to the assimilation.The level IIIb dataset contains both basic analysis, parameters as well as derived parameters. The basic parameters are uninitialized and consist of geopotentialheight, sea level pressure, and horizontal wind components. The derived parameters are temperature, relative humidity, and vertical velocity. The relative humidity is determined from the precipitab]e water ineach analysis layer (the basic analysis parameter forhumidity) and the temperature. The vertical velocityis calculated from initialized divergences.FEBRUARY 1992 SHEU AND CURRY 263 The "final" (1985/86) ECMWF FGGE analyses,which are utilized in this study, contained numerouschanges to the assimilation scheme and also containedcorrected and additional data (Pailleaux 1986). Thefinal dataset contained additional data from the regional experiments conducted during FGGE, additional ship data, higher-density satellite temperatureand humidity retrievals, and cloud-track winds.Changes in the mass and wind analysis algorithm aredescribed by Shaw et al. (1987). The main changes tothe humidity analyses are discussed by Illari (1985)and Pasch and Illari ( 1985); The incorporation of diabatic effects in the normal-mode initialization are discussed in Wergen (1988). The assimilating model wasa T63 spectral model (Girard and Jarraud 1982), andthe physical parameterizations are described by Tiedkeet al. (1988). The Arpe (1985a,b) showed that the finalanalyses agreed better with observational data than themain analyses. Both the initialized and uninitialized versions of thefinal ECMWF FGGE IIIb analyses were examined.Although the initialized analyses may possess dampened divergences, a number of other factors are moreattractive in the initialized analyses when comparedwith the uninitialized analyses. A comparison wastherefore made between the final initialized and uninitialized analyses on a gridpoint-by-gridpoint basisfor the region and time period under consideration. For horizontal velocity components, the average absolute difference between the initialized and uninitialized gridpoint values was 0.5 m s-j, although therewas no systematic difference. Slightly higher differenceswere found at the highest levels, with the maximumdifference being 4 m s-~. Derived vorticity values differed by an average of less than 10%. Differences inthe derived divergences were larger, averaging 30%, butit did not appear that the initialized divergences weresystematically smaller in magnitude. The divergencesof the two datasets had a correlation coefficient of 0.9.Vertical velocities for the uninitialized analyses werederived using the method of O'Brien (1970), whilevertical velocities for the initialized analyses were a byproduct of the diabatic nonlinear normal-mode initialization procedure. A comparison of the derived uninitialized vertical velocities with the initialized valuesshowed that the uninitialized vertical velocities weresystematically smaller than the initialized values, withlittle correlation and substantially different vertical-velocity profiles. The uninitialized temperatures were derived fromthe geopotential fields using the hydrostatic equation.The initialized temperatures were systematically higherthan the uninitialized temperatures. The average absolute difference was 1 -C and the maximum differencewas 5-C, the largest differences occurring at lower levels. The uninitialized mixing ratios were obtained fromthe layer precipitable water values after Lorenc andTibaldi (1980). A comparison of the initialized withthe uninitialized values showed that the 1000- and 850mb initialized values were systematically -~20% higherthan the uninitialized values. Above 500 mb the initialized values were systematically ~20% lower thanthe uninitialized values. The two datasets thereforehave markedly different vertical profiles of humidity.It is presumed that the use of the vertical structurefunctions (Uppala 1986) in the derivation of the initialized mixing ratios from the precipitable water valuesaccounts for this difference. In addition to the primary meteorological quantities,higher-order terms from the heat and moisture budgets(see section 3) were compared. The largest differenceswere associated with those budget terms that containedthe vertical velocity. In spite of rather large randomdifferences, the systematic differences for the meanmonthly budget residuals were less than 10%. In light of the aforementioned comparisons, the initialized analyses have been chosen for this study. Specific reasons for choosing the initialized analyses include the following: improved vertical structure of thetemperature and humidity fields, while spurious divergences have been eliminated, the initialized divergences do not appear to be damped; the initializationis generally believed to produce more realistic extratropical vertical velocities (e.g., Savijarvi 1983); andthe initialized analysis fulfills the integral constraintsand provides a dynamically consistent dataset. However, the overall quality of the humidity fields remainsuncertain. The fields obtained from the ECMWF initializedanalyses and employed in this study are temperatureT, absolute humidity q, height z, zonal velocity u, meridional velocity v, and vertical p velocity w, at levels1000, 850, 700, 500, 400, 300, and 200 mb, with ahorizontal resolution of 1.875- in both latitude andlongitude.b. Cloud-cover data The cloud-cover data used in this study are the U.S.Air Force 3DNEPH, which is described by Fye (1978).The 3DNEPH provides total cloud cover, cloudamount at 15 levels, heights of the lowest bases andhighest tops, cloud types, and significant weather, witha horizontal spatial resolution of about 44 km at 60-Nand a nominal temporal resolution of 3 h. The3DNEPH is a blend of satellite (threshold analysis)and conventional observations; the conventional observations are obtained from surface, aircraft, and radiosonde reports. An assessment of the quality of the3DNEPH for this region and period is given by Tianand Curry (1989). Because of the density of conventional observations in this region, the 3DNEPH provides a reasonable analysis of layer cloud amounts. The 15 layers of 3DNEPH were assigned to thenearest layers of the ECMWF analyses, which contains7 layers. Each of the lowest four ECMWF layers con264 MONTHLY WEATHER REVIEW VOLUM- 120sists of at least two 3DNEPH layers. An algorithm basedon random and maximum overlap assumption is employed to determine the cloud fraction for each of theseECMWF layers (Tian and Curry 1989).c. Precipitation data The microwave brightness temperatures measuredby the Nimbus-7 SMMR, described by Gloersen andBarath (1977), are employed in the determination ofprecipitation rates. Because of the relatively narrowswath of observations and due to the fact that the instrument was turned off every other day, there is notfull data coverage for the entire region and period underanalysis. Precipitation rates were determined afterCurry et al. (1990), which employed the 37-GHz vertically and horizontally polarized brightness temperatures.d. Sea surface temperatures Sea surface temperatures were determined afterSusskind and Reuter (1985) using the HIRS2-MSUsatellite data. The temperatures were determined on ahorizontal resolution of 2.5- latitude x 2.5- longitude;values were interpolated onto the' ECMWF grid spacing. Mean monthly temperatures at each grid pointwere used.3. Method of analysis The sensible heat and moisture budgets per unit massof air are derived following the bulk diagnostic methodproposed by Yanai et al. (1973), with the exceptionthat the heat budget equation is written in terms ofenthalpy cpT instead of dry static energy: 0~ v.v (1) - (a (c~r) + V.Vc~r + cop! = Q~ + L(c- e) (2) O-~+ V.Vq+-~-p =e-c. (3)Most of the notations bear the conventional meanings,with QR representing the net radiative heating, c therate of condensation per unit mass, e the evaporationrate, p pressure, L latent heat of condensation, % specific heat at constant pressure, and V- the horizontaldivergence operator on a constant-pressure surface. Theoverbar denotes the horizontal average over the gridbox, for example, (-) = A -~ ff (-)a2 cos-dXd4, whereA is the grid-box area, a the radius of the earth, X longitude, and 4 latitude. All of the terms on the left-handside of( 1 )-(3) can be evaluated using the gridded fieldsfrom the ECMWF dataset. Terms on the right-hand side of (2)-(3) representthe source terms, which cannot be directly evaluatedusing the gridded fields from the ECMWF IIIb dataset.Equations (1)-(3) may be rearranged to giveQ, --- (c,T) + V. Vc, T + = -V'V'coT' - (~p__R ICvoo, T,cvp / + QR + L(c - e)(4) a Q2m~+V'XZq+~ 90; 0 . =-V.V'q'-~ppO~'q'+e-c. (5)The cross-correlation terms in (4) and (5) representthe turbulent eddy fluxes ranging in scale fi'om convective and cloud-induced eddies to other mesoscalecirculations. The terms Q~ and Q2 denote the apparentsensible heat moisture sources, respectively, and canbe determined as the residual from the grid-scale variables. The residual heating is due to radiation, latentheat release, and the divergence of the eddy heat flux;the residual moisture source is due to condensation,and to the divergence of the vertical eddy moistureflux. The divergences of the horizontal eddy heat andmoisture fluxes are small (e.g., Pedigo and Vincent1990). In evaluating Q~ and Q: as residuals, it mustbe kept in mind that the residuals may also containcontributions from errors that are associated with theanalysis or with the finite-differencing schemes. Assuming that the horizontal subgrid-scale eddy fluxis small (after Pedigo and Vincent 1990), the verticaleddy flux of total heat F is obtained by combining (4)and (5): F = (Q~ + LQ2 - Qn)dp. (6) T By integrating (4) and (5) from the surface (P0) to200 mb (Pr), we obtain (after Yanai et al. 1973) -lg ~~-(Q' - Q~)dp = LP- +r So (7) I f,o LQ2dp L(Po Eo) (8) gdot - (Q~ + LQ: - Qjz)dp = LEo + So (9) g rwhere So is the supply of sensible heat from the surface,Eo is the rate of evaporation from the sea surface, andPo is the amount of precipitation received at the seasurface. Therefore, the vertical integrals of the largeFEBRUARY 1992 SHEU AND CURRY 265scale heat and moisture equations yield informationon the surface precipitation, evaporation, and sensibleheat flux as a lower boundary condition. When compared with independent observations or estimates ofSo, E0, and Po, (7)-(9) can be used to check the accuracy of the estimates of Q~, Q2, and QR.a. Radiative heating rates The net radiative heating rate QR is the sum of thesolar (SW) heating rate and longwave (LW) coolingrates. Both the LW and SW heating rates are calculatedafter Harshvardhan et al. (1987). For SW, ozone andwater vapor absorption bands are considered, andRayleigh scattering is included. Multiple scatteringfrom clouds is treated using a two-stream delta-Eddington approximation to provide fluxes for a rangeof conditions varying continuously from a clear sky tocloudy sky of arbitrary optical depth. Longwave radiation is calculated using an emissivity approach oversix water vapor bands, three carbon dioxide bands, anda single ozone band; water vapor continuum absorptionis also included. The parameterization allows for fractional cloud cover and random or maximum overlap.A computational scheme utilizing the probability of aclear line of sight between each layer and all other layers, the ground, and the top of the atmosphere is usedto treat the radiative transfer in the presence of clouds.The only assumptions required are that clouds do notreflect in the longwave, and that they fill the modellayer in the vertical. Nonblack clouds are assigned arandom overlap cloud fraction equal to the emissivity. Radiative heating rates are calculated for each gridpoint and time using the ECMWF temperatures andhumidities and the 3DNEPH cloudiness. Above the200-mb level, cloud fraction is assumed zero, and temperature and water vapor mixing ratio are taken fromMcClatchey et al. (1972) for midlatitude winter, whichalso supplies the vertical distribution of ozone concentration for the model.The rain rates P0 are then calculated using the followingalgorithm: Po(mmh-X)=(T~3C) (11)where C is determined to be C = rv - O. 8 *( TvcLR -- r~.cL~). ( 12 )c. Surface heat fluxes Surface latent and sensible heat fluxes are obtainedby using bulk aerodynamic properties. The parametedzation scheme introduced by Louis (1979) relatesMonin-Obukhov scale height to bulk Richardsonnumber. The surface sensible heat flux is evaluatedusing the following expression: a2 AOF zwhere R is the ratio of the drag coefficients for momentum and heat in the neutral limit, a is the dragcoefficient in neutral conditions, u is the wind speed,Zo is the surface roughness length, and RiB is the bulkRichardson number. Difficulty is encountered whendealing with cases of u -- 0, since RiB becomes infinite.For stable cases, the vertical heat flux approaches zerowhen wind speed is zero. For unstable cases (zX0 < 0),the heat flux can be obtained from u,O, = ~ -~ (A0)I (14)where b and c are constants ( see Louis 1979). Sensibleheat flux can be obtained by multiplying (13) or (14)by - pcp, where p and cv represent air density and specific heat capacity at constant pressure, respectively.An analogous approach is employed to derive the surface moisture flux.b. Precipitation rates The SMMR-derived precipitation rates are retrievedusing the algorithm described by Curry et al. (1990)in which the horizontal and vertical brightness temperatures at 37 GHz are used. The algorithm requiresthat a threshold brightness temperature be chosen forthe onset of rain. The threshold value is determinedaccording to the criterion P* < 0.8, where P* is definedby Petty and Katsaros (1990) as Tv- Tr~ P* = (10)where Tv and Tn are vertically and horizontally polarized brightness temperatures at 37 GHz, respectively,and the subscript CLR refers to clear sky conditions.4. Monthly mean conditions During this period, a subtropical high with smallvariation in position dominated the southern portionof this region. To the north was a region of strong baroclinic instability, characterized by a succession of frontal systems. The mean cloud characteristics for this region andperiod are described by Tian (1988), Tian and Curry(1989), and Curry et al. (1990). The average totalcloud cover of this region and period was 64%. Theperiod of our analysis was dominated by layered clouds,with cumuliform cloud types being reported for 10%of the observations and contributing little to the totalcloud cover. The most frequent cloud types occurringin this region were stratus and stratocumulus, with a266 MONTHLY WEATHER REVIEW VOLUME 120400~ ~o01oooTemperature (K)200 i Water Vapor Mixing Ratio (g/m3)1000~o 4b 6'o go '1ooRelative Humidity (%)1 ~.2~ .... : 1 ~ .... 6 .... 1~ ..... ~b U-Velocity (m/s) 400 6001 ooo-20''' :1~ ...... ~) .... 1'0 .... ~0 V-Velocity (m/s)40O6OO8001000 . . ~ '1:01 ' :0:5' ' ' ~ :0 ' tO:5 ..... F.O Vertical Velocity (10'~ mb/s)FIG. 1. Vertical profiles of areally averaged monthly mean quantities for January 1979 over the North Atlantic: (a) temperature, (b) absolute humidity, (c) relative humidity, (d) U velocity, (e) V velocity, and (f) vertical p velocity.combined frequency occurrence of 66%. The frequencyof cases with completely clear sky was about 10%. Figure 1 shows the vertical profiles of the areal-averaged monthly mean quantities obtained from theECMWF analyses for January 1979 in the region ofinterest. The monthly mean temperature and absolutehumidity profiles show typical decreases with height.Relative humidity is highest at the low levels, with asecondary maximum at 400 mb. The areally averaged mean monthly U-componentwind velocity is westerly, the magnitude increasingnearly linearly with a decrease in pressure from a nearlyzero value at 1000 mb. The mean monthly V-component wind velocity is nearly zero at all levels, although the instantaneous V velocity is not necessarilysmall, the average of positive and negative values beingresponsible for the nearly zero mean values. Themonthly averaged vertical p-velocity profile showsdownward motion at each level, with maximum velocity occurring at the 400-mb level.a. Heat and moisture budgets Figure 2 shows the mean monthly heat budget, averaged over the entire region. The terms in the :heatbudget equation (2) are expressed in units of de~eesCelsius per day. The most significant term in the heatbudget at lower levels is the horizontal cold-air advection, which is nearly balanced by the large-scale residualheat source. Above 500 mb, the adiabatic warming andvertical transport terms become increasingly dominant,and the horizontal transport becomes less significant.The residual term (~1 (which includes radiative heating,latent heating, and vertical eddy heat flux divergence)becomes negative above 500 rob. The positive valueof the mean local rate of change at each level signalsa warming trend during this season, although the magnitude is small compared to most of the other te~rms. Figure 3 shows the monthly mean moisture budgetaveraged over the entire region. The terms !in the moisture budget equation (3) are expressed in units of gramsFEBRUARY 1992 SHEU AND CURRY 267600/ /2004008001000 -3 -2 -1 0 1 2 3 -C day-~ FIG. 2. Vertical profile of components of the areally averaged meanmonthly heat budget. Units are given in degrees Celsius per day,which is obtained by dividing heat budget terms byof water vapor per cubic meter of air per day. Analogous to the heat budget, the horizontal moisture advection term is dominant at lower levels and is nearlybalanced by a large-scale residual moisture source. Themoisture source Q2 is associated with evaporation ofcloud drops and the vertical eddy moisture flux divergence. Positive vertical moisture advection dominatesat the upper levels and is offset by the large-scale residual moisture sink. It is seen from Fig. 4 that the net radiative heatingQR is dominated by the longwave cooling, resulting innet radiative cooling at each level. The local maximaat 400 mb in both shortwave and longwave heatingreflect the relatively sharp decrease in cloud fraction(Fig. 7) and cloud optical thickness between 500 and400 mb. Comparison of monthly mean vertical profilesof (l/cp)(Q~ - QR) and (L/c~,)Q2 is shown in Fig.200 -60040080O1000 -1.0 -0.5 0,0 0,5 1.0 g r~3 day'~FIG. 3. Vertical profile of components of the areally averaged mean monthly moisture budget.200 400'600 '800 total..... SW---- LW1000 -C day-tFIG. 4. Vertical profiles of the areally averaged mean monthly longwave, shortwave, and net radiative heating rates.5. At low levels (below 800 mb) there is a positive heatand moisture source, associated with the transport ofsensible and latent heat from the surface. Since theaverage vertical velocity at these levels is downward, itappears that the contributions to the Ql and Q2 budgetsare dominated by the periods of cloud formation, whichpresumably are principally associated with episodes ofrising motion. The negative moisture source and positive value of (1/%)(Q~ - Qn) at levels between 800200 4006008O01000 j (QI'QR)/Cp;( I ...... LQ,/C. I,/ . ~. ~;. ~.~.-C day-~FIG. 5. Vertical profiles of areally averaged mean monthly values of( 1/c~,)(Q~ - Qn ) and ( L / c~, ) Q2.268 MONTHLY WEATHER REVIEW VOLUME 1120and 300 mb are consistent with large-scale condensation occurring at these levels. At 400 mb, it is not clearwhy ( 1/cp)(Q~ - QR) is not balanced by the moisturesink, as would be expected if condensation is the onlycontributing physical process. Above the 400-mb levelthe heat and moisture sources are nearly zero. A comparison of these heat and moisture budgetscan be made with those determined for other geographical regions, specifically the summertime ArcticOcean (Curry and Herman 1985) and the tropicalocean (e.g., Yanai et al. 1973). Over the Arctic Oceanthe dominant features are warm-air advection and aresidual heat sink at all levels. These features representwarm-air advection over a cold surface. There is littlemoisture from the surface, the moisture sink at all levelsassociated with condensation. The Arctic Ocean heatand moisture budgets are clearly different from the situation in this study, where the underlying surface iswarm and the low levels are dominated by cold-airadvection. The tropical ocean heat and moisturebudgets, as typified by the study ofYanai et al. (1973),also present different characteristics in the heat andmoisture budgets. Strong convective activity in tropical'regions results in a heat source and a moisture sinkassociated with condensation, having a maximum between 500 and 800 rob. In the present study, the maximum values of Q~ and Q2 occurred lower in the atmosphere, near the surface. According to Eq. (6), the vertical eddy heat transportat each level can be obtained by integrating the quantityQ~ + LQ2 - QR from pressure p to the top of the model,2O04. OO~BO0800lOOO0 50 100 t50 200VERTICAL EDDY HEAT TRANSPORT (J m'2 S'1) F'IG. 6. Vertical profile of areally averaged mean monthly verticaleddy heat transport for the North Atlantic region (solid line) andthe tropics (dashed line; after Yanai et aL 1973). TABLE 1. Comparison of surface sensible and latent ]neat fluxesand precipitation determined from the heat and moisture budgetswith independently determined values. Also shown are the correlationcoefficients between the budget-derived and independently derivedvalues, and the values determined by Yanai et al. (1973) for thetropics.Budget Independent Correlation YanaiSensible heat(W m-2) 60 62 0.33 ~4Latent heat(W m-2) 104 108 0.30 188Precipitation(W m-2) 107 73 0.41 526assuming the vertical eddy heat transport at 200 mb iszero. The vertical profile of the mean monthly verticaleddy transport shown in Fig. 6 is seen to decreasesharply with height. This is in contrast to the result ofYanai et al. (1973) for the tropics, which shows a strongsecondary maxima at 700 mb. Notice that the valueof F0 in the present study is even slightly larger thanthe tropical value determined by Yanai et al. (1973).b. Calibration of the large-scale budgets Equations (7) and (8) can be used to derive valuesof the surface sensible heat flux and the surface precipitation, provided that a value is available for theBowen ratio, which is defined to be the ratio of thesensible to latent heat flux. The Bowen ratio was determined to be 0.58 from these data. Independent values of the surface latent and sensible heat fluxes mayalso be obtained from ( 13 ) or (14), and precipitationmay be determined from the SMMR data using ( 11 ).By comparing the budget-derived values of So, LEo,and LPo with the independently derived values, an assessment of the consistency of the heat and moisturebudgets can be made. Table 1 compares the budget-derived values of So,LEo, and LPo with the independently derived values(note that the budget-derived value of E0 has been implicitly determined by the assumed B0wen ratio).Comparison of the monthly averaged values of LEoand So determined by the two different methods agreeswithin 4%. Mean monthly precipitation values are seento differ by 30%. Although the relative errors of budgetderived and independently derived values are uncertain, this comparison indicates that (Ql - Q~) and Q2show a systematic error of less than a factor of 1..5. Comparison of S0, LEo, and LPo for the North Atlantic with values presented by Yanai et al. (1973) forthe tropics shows several differences. The Bowen ratiofor the tropics was determined to be 0.076 by Yanaiet al., with the sensible heat flux being substantiallysmaller for the tropics than for the midlatitudes. In thetropics, So can be neglected with respect to LPo andLEo; this is clearly not the case in the midlatitudes. InFEBRUARY 1992 SHEU AND CURRY 269the tropics, L(Po - Eo) is 338 W m-2, while the corresponding value in the midlatitudes is nearly zero. Also shown in Table I is the correlation coefficientbetween the budget values and independent values ofSo, LEo, and LPo for the twice-daily gridpoint values.The correlations are not seen to be particularly high,although all are significantly different from zero at the99% confidence level. This indicates that while themean monthly budgets show reasonable consistency,there is a larger random error for the instantaneousgridpoint values.c. Interpretation of mean cloud cover The vertical profile of monthly mean cloud covershown in Fig. 7 has a maximum of 40% at the 850-mblevel, and the layer cloud cover decreases to below 10%above 400 mb. A comparison of Fig. 7 with the verticalprofile of relative humidity shown in Fig. 1 indicatesthat there is no simple diagnostic relationship betweenmean monthly cloud fraction for a layer and the meanlayer relative humidity. An interpretation of the verticalprofile of mean monthly cloud cover can be made byconcurrent examination of the vertical profiles of theheat and moisture budgets, shown in Figs. 2 and 3. While the three-dimensional moisture convergencedrops to zero rapidly at high levels, the three-dimensional heat convergence becomes relatively large andcontributes to three-dimensional relative humidity di2004006OO8OOlOOOo lo ~,o 3o 40 CLOUD FRACTION (%) ~G. 7. Vertical profile ofareally averaged mean monthly layer cloud fraction.BOvergence (see Curry and Herman 1985 ). The majorityof heat convergence at high levels comes from adiabaticwarming, which results in the dissipation of clouds.Between 800 and 500 mb, there is three-dimensionalheat flux divergence plus three-dimensional moistureconvergence, resulting in relative humidity convergence in this layer; this is a layer of relatively highcloudiness. Below 800 mb them is little large-scale relative humidity convergence, the cloudiness associated principally with turbulent transport of moisture from thesurface. Despite the fact that maximum value ofmonthly mean relative humidity occurs at 1000 mb,the monthly mean cloudiness peaks at the 850-roblevel. The failure to account for the high cloudiness atthe 850-rob level by relative humidity can be attributedto the role of other boundary-layer characteristics, particularly the static stability. The more stable the layer,the morn likely it is that the moisture released fromthe surface will be trapped in the layer. The stabilityparameter O0/Op is calculated for both the 1000- and850-mb levels, with resulting values of -0.0228 and-0.0420 K mb-~, respectively. The static stability at850 mb is seen to be almost twice as large as at 1000mb. The moisture transported out of 1000 mb is apparently trapped in the 850-mb layer, so that the meancloud fraction is larger at 850 mb than at 1000 mb. In general, middle clouds are formed primarily dueto the benefit from large-scale three-dimensional moisture convergence; and low-cloud formation dependson surface moisture flux and the static stability.5. Relation of budgets and cloud characteristics to the synoptic situation Analysis of the mean monthly budgets concurrentlywith cloud observations and surface precipitation, latent and sensible heat fluxes allows the gross consistencyof the monthly heat and moisture budgets to be assessedand an interpretation of the mean monthly cloud coverto be made. However, hidden in the mean values area series of baroclinic waves with vastly different heatand moisture budget characteristics in different portions of the wave. In this section, the heat and moisturebudgets for different synoptic situations are examined. Figure 8 compares the mean heat and moisture budgets for surface anticyclonic and cyclonic conditions.The criterion for selecting a grid point as correspondingto a surface anticyclone/cyclone was simply that the1000-mb vorticity be in the lowest/top 20%. Shownin Fig. 9 are the vertical profiles of mean layer cloudcover for the corresponding anticyclonic-cyclonicconditions. It is seen that cloud fraction is substantiallygreater under cyclonic conditions at all levels exceptat 200 mb, where cloud fraction is very low in bothsituations. Comparison of the heat and moisture budgets forthe anticyclonic and cyclonic situations in Fig. 8 shows270 MONTHLY WEATHER REVIEW VOLUME 1202OO4006OO8OOIOO0SURFACE CYCLONEi ' /200 '4006008001000-20 -10 0 10 20 -C day- ~-3 -2SURFACE ANTICYCLONE-20-C day- ~'1'o2O..........? -~ o , 2 3 .~ .... .~ .... .i ........ ~ .... ~' ' '--3 -3 do>? m.3 g rn g day''~FIG. 8. Comparison of average heat and moisture budgets for cyclonic and anticyclonic situations.that all of the budget terms are of opposite sign at nearlyall model levels. In comparing the heat budgets, it isseen that the three-dimensional heat flux convergenceterm is positive for the anticyclone and negative forthe cyclone, the adiabatic warming term being the individual term of largest magnitude in both cases. Thethree-dimensional moisture flux convergence term ispositive at all levels for the cyclonic cases, while forthe anticyclonic cases the three-dimensional/noistureflux convergence is negative below 500 mb with small,slightly higher values at higher levels. For the cyclonicsituations the residual heat source is positive at all levelsexcept 400 mb (reflecting large radiative cooling rateat this level), and there is a moisture sink at all levels,the maxima of both terms occurring at 850 mb. Theseresidual terms are consistent with large-scale condensation .occurring at all levels during disturbed conditions. By contrast, in the anticyclonic cases, Q2 is positive at all levels, and only at 1000 and 850 mb is thereevidence of large-scale condensation, accompanied bya moisture flux from the surface. It is also of interest to examine the heat and moisturebudgets ina longitudihal cross section through a baroclini.c wave. Figure 10 shows the surface pressure fieldand the 500-mb heights for 1200 UTC 3 January, theregion of interest lying within the box. Figure 11 represent~ a longitudinal cross section at 46.875 -N of themeteorological fields across the baroclinic wave. 'Therelative humidity fibld is closely tied to the vertical velocities, thedriestregions associated with the strongestsinking motion tO the west of the upper-air trough, andin the region of the surface cold-air advection. Comparison of the relative humidity field with the cloudcover shows that peak cloud fractions are displacedapproximately 3.5- longitude to the west of the peakrelative humidities. The highest cloud amounts, particularly near -19-, correspond to low local relativehumidities, particularly above 800 mb. It is suggestedfrom examining this cross section that the clouds donot respond instantaneously to the large-scale relativehumidity field, but take a period of time on the orderof hours to adjust to relative humidity field in termsFEBRUARY 1992 SHEU AND CURRY 271200 l400 ,,,, '~ %~. "~, 'x600 ~ ~,%, '~ '~~800 '~ ~ ~ ~ i ~ , i , ~ ,o io io Cloud Fraotion (%~G. 9. Comparison of cloud cover for cyclonic (solid)with anticyclonic (dash) situations.1000of evaporation and condensation. This is further supported by examining the Q~ and Q2 fields shown inFig. 11. As the cloud fields progress from west to east,there is a moisture soume as the cloud evaporates onthe westward side and a moisture sink as condensationoccurs on the eastward side.6. Cloud diagnostic relationships Central to all cloud parameterizations in GCMs, bethey diagnostic or prognostic, is the determination ofa grid-scale threshold relative humidity below whichcloud does not occur. It is observed that cloud formation occurs well before the large-scale relative humidity reaches 100%, which is believed to be associatedwith subgrid-scale fluctuations in relative humidity.Values for the threshold relative humidity RHc thathave been employed in GCMs include: 100% (Somerville et al. 1974); 97% (Wetherald and Manabe 1980);and 80% (Sundqvist 1978). More complex specifications have been made, whereby the value of RHc varieswith height in the model: 80% for low and high clouds;65% for midclouds (Slingo 1987), from 38% to 56%(Mitchell and Hahn 1990); 92.5% for the lowest twomodel levels and 85% for higher levels (Smith 1990);and polynomial function of pressure, with RHc varyingfrom 97% at I000 mb, reaching a minima of 43% at700 mb, and increasing 85% to 200 mb (Geleyn 1981 ).Mitchell and Hahn (1990) have pointed out the dependence of RHc on the characteristics of the modelinitialization and physics, since significant errors seempossible in model moisture fields. To determine RHc, a scatter diagram of observedcloudiness against analyzed relative humidity can, inprinciple, be employed. It is, however, difficult to determine RHc from Fig. 12 (note that relative humidifiesat levels 500 mb and above are determined with respectto ice, since temperatures at these levels are generallybelow -30-C). The relationship between fractionalcloud cover and model relative humidity deteriorateswith height; at 200 and 300 mb there is in fact a negativecorrelation between cloud fraction and relative humidity, and at 200 mb no clouds occur at relative humidities (with respect to ice) exceeding 65%. It would500 MBSURFACE FIG. 10. Surface pressure field and 500-mb heights for 1200 UTC3 January. Region analyzed here is indicated by the box (40--60-N,10--50-W).272 MONTHLY WEATHER REVIEW VOLUME 120 (o (mb sec-t) ~ o,1~o.o5 . -50 -40 '-30 -20 -10 RELATIVE HUMIDITY (%) 800,ooo -40 -~ -~0 -~ 0 CLOUD FRACTION (%) 2o0 -~ -40 -30 .20 -10 Ol/Cp (-C day-~) :50 -40 .30 -20 - ~ 0 Q2 (g m-3 2001~0 ......... , . -50 -40 -30 -2~ -~0 kon~itudo ~G. 11. Lon~tudinal cross ~ction at 46.875-N of cloud fraction (%), ~lative humidity (%), vertical p velo6ty (rob s-~), Q (-C day-~), and Q2 (gm-3 day-~)-appear that this relationship at 1000 mb is so goodbecause of the fairly large number of surface (ship)observations in this region. At higher levels, the analyzed moisture field becomes increasingly' dependenton the model vertical transport of moisture (i.e., theconvective parameterization). From this. analysis itFEBRUARY 1992SHEU AND CURRY273I .... ' - '60 ~000 mb . ,, ]500 mb . '':. -.'. ~';.:',~..~.~.'~ - . : ' '.,'~,.h.' ~ - ' - ' . ..~ '"c~' :':':r~ , - .~'.,, '.~,~ . . . .. .... ... :.;~,, : - .:: ~,,. ~. ~. .. .' ~......:. :.~ '~ .::.:~.. :~'~.:~: :.~?~ - . . - :.~...'~ ~ , ~~ .' .... . ~.,~ . ~ .... - ... '.- : ;: .~ :.~ ~...~::.-?~ ' ' ' '.~e' ~a~ ~ . :~ - ~,~ ~&.~ [ - ' : ':.'- '-' '~ae~n - . . . - . ...' . - . .,~'~.~?..;, :.'.~ : ... ~:,~:~:~ ~?~ ~ . . ..,....-:. . .,~ ..::..:,-.z~.:~o::;.~ ' '~' '.~;n2;? ~ . '.;;' : . .... ..-,.~o~ . . :-~':?~ ~ ~ .' .,.z .. -"~:.:-.'..."::'.':.e':x.~:?~.~%: ., -:."' ~a?~O ~ ~ ..... ~ ,. ,:. /.. .... . ~..-~...,;.....~.~:...~:,~:~ - ' '~':: ~ ~ ,o ' - "" ' -.". ',' "~ '~. ', :','.~a..~.~ . - ,. ~ - ~ * ., ,,..... ~-~ ~.~ ~ - ... ~ .. . .... . ... ...... ~. I '' ~' ' '~. ~ - .~..'~.*':"~",. -.'.~ ~ ~ t ...., .v ...,,. ~: .....~., ~..:. ~, -z...:~--..,~,,,. ,~ - .. ,::~,~?~ ~:'~ ~ .- .. ....... . ......... ~..,_ ....... ....,.~. I -" ' - ' ~' .~' ,' '~, '. ~.',~,'.~ e~.-.'~ ~.~:0~:,~ '~ '.'~ ~' , I t ~ ' ~'. 2~ '.~"".~ ~ ~.' 'x '~.'.' :~ '.~.*~ ?~ ,,.. ..... , ~ . . .~.n ~'.." ~ .~"~ .' '~. - *.,' ea*'.'~ n. a.-t,,..c~ - .".:~:.,. . - ~-, ...... .. ~ ~ ....v', ~ -~. ,., .... I ~..:.., ~,.:,Y...~?' p2~ TM~ '~.~-~ . .~ ~l~:;~ '~ ~'~~ ', ~~ ~ ~o! ~ :~ g.0! o. , o ~; 0[ 0 ~0 4~ 60 ~ 1~ 0 ~ ~ ~ 80 ~ RELA~VE ~!D~ (%) RELATIVE HUMIDITY (%) - ~'-8-50 mb ..... ' .'' ..:. ". "-'.'..:'.'..~-;;:--~-~ '~300 mb .... ~ ............ ~ ---' ~ ' " ' ' ' ...... ' ' ' ' :' '' ' ' '' ' ~r ' .... ' ' ' ' ' :~,~..~~ :~ .~. !~ ~, ~ "'~.~ '~~.' ' ' ' ": ...':.'.:;' .' ' ' ' .' ......," ~. . - - . ~:.'~ : .:? ' ~ .'.~., :~ ,.~.~:'- ;., ~~ a~ j . - . ~ .~... ~... ~- ~., ~ 4 ~~ : ..... .... .. :. ~,.~: -, :~,:~ ...'-:.: ~ . ... ;..., ...:.~,(,~.~;~.~ ,t . . .. ....: . .-;.~: ~...'. ,. ~'I. '. ' "':"::"' "'~'~: ~:'n~~'' ~'. : '' ':' "-'.'' ".'~?" ." " ......... ,.....~.~:~:.,,.:,~~ ~......,....., .,-...::.., ........~ .~ ... ..... ,.,.. ,~.~. ::~ ' . ' - ' -. '.'..,2,.'."~-.~."'~.~, ~ ~ . ... ...... . ,~ .*. ,:y~.~ ~,~ ... ~ ~." -. ':'-:-Z..:~'.::,.'~..; ' ;':.~'."' - -, .., . .. :.. ,: ..::. :.::,~.:~.~~ . .. .....: .... .,..: ~ ...... :.-. ~.~ :.-... .., , . ~ .1' ..:....- -.~,~.~ -~~ , . .: . - ...... ...~,. ....... . ~ : . :. ,, ~.,..-.~ .~. ~~ ,' ~ - .. , . .. %. .- .... .. . o ..... - ...... :.:~:.,.:~.=:~., ,.. ., ,,.' :'~ ~ .~' ~.~-~ .. ~.. , .~.:. :..~ ..~:.~ 7..~.-~::,.-'~.'...: - ....... ~ ~ ' - - '' .... - :~'~-' :~;~'~:~ ~'. ;.~-~.~.~c::,b'.'a~...:: ~,.;-..~. r....' .' .... ., ,/..- .~..., ~, ,-,~.-~,~:~ : - - .- ,~ ~..~.~ - -~ .+ .~ - .. .. '.~.7 ~.t .... ,,: .. - . ' . .. ' -'- 7':..~ ~... ~'~.~.,. ~ .. ,~., :; :,:,~. ~.~. ~',~~, ~ . ..~. ~..~.... -~'. "~~~~~.~ ~,.':".'~ :..~.. ~. ,,.~ ...,...,.: ~... ~., ~.~.:... :..... L '~.'~/~ ~';~ ~?~'".~:~.~' '.t~ '..'..' -, ....... , ........ ..-~ ,. .... . ....... ~ '~'~~ '~~ ~-_~.,~ ..: ..L.-.... o~ ~ '-. ',~:~ '~--'-~~. '~ o ' - ~ ~'_'~ ~; .... 0 20 ~0 ~ ~ i ~ 0 ~ 40 ~ ~ 1 ~ RELATIVE HUMIDITY (%) RELATIVE HUMIDITY (%) *'0oI .. .. ....:.,.~ 700' mb ' ' ~ "'" ; '"" : '.'"? :..'::.'iA ao~- 60oRELATIVE HUMIDITY (%)200 mb t" .': ::.- ' .-'~.' " ..20 ~'-t'"-' * I '. .' :'. '~~C~;.~,.,~:.~'.,. :' :':.-': :-.....I~l~-'~-~;'~:'~.,':~, ~ .v....'~.4a,~.~.~-,.~,O..;,..'.~ ,...,.....,, . .o %~n~ ~_~x~n: :."~; - .,':.~ :~,. .... 0 20 40 60 RELATIVE HUMIDITY (%) *FIG. 12. Scatter diagrams of cloud fraction versus relative humidity at each analysis level. Asterisks refer to relative humidity with respect to ice.would appear that the model is not transporting sufficient moisture to high levels. An approach to determine the threshold relative humidity, taking into account inadequacies in the analyzed relative humidity field, was recently proposed byMitchell and Hahn (1990) in which the cumulativefrequencies of observed cloud fraction and analyzedgrid-scale relative humidity are used. The point of using274 MONTHLY WEATHER REVIEW VOLUME 1.20 TABLE 2. Threshold relative humidity determined after Mitchelland Hahn (1990) and the exponent in cloud fraction predictionequation (15). Thresholdp (mb) relative humidity Exponent1000 73 2.8850 42 3.6700 29 2.2500 51. 3.0400 83* 2.8300 46* 1.5200 22* 2.3* Asterisks refer to relative humidity with respect to ice.this technique is that it reflects the statistical propertiesof the model's forecast RH fields. Therefore, if there isa model bias in relative humidity, it can be partiallyaccounted for in the determination of RHc. This technique consists of first calculating the cumulative frequency of the model RH and the fractional cloud-coveranalysis for the same layer, region, and time. The frequency distribution of the cloud analysis is then projected onto the RH analysis, yielding a specification ofcloud cover as a function of RH. RHc is determinedfrom this projection to be the value of RH corresponding to a cloud amount of zero. The threshold relativehumidity determined from this technique at each levelis listed in Table 2 in which RHc varies from 22%to 83%.a. Relative humidity relationships In GCMs, relative humidity has been the most commonly used parameter to diagnose cloudiness. A linearrelationship between relative humidity and cloudinesshas been employed by Kasahara and Washington( 1971 ), Gates and Schneider (1977), and Schneideret al. (1978), the latter including a vertical velocityconstraint. A quadratic relation has been adopted bySlingo ( 1980, 1987) in diagnosing layer clouds. In addition, Slingo emphasized the importance of static stability in low-cloud prediction. The following algorithm is the general expressionfor cloud diagnosis from relative humidity (afterMitchell and Hahn 1990): ( RH_-_RHc Ix Cg ~ ~RHrn - RH-/ (15)where CF is the predicted cloud fraction, RH the relative humidity, RHc the threshold relative f, RHm therelative humidity greater than which (usually 100%)the cloud fraction is unity, and x the exponent. Theexpression is similar to the Slingo (1987) algorithm inwhich the exponent is 2. Mitchell and Hahn proposeddetermining the exponent in Eq. (15) by fitting to therelative humidity-cloud fraction curve, which is obtained from the projection of the frequency distributionof the cloud analysis onto that of the RH analysis. Thebest-fit exponent is determined to lie between 1.5 and3.6 at different levels,, as shown in Table 2. Smith ( 1990; appendix C) developed an expressionfor cloud fraction in terms of relative humidity usingthe cloud distribution concepts developed by Sommefiaand Deardorff (1977) and Mellor (1977). The parametefization takes the following form:CF = 4 cos + L[ 3 /RH- RHc\] where O= [2V-~ l-RHc cos- ~ ..... for RHc < RH < (5 4-- RHC)/6. for (5+RH~)/6<RH<I. (16) Table 3 gives a comparison of the observed meanmonthly layer cloudiness and the predicted cloudamount at each level, using the Slingo (1987), Mitchelland Hahn (1990), and Smith (1990) parametefizations. In calculations using the Mitchell and Hahn(1990) and Smith (1990) parameterizations, the va]~uesof RHc in Table 2 were employed; for the Slingo (1987)parameterizafion, the values of RH- reported in ~hatstudy were used (note that at 1000 mb the stabilityadjustment is not employed here in using the Slingoparameterization). Total cloud amount was determined from the parameterizations by assuming maximum overlap for adjacent layers, and random overlapfor cloud layers separated by a clear layer. In parentheses is shown the coefficient of correlation betweenthe parameterized and observed cloud fractions, usingtwice-daily p~ridpoint values. In terms of mean monthlylayer cloud fraction, the Mitchell and Hahn (1990)and Smith (1990) values agree significantly better with TABLE 3. Comparison of observed and predicted monthly :meancloud fractions (correlation coefficients of observed gfidpoint valueswith predicted values are given in parentheses; * indicates corre]tationis not significantly different from zero at the 99% confidence level).Slingo Mitchell and Smithp (mb) Observed (1987) Hahn (1990) (1990) 1000 26 22 (0.032) 23 (0.031) 36 (0.037) 850 40 15 (0.183) 36 (0.222) 37 (0.223) 700 29 12 (0.311) 30 (0.399) 21 (0.400) 500 18 15 (0.370) 22 (0.415) 21 (0.413) 400 7 15 (0.236) 11 (0.209) 9 (0.200) 300 5 0 (0.113) 5 (0.221) 2 (0.212) 200 2 0 (0.000)* 2 (0.044) I (0.046)Total cloud cover 65 55 (0.350) 66 (0.378) 62 (0.382)FEBRUARY 1992 SHEU AND CURRY 275observations than does the Slingo (1987) paramete.rization, particularly at the 850- and 700-rob levels. Total cloud fraction is best parameterized by Mitchell andHahn, with the Smith parameterization performingadequately. The correlation of the observed with theparameterized layer cloud fractions for twice-dailygridpoint values is generally poor, particularly at 1000mb, although the correlations using the parameterizations of Mitchell and Hahn and Smith are slightly largerthan those using the Slingo parameterization. From these results, R is seen that appropriate tuningof a diagnostic relative humidity-based parameterization can result in accurate parameterized meanmonthly total cloud amount for the region, and layercloud fractions to within 5% of observed layer cloudfractions. However, this type of cloud fraction parameterization, as indicated by the low correlations, appearsto be unable to diagnose layer cloud fraction on thesmaller time and space scales that are undoubtedly required for obtaining the correct local cloud radiativeand hydrological feedbacks with the dynamics.b. Other diagnostic relationships In the previous discussion, it was shown that diagnostic parameterizations based solely on relative humidity are not very successful for daily gridpoint values.Since large-scale layer clouds can also be related todynamical processes, we examine here whether gridpoint layer cloudiness is diagnostically related to vertical velocity, moisture and relative humidity transport,height tendency, static stability, and surface heat andmoisture flux for low clouds. Table 4 gives the correlation of layer cloud fractionwith vertical velocity. It is seen from the table that thecorrelation of cloud fraction with vertical velocity ishigher even than those for relative humidity as shownin Table 4, particularly for levels between 700 and 300mb. Correlations of cloud fraction with height tendency, horizontal moisture advection, and three-dimensional relative humidity convergence are all insignificantly different from zero at the 99% confidencelevel and are not shown here. Table 5 gives the correlation of the 1000- and 850mb layer cloud fraction with static stability and surface TABLE 4. Correlation coefficients between cloud fraction andvertical p velocity ~o. Asterisk indicates correlation that is notsignificantly different from zero at the 99% confidence level.p (rob) Correlation1000 -0.0021'850 -0.1851700 -0.3733500 -0.4436400 -0.3822300 -0.3019200 -0.0188'TABLE 5. Correlation coefficients of low-level cloud fraction withsurface sensible and latent heat fluxes and static stability.p (mb) Sen~b~heat Latent heat Static stability I000 0.1604 0.1312 0.1648 850 0.1096 0.0633 0.0945sensible and latent heat fluxes. Particularly at 1000 mb,correlations with the sensible and latent heat fluxes areseen to be larger than any other parameter that hasbeen tested. All correlations in Table 5 are significantlydifferent from zero at the 99% confidence level.7. Summary and conclusions This study has examined the relationships betweengridscale cloudiness and the large-scale environmentin the North Atlantic. The ECMWF initialized analysesand the U.S. Air Force 3DNEPH were employed toconstruct a joint time series of gridpoint values ofcloudiness and large-scale meteorological fields forJanuary 1979. Heat and moisture budgets were determined following the techniques ofYanai et al. (1973).Observations of precipitation using satellite microwavemeasurements and calculations of surface sensible andlatent heat fluxes by bulk aerodynamic method provided a check on the accuracy of the heat and moisturebudgets. It was determined that the mean monthly values of Q~ and Q2 were correct to within a factor of 1.5,although individual gridpoint values may have a largererror. The Bowen ratio and value of L(Po - Eo) determined for this North Atlantic dataset showedmarked differences to values determined for the tropics(e.g., Yanai et al. 1973). The North Atlantic Bowenratio was determined here to be 0.58, compared to atropical value of 0.076. In the tropics, L(Po - Eo) was338 W m-2, compared to a value of nearly zero forthis dataset. The most significant term in the mean monthly heatbudget at lower levels was the horizontal cold-air advection, which was nearly balanced by the large-scaleresidual heat source. Above 500 mb, the adiabaticwarming and vertical transport terms became increasingly dominant, and the horizontal transport less significant. The residual term became negative above 500mb. Analogous to the heat budget, the horizontalmoisture advection term was dominant at lower levelsand nearly balanced by a large-scale residual moisturesource. Positive vertical moisture transport dominatedat the upper levels and was offset by the large-scaleresidual moisture sink. At levels below 800 rob, thepositive heat and moisture source was associated withthe transport of sensible and latent heat from the surface. The negative moisture source and positive valueof(Q~ - Q,~) at levels between 800 and 300 mb wereconsistent with large-scale condensation occurring atthese levels. Interpretation of the mean monthly cloud276 MONTHLY WEATHER REVIEW VOLUME 120cover in the context of the heat and moisture budgetsshows that middle clouds are formed primarily due tothe benefit from large-scale three-dimensional moistureconvergence; and low-cloud formation depends onsurface moisture flux and the static stability. The quality of the upper-level moisture analyses was deemed tobe too poor to make inferences about high clouds. Heat and moisture budgets were also compared foranticyclonic and cyclonic situations. Cloud fraction issubstantially greater under cyclonic conditions at alllevels except at 200 rob, where cloud fraction is verylow in both situations. Comparison of the heat andmoisture budgets for the anticyclonic and cyclonic situations shows that all of the budget terms are of opposite sign at nearly all model levels. For the cyclonicsituations the residual heat source is positive at all levelsexcept 400 mb (reflecting large radiative cooling rateat this level), and there is a moisture sink at all levels,the maxima of both terms occurring at 850 mb. Theseresidual terms are consistent with large-scale condensation occurring at all levels duririg disturbed conditions. By contrast, in the anticyclonic cases, Q2 is positive at all levels, and only at 1000 and 850 mb is thereevidence of large-scale condensation, accompanied bya moisture flux from the surface. Heat and moisture budgets in a longitudinal crosssection through a baroclinic wave were also examined.The relative humidity field is closely tied to the verticalvelocities, the driest regions associated with the strongest sinking motion to the west of the upper-air troughand the surface cold-air advection from the south.Comparison Of the relative humidity field with thecloud cover shows that peak cloud fractions are displaced approximately 3.5- latitude to the east of thepeak relative humidities. It is suggested from examiningthis cross section that the clouds do not respond instantaneously to the relative humidity field, but take aperiod of time on the order of hours to adjust to thelarge-scale relative humidity field in terms of evaporation and condensation. This is further supported byexamining Q~ and Q2. As the cloud fields progress fromwest to east, there is a moisture source as the cloudevaporates on the westward side and a moisture sourceas condensation occurs on the eastward side. Determination of the grid-scale threshold relativehumidity below which cloud, on average, does not occur was determined after Mitchell and Hahn (1990)to vary with height, ranging from 22% to 83%. Mitchelland Hahn (1990) have pointed out that the thresholdrelative humidity should reflect the statistical propertiesof the model's forecast relative'humidity fields, so theactual values of the threshold relative humidity andtheir variation with height will be model dependent.The relationship between fractional cloud cover andmodel analyzed relative humidity was determined todeteriorate with height; at 200 and 300 mb there was,in fact, a negative correlation between cloud fractionand relative humidity, and at 200 mb no cloucls occurat relative humidities. (with respect to ice) exceeding65%. From this analysis it is suggested that tbe modelis not transporting sufficient moisture to high levels. Comparison of the observed mean monthly layercloudiness and the predicted cloud amount at each levelusing several relative humidity-based diagnostic cloudparameterizations. It was shown that appropriate tuning of a diagnostic relative humidity-based parameterization can result in accurate parameterized meanmonthly total cloud amount for the region, and layercloud fractions to within 5% of observed layer cloudfractions. However, this type of cloud fraction parameterization, as indicated by the low correlations, appe:xrsto be unable to diagnose layer cloud fraction on thesmaller time and space scales that are undoubtedly :required for obtaining the correct local cloud radiativeand hydrological feedbacks with the dynamics. Thecorrelation of cloud t?action with other meteorologicalparameters was investigated; correlation of cloud fraction with vertical velocity was significant, as was correlation of low-cloud fraction with static stability andsurface heat fluxes. The deficiencies of purely diagnostictechniques emphasize the need to develop more physical models of the mechanisms controlling cloud cover,including additional prognostic equations for cloudprocesses. From the results of this study it is inferred that meanmonthly cloud amounts and heat and moisture budgetscan be determined accurately from the ECMWF axialyses, although the instantaneous gridpoint values canshow large errors. This may reflect deficiencies in ,ourunderstanding of the diabatic processes associated withlarge-scale processes and may also reflect problems vhththe analyzed humidity fields. We cannot expect a realistic parameterization of cloud in terms of'grid-scalemoisture until we are confident of the grid-scale moisture fields. Acknowledgments. Comments from P. J. Smith,G. F. Herman, and Harshvardhan are gratefully appreciated. This research was supported by NSF ATM850527 and DPP-8858830.REFERENCESAnthes, R. A., Y.-H. Kuo, and J. R. Gyakum, 1983: Numerical sim ulation of a case of explosive cyclogenesis. Mon. IFea. Rev., 111, 1174-1188.Arking, A., 1991: The radiative effects of clouds and their impact on climate. Bull. Amer. Meteor. Soc., 72, 795-813.Arpe, K., 1985a: Comparison of FGGE Level IIIB analys6's by ECWMF and by GFDL for the period 27 Februm~ to 7 Iv[arch 1979 taking recent improvements of the ECMWF analysis system into account. Report of the Seminar on Progress in Diagnostic Studies of the Global Weather Experiment, GARP Special Re port No. 42, WMO, Geneva, Switzerland. III, 38.-42.~EBRUARY 1992 SHEU AND CURRY 277 , 1985b: Fit of FGGE level lib analyses by ECWMF and by GFDL observational data during the period 27 February to 7 March 1979. 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