Atmospheric Research 124 (2013) 170–180

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Atmospheric Research

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Precipitation correlation between convective availablepotential energy, convective inhibition and saturation fractionin middle latitudes

Sanda Barkiđija⁎, Željka FuchsPhysics Department, Faculty of Science, University of Split, Split, Croatia

a r t i c l e i n f o

⁎ Corresponding author. Tel.: +38 5 9829 8028.E-mail address: sanda@pmfst.hr (S. Barkiđija).

0169-8095/$ – see front matter © 2013 Elsevier B.V. Ahttp://dx.doi.org/10.1016/j.atmosres.2012.12.010

a b s t r a c t

Article history:Received 19 January 2012Received in revised form 4 November 2012Accepted 19 December 2012

Saturation fraction (SF), convective inhibition (CIN) and convective available potential energy(CAPE) are discussed to see with which of these parameters' precipitation rate is bettercorrelated in the middle latitudes. The study is based on measurements from 20 Europeanstations for the period of 1972–2009. We also use the results of the Global Forecasting System(GFS) model to see how mentioned parameters behave in numerical models.Our research results indicate that CAPE is not a good measure of precipitation rate for all latitudes,although, in model results, CAPE and precipitation rate are found to be better correlated for middlelatitudes then in higher latitudes and tropical regions. The best correlationwith precipitation rate inmiddle latitudes is one with SF. Our results suggest that moisture is underestimated in numericalmodels for middle latitudes and encourage further work in including SF or similar parameter intoprecipitation parameterization in addition to the current one.

© 2013 Elsevier B.V. All rights reserved.

Keywords:Precipitation parameterizationConvectionMoisture

1. Introduction

Precipitation is one of the most important phenomenathrough which we experience the weather and it is veryimportant to be able to model it properly. Precipitation entersthe primitive equations in the models in a parameterizedform. However, convection in numerical models is still hardto parameterize. Precipitation will form if there is a localportion of the atmosphere which is saturated with respect towater vapor, so that the water condenses and precipitates.The major physical process that leads to precipitation inmiddle latitudes is cyclonic forcing. Inmiddle latitudes a minorpart of precipitation development processes are due to theconvective forcing, but in the flash-flood producing storms,convection plays an important role, especially over complexorography regions (Doswell et al., 1996). The above reasoninghas historically led to most numerical weather predictionmodels emphasizing precipitation parametrized in terms of

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cyclonic forcing. Still, precipitation parameterization throughcyclonic forcing leads to certain problems, e.g. the modelstend to give inaccurate results when convection plays a majorpart in the precipitation and when fronts are negligible. Thisis mostly the case in the tropics. Furthermore, even if thecontribution of local convection is small, ignoring its influencemight badly impact model results because of non-linearityof the governing equations. Parameterization of convectiveprecipitation continues to be needed to improve precipita-tion forecasts in both the tropics and mid-latitudes for manyapplications that use numerical weather prediction models(Frank, 1983).

In the quantification of the local convective-storm forma-tion and its organization the larger-scale vertical distributionsof temperature, humidity and horizontal wind are referredto as environmental controls. They also include vertical shearof horizontal wind over the lower half of the troposphere,convective available potential energy (CAPE) and convectiveinhibition (CIN). All severe thunderstorms require mois-ture, CAPE and some lifting mechanism to trigger themwhile CIN has a control on where convection develops but isnot a requirement for convection. Products between those

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variables, computed from global reanalysis data, stronglymatch the distribution of deep convective cloud observations(Brooks et al., 2003b). The question that arises is the following:how do we incorporate CAPE, CIN, moisture and instabilitymechanisms into a precipitation parameterization that will bevalid for all weather systems?

Convective development and the precipitation rate innumerical models are mostly related to CAPE (Brooks et al.,2003a). Many of the theoretical concepts such as statisticalequilibriumor quasi-equilibrium (Arakawa and Schubert, 1974;Emanuel, 1987 and many others) are based on this parameter.Furthermore, it is useful to consider CAPE and shear over adeep layer of the atmosphere to distinguish between signifi-cant severe thunderstorms and less severe events (Rasmussenand Blanchard, 1998; Craven et al., 2002; Molini et al., 2011).The probability of the environment being associated with asignificant severe storm increases if the environment movestowards the deep shear and higher values of CAPE (Brooks andDotzek, 2007a). Donner et al. (2001) found that convectivevertical velocities are greater over land than ocean, even forsimilar CAPE values.

The parameterization of convective mass fluxes in mostGlobal Circulation Models (GCMs) is based on the consump-tion of CAPE. CAPE and deep shear tend to be out-of-phase intheir annual cycle (Brooks et al., 2007). Looking into theprecipitable water and CAPE from observations duringsummer months in southern Arizona, Dixon (2008) showedthat precipitation likelihood increases with CAPE, and thatprecipitation is far more likely to occur when CAPE values aregreater than 600 Jkg−1. Früh and Wirth (2007) analyzedseveral soundings with CAPE greater than 3000 Jkg−1 inmiddle latitudes and found that absolute differences of CAPEbetween various processes are similar to those in tropicalmean conditions. Nicholls and Mohr (2010) found both largerCAPE and stronger impact of CINpresent during intense eventswhen compared to less-intense occurrences in West Africaregions. Computation of CAPE may have various issues. Frühand Wirth (2007) found that CAPE is sensitive to parametersused to initialize a parcel and is affected by magnitude of thebuoyancy and the thickness of the layer for which the parcel ispositively buoyant. They also showed that isobaric freezing ata rather warm temperature (e.g.−5 °C) yields to a significantoverestimate of CAPE.

The other parameter used to capture the interactionbetween the local convection and large scale processes isCIN. Mapes (2000) stated that a strong CIN dependence of adeep convection is impossible to justify within traditionalcumulus-dynamics reasoning. Mapes used a toy model withparameters set such that CAPE variations control convection.He found that when CAPE control dominates, all waves aredamped by convection, but when CIN control dominates,“stratiform instability” generates large-scale waves. This mech-anism includes lower-tropospheric cooling by stratiform pre-cipitation, which preferentially occurs where the already coollower troposphere favors deep convection, through smallervalues of CIN. Raymond (1995) showed that surface fluxestend to decrease CIN until enough moist convection is able togrow from these roots and establish “boundary layer quasi-equilibrium”. Raymond and Fuchs (2007) showed that CIN, inparticular, was the responsible factor for the creation of theunstable convectively coupled Kelvin waves, the large scale

disturbance that is, after the Madden–Julian oscillation, themost dominant precipitable event in the tropics.

Emanuel (1994) claimed that the release of the excesssensible and latent heat may not happen exactly where it wascreated because the associated CAPE is “stored” in theatmosphere until it can be released. CIN is then the mainreason for the storage of sensible and latent heat and thesynoptic-scale processes can transport the excess heat to alocation well away from where it entered the atmosphere. Asthe release of the instability might not occur at the time andlocation of the destabilization processes that created it, theparameterization becomes very complex. Raymond et al.(2003) analyzed the data from the field project in EasternPacific, EPIC2001. They have observed that there were manycases when CAPE was large and CIN was small, but theconvection was not developed. The values of CAPE werecomparable to the ones when convection was developed.They proposed a new parameter, deep convective inhibition(DCIN) which states that deep convection over tropicaloceans needs a deep, conditionally unstable layer fromwhich the lifted parcels will reach a level of free convection.They found that DCIN correlates with deep convectiondevelopment and they proposed that the use of DCIN ismore appropriate than the one of CIN or CAPE.

Intuitively we should be able to note that the amount ofmoisture will be strongly correlated to the precipitation rate.Although humidity content is often mentioned as important,it was under appreciated until the last few decades, in theoryas well as in models. Raymond (2000) postulated that thereis a direct relation between the saturation fraction (SF) andprecipitation rate. This simple idea has led to numeroustheoretical discoveries (Fuchs and Raymond, 2002, 2005,2007; Raymond and Fuchs, 2007; Fuchs and Marki, 2007;Raymond et al., 2007, 2009; Raymond and Fuchs, 2009) inwhich themoisture closure plays an important role. Numerousother works show that the precipitation rate in the tropicsis very sensitive to the precipitable water in the troposphere(Lucas et al., 2000; Sobel et al., 2004; Bretherton et al., 2004;Derbyshire et al., 2004; Raymond and Zeng, 2005). It should benoted here that in the tropics, where the temperature does notchangemuch, the precipitablewater can be used instead of theSF. However, as that is not the case in the middle latitudes wewill use the SF parameter.

Fig. 1 shows infrared brightness temperature and inferredprecipitation rate versus SF computed from soundings in theeast Pacific and the southwest Caribbean (Raymond et al.,2007) as well as the results from a Cloud Resolving Model(CRM). There is a noticeable correlation between precipita-tion rate and SF in both data and model results.

Figs. 2 and 3 show CAPE and SF values respectivelycalculated on Global Forecasting System (GFS) model outputsfor time period March 10–May 22, 2010. The results aredivided into three sections: higher latitudes, middle latitudesand tropics. The left panels show the correlation between CAPEand SF contribution over the sea and CAPE and SF contributionon the whole planet and right one shows same, but over theland. Although we will discuss Figs. 2 and 3 in Results section,it is immediately apparent that the correlation between SFand precipitation rate is better than between CAPE andprecipitation rate even for the middle latitudes. Note that thedeep convection closure of the GFS model is based on the

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consumption of CAPE which implies an equilibrium betweenthe large-scale destabilization of the atmosphere and theconvective damping. The idea originates in convective adjust-ment schemes and in the original Arakawa–Schubert cumulusparameterization scheme (Arakawa and Schubert, 1974) andis closely related to that of convective quasi-equilibrium.

In this paper we extensively explore CAPE, CIN and SFcorrelation with precipitation rate for middle latitudes. We

Fig. 2. CAPE calculation from GFS model outputs for: upper middle latitudes (uppanels). On the left, a set of panel precipitation versus CAPE over sea (blue) in compshown. On the right, a set of panel precipitation versus CAPE over land (red) in coshown.

will do this by using the data for Europe, for the time period1972–2009.

2. Theory and measurements

2.1. Theory

Atmospheric conditions and thermodynamic control ofrainfall may be considered through Navier–Stokes equations,conservation of mass (for air and water vapor) and the firstlaw of thermodynamics. While condensate is produced byconvective and large-scale lifting, it is the net condensationor precipitation that dynamically feeds back. In this studywe consider the influence of humidity on precipitation ratethrough the SF parameter.

Raymond et al. (2007) postulated that the precipitationrate over a warm tropical ocean is related to SF rather thanCAPE. SF is a ratio between precipitable water and saturatedprecipitable water. Using SF instead of CAPE could provide analternativemodel for the forcing of precipitation. The proposedcorrelation between precipitation rate and SF is given by:

P ¼ RrSc−SrSc−SF

; ð1Þ

where Rr and Sr are reference precipitation rate and saturationfraction, respectively attained in the radiative–convectiveequilibrium, while Sc is the critical saturation fraction towardswhich the precipitation rate asymptotically rises to the infinity.

Second parameter that we focus on in our analysis isCAPE. An air parcel needs to have sufficient potential energyto continue rising without forced ascent. CAPE represents

per panels), middle latitudes (middle panels) and tropical regions (bottomarison with CAPE versus precipitation calculated for whole planet (green) ismparison with CAPE vs. precipitation calculated for whole planet (green) is

Fig. 3. Same as Fig. 2 except for saturation fraction.

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the amount of buoyant energy available for the verticalacceleration of a buoyant air parcel:

CAPE ¼ g ∫EL

LFC

Tp−Te

Te

� �dz; ð2Þ

where Tp and Te are temperature of parcel and environmentrespectively; LFC is level of free convection and EL is equilibriumlevel.

The third parameter is CIN and it represents the negativeenergy area on the soundings. It is the amount of negativebuoyant energy available to inhibit or suppress upward verticalacceleration. It is defined as:

CIN ¼ g ∫ztop

zbottom

Tp−Te

Te

� �dz; ð3Þ

where zbottom is the height of the lower level and ztop is theheight of the upper level.

2.2. Measurements

SF, CIN, CAPE and precipitation rate are calculated frommeasurements (disposable radio sonde data; source of globalradiosondes is University of Wyoming) and rain-gauge data(Haylock et al., 2008) for the period of 1972–2009. Data wasavailable for 20 European stations (Fig. 4). Each station has adifferent time period of measurements which is in the rangefrom 10 to 30 years. Sundsvall–Härnösand (Sweden) andBrindisi (Italy) are the stations that have been chosen as areference for higher and middle latitudes, respectively. Theyare also chosen because their data time period extends to30 years. As the sounding data is available twice a day, thedaily SF, CIN and CAPE values were calculated as the arithmetic

mean of the measurements at noon and the subsequentmidnight.

The upper air sounding data includes measurements ofvarious parameters (atmospheric pressure, geopotential height,temperature, dew point temperature, relative humidity, mixingratio, wind direction, wind speed, potential temperature, equiv-alent potential temperature and virtual potential temperature)at different pressure levels. To calculate the SFwemust express itthrough thesemeasured parameters. Furthermore, themeasure-ments are discrete andwe need discrete forms of the parametersin our calculation. SF is defined as

SF ¼ PWPWs

: ð4Þ

Precipitable water (PW) definition and its discrete formis:

PW ¼ 1g∫rdp ¼ 1

g∑rΔp: ð5Þ

Saturated precipitable water (PWs) definition and itsdiscrete form is:

PWs ¼1g∫rqdp ¼ 1

g∑ r

qΔp: ð6Þ

In the above equations p is the atmospheric pressure andΔp is the difference between measurement's layers:

Δp ¼ pi−piþ1: ð7Þ

r is the mixing ratio, in discrete form it is:

r ¼ ri þ riþ1

2; ð8Þ

Fig. 4. Station locations.

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while q is relative humidity, in discrete form given as:

q ¼ qi þ qiþ1

2: ð9Þ

Subsequent pi, ri and qi are measured at one measurementlevel, while pi+1, ri+1 and qi+1 are measured at the followinglevel.

3. Results

Analysis of SF, CIN and CAPE is presented in this section. Itshould be noted that the separation of stratiform and deepconvective events is not done in this study. Although, keepingin mind that CAPE precedes convection, it is possible to havehigher values of CAPE and have no convection or precipita-tion. There are also clouds which contain both stratiform andconvective parts. However, we will base our discussion onunclassified precipitation data.

Figs. 2 and 3 show CAPE and SF values calculated on GFSmodel outputs from March 10 to May 22, 2010 for the wholeplanet. The correlation between precipitation rate and CAPEis questionable in all regions; the best correlation is in thetropical ocean regions where for any value of CAPE is possibleto have high precipitation rates. SF distribution ismore uniformthan CAPE's through all regions. SF (Fig. 3) results have similar

Fig. 5. A) Precipitation rate dependence on CAPE (upper panel), CIN (middle panel) aones: probability density function for precipitation rate, CAPE, CIN and SF, respectiv

distribution to the one measured over tropics (Fig. 1), i.e. highvalues of precipitation rate are correlated with high valuesof SF and they reach some critical value of SF in all regions. Inessence, land–ocean distribution is similar for all latitudes.

Fig. 5A shows the dependence of precipitation rate onCAPE (upper panel), CIN (middle panel) and SF (lower panel)for 20 European stations (Fig. 4) for period of 1972–2009. Itcan be seen that for any value of CAPE we can have highvalues of precipitation rates, while higher values of SF arecorrelated with higher values of precipitation rates. However,results for CAPE seem to have most data points in the rangefrom 0 to 1000 J kg−1. Most of CIN values are distributed inthe range from −3000–0 J kg−1. Small absolute values ofCIN are associated with higher precipitation rates. Fig. 5Brepresents probability density function (PDF) calculated forthe precipitation rate, CAPE, CIN and SF, respectively fromupper to the lower panel. Data used for PDF calculation isthe same one as for Fig. 5A. PDF is calculated with normaldistribution where mean value for CAPE is 43.81 J kg−1, forCIN −14.10 J kg−1, precipitation rate 4.60 mm day−1 and0.73 for SF. Standard deviations are: 173.59 J kg−1 for CAPE,64.67 J kg−1 for CIN, 6.81 mm day−1 for the precipitationrate and 0.12 for SF. Precipitation rate has the highestdispersion from the mean value and SF has the lowest. PDFrepresents the probability that the random variable takes avalue in a given interval. In respect to this, most probable is

nd SF (lower panel) for Europe, for 1972–2009, B) from upper panels to loweely for Europe, for 1972–2009.

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Fig. 6. Precipitation rate dependence on CAPE (upper panel), CIN (middlepanel) and SF (lower panel) for Brindisi, Italy.

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that CAPE values in the range 0–415 J kg−1 will occur. Mostprobable values for CIN are in the range from −165 to0 J kg−1, for precipitation rate 0–20 mm day−1 and for SF0.4–1. PDF for SF data has normal distribution shape andall others are ‘half bell’ shaped. Comparison of Fig. 5A and Bshows similar shape and distribution. Probability densityfunction plots of CAPE, CIN and SF show similar distributionsfor different seasons.

Out of the analysis performed on 20 European stations,Sundsvall–Härnösand (Sweden) and Brindisi (Italy) are takenas two reference stations for two different latitude belts:middle latitudes and higher latitude regions. Those stationsalso have the longest measurement period. Fig. 6 shows CAPE(upper panel), CIN (middle panel) and SF (lower panel) resultsfor the reference station Brindisi. Smaller values of CAPEare correlated with higher precipitation rates, while thereare some cases when CAPE has a value of 2000 J kg−1 andprecipitation rate is still small. Most of the precipitation ratevalues are concentrated on the lower end of the CAPE and therelationship with precipitation rate is characterized by a steepgradient making CAPE extremely sensitive to the influence ofmeasurement errors and small perturbations. CIN reachessmall values, i.e. not more than 500 J kg−1, which allows theformation of precipitation. SF is correlated with precipitationrate (higher than 30 mm day−1) in a sense that higher SFresults in more precipitation. SF reaches critical value ofapproximately 0.9 for higher precipitation rates.

Fig. 7 shows CAPE (upper panel), CIN (middle panel) and SF(lower panel) results for Sundsvall–Härnösand. This station isin higher latitude belt and has different precipitation depen-dence on CAPE then Brindisi. There are no high values of CAPEand its distribution is confined to a small region i.e. approxi-mately in the range of 0–500 J kg−1, which is also the mostprobable CAPE range for Europe (Fig. 5B). CAPE relationshipwith precipitation rate is characterized by a steeper gradientthen for Brindisi making CAPE even more sensitive to theinfluence of measurement errors and small perturbations. CINis similar to the one from Brindisi, i.e. its small values allowprecipitation to develop, but its shape is more concentratednear zero then for Brindisi. CIN is also confined in a small rangeof values, −200–0 J kg−1. The range of values for SF is ap-proximately 0.2–0.99. SF reaches the critical value above 0.9 forhigh precipitation rates and its distribution shape is differentthan for Brindisi; it is skewed more to right. Correlationbetween SF and precipitation shows that higher SF results inmore precipitation.

Fig. 8A–B shows precipitation rate dependence on CAPEfor different seasons for Brindisi and Sundsvall–Härnösandrespectively. For Brindisi, CAPE shows change from seasonto season while that is not the case for Sundsvall–Härnösand.If we compare summer plots for these two stations, we see thatin summer time Brindisi can have higher precipitation rates forany value of CAPE. There are also large CAPE values associatedwith zero precipitation rate for summer season in Brindisi.Similar shape of CAPE for summer time for Brindisi is found inGFS model results (Fig. 2) for oceanic tropical regions. Brindisihas much more scattered plots than Sundsvall–Härnösandstation. Fall and summer are seasons with the most scattereddata at the Brindisi station (e.g. CAPE is summer time hasvalues from 0 to 3000 J kg−1). It is also noticeable that falland winter are the rainiest seasons at Brindisi station while

Sundsvall–Härnösand's season with the most precipitation issummer. In higher latitudes, lowest values of precipitationare in the fall season.

Fig. 9A–B shows precipitation rate dependence on SF forBrindisi and Sundsvall–Härnösand, respectively. The shape ofthe SF distribution does not show major changes through theseasons like CAPE does in Brindisi case, but there are stillsmall seasonal changes again for Brindisi and in particularbetween summer and winter. SF plot for fall season forBrindisi resembles Fig. 6 themost. The SF is the least scatteredat Brindisi in the summer. In particular, SF for Brindisi insummer time is in the range from 0.4 to 0.8, while otherseasons have data in approximate range 0.3–0.9. This datarange also corresponds to Sundsvall–Härnösand data for allseasons. Although Sundsvall–Härnösand SF plot does notshowmajor differences in distribution shape, its spring plot isthe least scattered. Comparing station differences, we see that

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critical SF value is always higher for Sundsvall–Härnösandthan for Brindisi and SF shape for Sundsvall–Härnösand isshifted to the right, i.e. towards larger values of SF.

Results for CIN are not shown here because CIN does notshowanymajor changes due to the seasonal or regional changes.

Lastly we look at the correlation coefficients betweenprecipitation rate and CAPE, CIN and SF, respectively (Table 1).Table 1 shows correlation coefficients for our reference stationsSundsvall–Härnösand and Brindisi as well as Milan, Praha,Lerwick and St. Petersburg. Note that all stations have similarcorrelation coefficients. Correlation between CAPE and pre-cipitation rate is almost non-existent (e.g. Lerwick 0.0067),some stations even have negative correlation (e.g. −0.0025for Brindisi) which indicates that as one variable increases,the other decreases and vice versa. In our case, we haveincrease of CAPE and decrease of precipitation rate. CIN has

higher values of correlation coefficients than CAPE (valuerange −0.0046–0.0787) but coefficients for both, CAPE andCIN, are likely to be in the noise of the data. The most con-sistent signal for moderate correlation is for SF (value range0.3189−0.4846). However, there is one high value of correla-tion coefficient between precipitation rate and CAPE, i.e. 0.938for Praha-Libus station. This might be a spurious result to-gether with Emeden–Flugplatz station (not shown here)which correlation coefficient between CAPE and precipitationrate is 0.1041.

4. Conclusions

Saturation fraction (SF), convective inhibition (CIN) andconvective available potential energy (CAPE) are discussedto see with which of these parameters is precipitation ratebetter correlated in middle latitudes. Out of twenty stations,two were discussed as representative: Brindisi (Italy) andSundsvall–Härnösand (Sweden). The idea of looking into SFcame from the study of Raymond et al. (2007).

It has been known for the last decade that precipitationdoes not correlate well with CAPE in the tropics. Our GlobalForecasting System (GFS) analysis shows that the same istrue for higher latitudes and to some extent tomiddle latitudes.Our results from the measured data for Europe for time periodof 30 years show that there is almost no correlation betweenCAPE and precipitation rate. CAPE shows a seasonal changein shape for Brindisi due to the land–sea influence and latitu-dinal dependence. The summer CAPE distribution for Brindisiis similar to the one over tropical ocean regions as the seainfluence plays an important role. Large CAPE is more thanoften found in zero precipitation rate regions in particularin southern parts of Europe. This indicates that in southernlatitudes CAPE is a necessary, but not sufficient condition forprecipitation. It can be assumed that although the atmosphereis unstable, there is not enough humidity for precipitationformation. There is likely not enough lift for precipitationformation which might be the reason why often precipitationdoes not occur with CAPE in the tropics.

Raymond et al. (2003) analyzed the data from a fieldproject in Eastern Pacific. They have observed that there weremany cases when CAPE was large and CIN was small, butconvection was not developed. The values of CAPE werecomparable to the ones when convection was developed.Convection becomes much more likely as CIN values becomesmall. In our study we found that small values of CIN arecorrelated with high precipitation rates. This was the case inboth, higher and middle latitudes.

Our work on SF shows that SF has a better correlationwith precipitation rate than CAPE and CIN, especially inhigher latitudes, and SF does not show major dependenceon seasons. SF correlation with precipitation rate in middlelatitudes is not as good as in the tropics, but the shape of thedistribution from the tropics is still present. This shows thatprecipitation parameterization in middle latitudes should besensitive to moisture parameters perhaps to a greater extentthan to CAPE. Over the whole domain of its possible values,SF gently and almost constantly rises. The estimation of pre-cipitation rate from SF is robust in the face of measurementerrors, especially if we compare it to the CAPE which fallssteeply and is extremely susceptible to the influence of

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Fig. 8. Precipitation seasonal dependence on CAPE: winter, fall, spring and summer, respectively from upper to bottom panel for A) Brindisi and B) Sundsvall–Härnösand.

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measurement errors. Results from this study show thatprecipitation is sensitive to the humidity and thus modelsthat do not have a sensitivity to humidity will not parame-terize it properly. SF characteristics give us hope for futurework and single out SF as a parameter that can improve theparameterization of precipitation in middle latitudes.

Results from our study query the importance of CAPEand CIN in parameterizing precipitation. Of the parametersdiscussed in the paper, saturation fraction (SF) is the mostsignificant, but is unlikely to be the sole parameter for pre-cipitation parameterization. Further work may identify otherparameters by investigating mechanisms which increase the

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/day

)

SUMMER

0.4 0.8

SF

0

50

100

Pre

cipi

tatio

n ra

te (

mm

/day

)

SPRING

0.4 0.8 1

SF

0

50

100

Pre

cipi

tatio

n ra

te (

mm

/day

)

FALL

SF

0

50

100

Pre

cipi

tatio

n ra

te (

mm

/day

)WINTER

0.4 0.8

0

50

100

Pre

cipi

tatio

n ra

te (

mm

/day

)

SUMMER

0.4 0.8

0 0.2 0.6 1

0 0.2 0.6 1

0 0.2 0.6 1

0 0.2 0.6 1

SF

0

50

100

Pre

cipi

tatio

n ra

te (

mm

/day

)

SPRING

0.4 0.80 0.2 0.6 0 0.2 0.6 1

SF

0

50

100

Pre

cipi

tatio

n ra

te (

mm

/day

)

FALL

0.4 0.80.2 0.6

SF

0

50

100

Pre

cipi

tatio

n ra

te (

mm

/day

)

WINTER

0.4 0.80 0.2 0.6 1 0 1

A B

SFSF

Fig. 9. Same as Fig. 8, except for SF.

179S. Barkiđija, Ž. Fuchs / Atmospheric Research 124 (2013) 170–180

SF. One possibility is the concept of gross moist stability(GMS). Introduced in the context of tropical convection,Neelin and Held (1987) defined GMS to be the ratio of thevertically integrated horizontal divergence of some intensivequantity conserved in moist adiabatic processes, to a measureof the strength of moist convection per unit area. In this sense,it can be applied to understand middle latitude systems in

terms of conservation of moisture, most entropy ormoist staticenergy, and how those influence the SF.

Acknowledgments

The authors thank Ivica Crljenica and Stipo Sentic for theircontributions for this work and Dr. David J. Raymond for his

Table 1Correlation coefficients between precipitation and: CAPE (Rcape), saturationfraction (Rsf) and CIN (Rcin).

Station code Station Rcape Rsf Rcin

01415 Sundsvall–Härnösand 0.0844 0.4846 0.008903005 Lerwick 0.0067 0.4139 0.011411520 Praha-Libus 0.938 0.3189 −0.029916080 Milano/Linate −0.0166 0.3967 0.01716320 Brindisi −0.0025 0.3683 0.078726063 St. Petersburg 0.0506 0.3297 −0.0046

180 S. Barkiđija, Ž. Fuchs / Atmospheric Research 124 (2013) 170–180

grateful comments and help. We acknowledge COST ActionES0905. We also acknowledge the E-OBS data-set from theEU-FP6 project ENSEMBLES (http://ensembles-eu.metoffice.com) and the data providers in the ECA&D project (http://eca.knmi.nl). This work was partially supported by U.S.National Science Foundation Grant ATM1021049.

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