Atmospheric Research 161–162 (2015) 116–124

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Atmospheric Research

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Relationship of convective precipitation with atmospheric heat flux — Aregression approach over an Indian tropical location

Swastika Chakraborty a, Upal Saha b,c, Animesh Maitra b,c,⁎a Department of Electronics and Communication Engineering, JIS College of Engineering, Kalyani, West Bengal, Indiab S. K. Mitra Centre for Research in Space Environment, Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, Indiac Institute of Radio Physics and Electronics, University of Calcutta, Kolkata, India

⁎ Corresponding author at: Institute of Radio PhysicsCalcutta, Kolkata, India.

E-mail address: animesh.maitra@gmail.com (A. Maitra

http://dx.doi.org/10.1016/j.atmosres.2015.04.0080169-8095/© 2015 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 29 January 2015Received in revised form 2 April 2015Accepted 5 April 2015Available online 16 April 2015

Keywords:Convective precipitationLatent heatSensible heatBowen ratioSurface evaporation

The response of atmospheric heat fluxes and sea surface temperatures on the convective precipitation over thetropics has been an important area of research in recent decades. A long-term observation (1979–2008) of theincrease in convective precipitation in relation to the latent and sensible heat fluxes on a tropical location,Kolkata, has been investigated in the present study. Invigoration of convective precipitation has been causedby vertically integrated divergence of moisture flux, rise in sea surface temperatures, convective cloud cover andsurface evaporation rate over the tropical region. A convectiveprecipitation estimation (CPE) index is proposed, con-sidering the Bowen ratio, surface evaporation rate, sea surface temperature and temperatures at 500 hpa pressurelevel during the pre-monsoon season (March–May), to estimate the amount of convective precipitation over thetropics using multiple linear regression technique is also another aim of this study. A good agreement is obtainedbetween the results from the proposed model and the MERRA observations during the years 2009–2013.

© 2015 Elsevier B.V. All rights reserved.

1. Introduction

Moist convection over the continent is significantly associated withthe heat fluxes of the atmosphere. In terms of the heat fluxes thereexists a definite coupling between land surface and the atmospherewhich leads to the convection (Alfieri et al., 2008). Sensitivity of theconvective rainfall frequency to the partitioning of sensible heat fluxand latent heat flux over North America has been analyzed (Berget al., 2013) using North American Regional Reanalysis (NARR) data.Most of the general circulation model (GCM) and other models(Chakraborty andMaitra, 2012, 2013) successfully predictmean rainfallbut fail to estimate precipitation intensity and frequency. The EuropeanCentre for Medium-Range Weather Forecasting (ECMWF) model isused to study the triggering algorithm of diurnal cycle of convectiveprecipitation over tropical South America and Africa where a strongdiurnal cycle is observed (Bechtold et al., 2004). The North AmericanMesoscale (NAM) Forecast System model is used over the CarolinaSand hills region to predict the summer convective rainfall asmesoscaleand local scale effects are prominent during summer (Wootten et al.,2010), and they are enhanced by surface heat fluxes. Convective rainfalltriggeringmechanism is explained (Juang et al., 2007) by a semi analytical

and Electronics, University of

).

model using surface heat flux and moisture. The model performance isnot satisfactory during night, but boundary layer growth and boundarylayer development plays a triggering phenomenon for the convection tobe happened (Gentine et al., 2013). According to the atmospheric ther-modynamics, hydrological cycle is very much dependent on theinteraction between land and atmosphere during warm season.Evapotranspiration (Schär et al., 1999) process successfully explainsthe water vapor balance of the planetary boundary layer. Intense trans-fer ofmoisture at the near surface atmosphere causes enhanced convec-tive precipitation. Bowen ratio, i.e. the ratio of surface heat flux to latentheat flux, and potential evaporation rate have a very good impact onconvective precipitation. Dryness of the soil moisture results in shallowcumuli and thereby deep convection. Explanation of continental moistconvection will be incomplete without considering the partitioning ofheat flux (Gentine et al., 2013).

Tropical precipitation is mostly dominated by convective phenome-non followed by stratiformprecipitation (Houze, 1997). As the tropics isin close vicinity of the equator getting direct heating from the sun,clouds are of mostly cumulonimbus and cumulus types. Precipitationparticles from vigorous convective region of cumulonimbus gathermass by collecting cloud water and break down into heavy shower.Over the last few years an increase of convective precipitation at pre-monsoon (warm) season is the main motivation behind this study. Inthe last decade, the study on convective precipitation around theworld has been a topic of prior interest to the mesoscale research com-munity (Soriano and Pablo, 2003; Guo et al., 2006; Dimitrova et al.,

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2009; Siingh et al., 2013; Ruiz-Leo et al., 2013). Entrainment ofmoisturein the lower troposphere following the formation of shallow cumulus isthe primary necessity to form deep convection (Saha andMaitra, 2014).Deep convective large clouds bring stronger precipitation after pene-trating more deeply through the troposphere, which produces strongercold pools and yet larger buoyant clouds. Lapse rate is another impor-tant factor to initiate convection. In some cases where buoyancy is lostby air parcel because the rate of increasing buoyancy due to parcelascent is smaller than the rate of reducing buoyancy due to entrain-ment. In this case though the environment is conditionally unstabledeep convection will not initiate. Convective boundary layer (Parasnis,1999) has a greater contribution in regulatingupdraft of energy andmois-ture from earth surface over land. Moisture penetrates from convectiveboundary layer through tropical tropopause layer to the lower strato-sphere. On the contrary, deep convection does not depend on a particulartime of the day or any particular time of a year, but following suitable at-mospheric condition cumulus clouds grown up into cumulonimbusclouds. Cumulonimbus cloud releases energy in the form of watervaporwhich condenses into precipitation (Adams et al., 2013). As aero-sol particle provides a good surface for the condensation of the cloud(Tao et al., 2012), the interaction between water vapor, aerosol anddeep convection is important (Yang and Yum, 2007). In this paper,an effort has been made for the first time to define the land atmo-sphere interaction by proposing convective precipitation estimation(CPE) index to quantify convective precipitation over the tropicalregion in a simplistic approach.

2. Data and methodology

NCEP reanalysis project provides data for analysis towards forecast-ing a climate system (Kalnay et al., 1996). Physical science division givesa subset of the above data. Latent heat flux and ground heat flux havebeen obtained from NCEP/NCAR reanalysis data, directly obtainedfrom the website http://www.esrl.noaa.gov/psd. The sensible heat fluxis thus calculated from ground heat and latent heat flux. The Modern-Era Retrospective analysis for Research and Applications (MERRA) is aclimate-quality analysis that places NASA's EOS observations into a cli-mate context. The Global Modeling and Assimilation Office (GMAO)has used its GEOS-5 atmospheric data assimilation system (ADAS) tosynthesize the various observations collected over the satellite era(from 1979 to the present) into an analysis that is as consistent aspossible over time because it uses a fixed assimilation system.MERRA observations are directly obtained from the website http://gdata1.sci.gsfc.nasa.gov. Convective precipitation rate, latent heatflux, sensible heat flux and surface evaporation rate are also obtainedfromMERRA whereas sea surface temperature data is obtained fromNOAA Optimum Interpolation (OI) SST V2. Convective cloud coverdata has been obtained from ISCCP D2 Monthly climatology from1997 onwards.

Bowen ratio is calculated as the ratio of sensible heat flux to latentheat flux in the following three ways:

i) According to Monin–Obukhov (Emanuel et al., 1994) theory,sensible heat flux is

Fsh ¼ ρcpchua Ts−Tað Þ ð1aÞ

and latent heat flux is

FLE ¼ ρlvclua qs−qað Þ ð1bÞ

where ua, Ta, qa are thewind velocity, air temperature and specif-ic humidity at reference level, Ts and qs are surface temperatureand specific humidity at surface; Ch and Cl are aerodynamicbulk coefficients; ρ is the density of air, Cp is the specific heat of

air at constant pressure and lv is the latent heat of vaporization.Thus Bowen ratio (Bo) is calculated as,

Bo ¼FshFLE

: ð2Þ

ii) The data for sensible heat flux, latent heat flux are directly avail-able from MERRA website [http://gdata1.sci.gsfc.nasa.gov].

iii) The data for ground heat flux, latent heat flux are directly avail-able fromNCEPwebsite [http://www.esrl.noaa.gov/psd], therebysensible heat flux is calculated from there as follows:

HS ¼ RN– HL þHGð Þ ð3Þ

where,

HS (often just called H) is the upward surface sensible heat flux,HL (=LE) is the upward surface latent heat flux due to evapora-tion at rate E,HG is the downward groundheat flux into the subsurfacemedium,RN is the net downward radiative flux (longwave + shortwave),L (=2.5 × 106 J kg−1) is the latent heat of vaporization.

The data for sensible heat flux, latent heat flux and potential evapo-ration rate are taken fromMERRA for the year 1979 to 2013. Convectiveprecipitation estimation (CPE) index is formedby dividing surface evap-oration rate by Bowen ratio, the significance ofwhich is explained in thesubsequent sections. Convective precipitation amount is plotted againstconvective precipitation index. Hence, the purpose of the present studyis to investigate the long-term pattern of convective precipitation ratewith the changes in atmospheric heat flux (latent heat and sensibleheat) over the tropical location, Kolkata (Fig. 1) from 1979–2008. Mul-tiple linear regression analysis is done on the above dataset. From theregression equation, the estimated convective precipitation amountcan be validated taking the data for the year 2009 to 2013. Fig. 2(a)shows the yearly variation of Bowen ratio as calculated from theabove mentioned three sources. There is a decreasing trend of Bowenratio over the years, which signifies the increase in the atmosphericheat fluxes in context to the precipitation involved with convectivephenomena. Fig. 2(b) shows the variation of Bowen ratio (as calcu-lated from the three sources) with convective precipitation rate from1979–2013 over the same location. The figure indicates a decrease inconvective precipitation rate with the increase in Bowen ratio. Alterna-tively, it may be mentioned that with lower values of the Bowen ratiothere is an increased rate of convective precipitation. As we have calcu-lated Bowen ratio from three different sources or techniques, the figuremay also be an indicative of the fact that the Bowen ratio as calculatedfrom MERRA observations is the best one over this tropical region.Therefore, Bowen ratio calculated in the further study from latent andsensible heat fluxes is taken from MERRA data source.

3. Results and discussion

The cycling of combined atmospheric heatflux andmoisture contentis an important aspect of Earth's climate system, which plays an impor-tant role in determining the atmospheric energy budget. The role ofconvective precipitation over the tropics can have a significant associa-tion with the scavenging of aerosols and also acts to remove and trans-port aerosols and soluble gases both within and below clouds, and thusstrongly affects the chemical composition and aerosol distribution. Thepurpose of the study is to determine the long-term relationship of con-vective precipitation with atmospheric heat flux and to quantify it in atropical urban metropolis like Kolkata via multiple linear regressionapproach.

Fig. 1. Political map of India, the zoomed portion in a square box is shown outside themap presenting the geographical location of Kolkata showing the area of interest (black square) forthe present study (after: Saha et al., 2014a, 2014b).

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3.1. Long-term variations of convective and non-convective precipitation

Increase of convective precipitation has been favored over a rise innon-convective precipitation but the relative contributions of thesetwo types of precipitation have been difficult to disentangle. The long-term variations of convective and non-convective precipitations showan increase in the respective precipitation rates during the pre-monsoon season (March–May) over Kolkata from 1979–2013 (Fig. 3).

The estimate of convective precipitation suggests the sensitivity ofthe hydrological cycle in climate models to changes in the increase ofsea-surface temperatures. Kolkata, being a tropical region, experienceshigh moisture content and due to its orographical features moistureconvergence is likely to be proportionately enhanced, which shouldlead to similarly enhanced convective precipitation rates. The steepnessof the increase in convective precipitation rate is much more than thatof the non-convective precipitation rates during the pre-monsoonseason, which may be due to the yearly changes in convective cloudcover, sea-surface temperature and surface evaporation rate.

3.2. Reasons for the increase of convective precipitation

During the pre monsoon season, intense convective precipitationhas been occurred over this tropical region over the past three decades.The south-westerlyflow fromBayof Bengal constituted themajormois-ture influx bringing about deep wet layers and moisture divergence.Convective instability depends on the balance between low-levelvorticity convergence and surface friction (Raymond et al., 1998).Thus, intense convective precipitation implies more low to middlelevel moisture convergence. Fig. 4(a) depicts the yearly variation ofvertically integrated divergence ofmoistureflux over the tropical regionfrom 1979–2013, which clearly indicates that the supply of moisture

influx causes the precipitation to occur due to a pre-mature convection.The lower the level of non-divergence, the more this inflow is concen-trated near the surface, resulting in increased low-level potential vortic-ity (Raymond and Sessions, 2007). But, Fig. 4(b) clearly indicates thatthere is a decreased or almost constant variation of potential vorticityover the tropical region during pre-monsoon from 1979–2013. Thisdepicts the fact that the severe convective activity over Kolkata has beendecreased (Saha et al., 2014a) but there have been an increase in convec-tive precipitation from these pre-mature convective environments.

Other reasons for the increase in convective precipitation over Kolka-tamay be due to the increase in sea surface temperatures (SST), convec-tive cloud cover and surface evaporation rate (Fig. 5). Fig. 5(a) indicatesan increase in SST during 1979–2013, which may be one of the possiblereasons for the increased convective precipitation over Kolkata.Rondanelli and Lindzen (2008) showed a fraction of convective precip-itation increases with SST at a rate of about 6 to 12%/K. Absorption ofradiation at the surface will increase the surface temperature creatingunstable conditions in the lowest layers of the atmosphere. Johnsonand Xie (2010) indicated that sea surface temperature increasessubstantially with global warming which consequently increases tropi-cal convection. A cloud can only produce precipitation if the cloudlayer is thick enough and/or the temperature in the upper part of thecloud is low enough. Deep convective clouds play a crucial role in thegeneral circulation, energy, and hydrological cycle of our climate system(Fan et al., 2013). Fig. 5(b) indicates an increase in convective cloudcover over the region which initiates intense convective precipitationover Kolkata. As a significant contributor of water vapor to tropical con-vection, surface evaporation has been given attention by the meteoro-logical research community (Cui and Li, 2006; Webster, 1994; Waliser,1996; Lau et al., 1997). There is a direct influence of global warmingon total precipitation. As a consequence of increased heating that leadsto greater evaporation, the water holding capacity of air increases by

Fig. 2. (a). Yearly variation of Bowen ratio over Kolkata as obtained from three different sources for the period of 1979–2013. (b). Variation of Bowen ratio with convective precipitationrate over Kolkata as calculated from three different sources for the period of 1979–2013.

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about 7% per 1 °C warming, increasing water vapor in the atmosphere.Hence, storms, whether individual thunderstorms, tropical rain ortropical cyclones, supplied with increased moisture, produce more

intense precipitation events (Trenberth, 2011). Fig. 5(c) also depicts anincrease in surface evaporation rate over this tropical region, whichleads to increased convective precipitation.

Fig. 3. Yearly variation of convective and non-convective precipitation rates over Kolkata from 1979–2013.

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3.3. Implementation of atmospheric heat fluxes over convective precipitation

Thermal effect over tropics has a greater role in understanding thedramatic changes in land–atmosphere interactions and thereby fore-casting seasonal change and climate prediction. The earth and the atmo-sphere interaction becomes complicated than the usual at the transitionseason betweenwinter and summer. The tropical region is not at the vi-cinity to the region of snowmelt and thawing–freezing processes(Zhang et al., 2000); hence, a good correlation is obtained between sen-sible heat flux and latent heat flux as shown in Fig. 6. Buoyancy forcecauses strong deep air convection in tropics. Sensible heat flux is gener-ated by the surface wind divergence which is in turn caused by verticalairflow in tropics. When the wind is more continental or more towardsequator than thenormalwindflow, Bowen ratio canbe a deciding factorcausing convection.

Fig. 7 shows the variation of convective precipitation with latentheatflux and sensible heat flux respectively. The dependence of convec-tive precipitation over atmospheric heat fluxes shows the relationbetween the intensity of convective precipitation and the partitioningof heat fluxes. In quasi-equilibrium cases a positive surface flux anomalyenhances precipitation not through simple moisture recycling butthrough the effect of buoyancy. According to large scale dynamicsparameterization convective precipitation has a very strong responsewith surface turbulent heat fluxes.

The vertically transported air causing warm convection will beenriched by the vapor from surface evaporation relative to its surround-ings whichwill initiate the atmosphere to be unstable generatingmoistconvection. Fig. 8 depicts the increase in convective precipitation ratewith the increase in surface evaporation rate (SER) over Kolkata during1979–2013. The water vapor condenses to form precipitation by releas-ing latent heat, which is an important energy source for atmosphericmotion and convective weather systems. The vertical transport ofwater vapor, through cumulus convection, is themost important mech-anism for upward transport of heat in the tropics. Water vapor entersthe atmosphere through surface evapo-transpiration, whereby latentenergy is absorbed. When the vapor condenses, the latent heat isreleased to the atmosphere, thereby increasing convective precipitationrate over the tropical region.

4. Formation of a new index— Convective precipitationestimation (CPE) index

Direct solar heating of ocean in the tropics is the primarymechanismcausing convection. The spatial and temporal development of this con-vective system lead to deep convection by interactionwith cloud, mois-ture and temperature of the troposphere. Main source of water vapor inthe upper troposphere is deep convection. Upper tropospheric humidityis the responsible factor for maintaining greenhouse effect in the atmo-sphere. SST has a prior control on the generation of surface evaporationwhich can consequently help in the formation of convective precipita-tion processes. The 500 hpa pressure-level lies very near the level ofnon-divergence. This allows for an efficient analysis of vorticity andthe temperature at 500 hpa pressure level (T500) is another importantparameter that can affect the strength of the convection and thusprecipitation events. Since these types of precipitation are the indicatorsofflooding risk, hence, an indexing is required to specifically identify theconcept of convective precipitation in this tropical region. The increaseof convective precipitation during past decades makes the index amore valuable parameter to measure rainfall in a consistent way.Thus, convective precipitation estimation (CPE) index is proposedby using monthly values of SER, SST, Bo and temperature at 500 hpapressure level (T500), as follows:

CPE Index ¼SER

.SST

T500j j.Bo

264

375: ð4Þ

4.1. Estimation of convective precipitation by CPE index using simple linearregression analysis

Multiple linear regression analysis is used here to find a predictivemodel of convective precipitation from the observed convective precipi-tation estimation index formed by SER, SST and Bo. After the developmentof such model for convective precipitation, it can be predicted in spite ofabsence of any of the variable from SER, SST and Bo. Linear regression

Fig. 4. (a). Yearly variation of vertically integrated divergence ofmoisturefluxes over Kolkata during 1979–2013. (b). Yearly variation of potential vorticity over Kolkata during 1979–2013.

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analysis can also be used to find the strength of the relationship betweenthe above variables.

Convective precipitation rate is found to increase linearly with thecalculated convective precipitation estimation (CPE) index (Fig. 9).Therefore, a linear regression model of convective precipitation is fittedwith the equation

y ¼ 1:849xþ 123:28 ð4Þ

where, x being the CPE index and y being the convective precipitationrate with a regression coefficient of 0.896.

4.2. Validation and comparison

In order to assess the performance of the proposed model, the CPEindex values are calculated using the data for the period 2009 to 2013over Kolkata. The value of convective precipitation is calculated from

Fig. 5. Increase in (a) sea surface temperature, (b) convective cloud cover and (c) surface evaporation rate over Kolkata during 1979–2013.

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the estimated CPE using the linear equation obtained bymultiple linearregression approach. In order to provide some statistics of errors, thepercentage error has been calculated for each of the year of the timeperiod 2009 till 2013. The percentage error remains around 8% showinga good agreement between the estimated and measured value of con-vective precipitation rate. Our estimated result under-estimates theactual result in the years 2009–2012, however, it over-estimates forthe year 2013. The observed data for convective precipitation rate forthe year 2009 to 2013 is plotted with the calculated data from Eq. (4)in Fig. 10(a). Error percentages are calculated between the actual andpredicted values of convective precipitation rate. Fig. 10(b) shows agood agreement between the observed and estimated values of convec-tive precipitation rate over Kolkata, having maximum error percentage

Fig. 6. Relationship between sensible and latent heat fluxes over Kolkata during 1979–2013.

of 8%. Thus, this CPE index modeled approach gives almost near-valuesas that of the MERRA observations via simple linear regression. Thismodel approach can be used in any part of the Indian sub-continent,where convective precipitation mostly occurs.

5. Conclusions

The interrelationship between atmospheric heat fluxes and evapora-tion rate is quite strong in the tropical region. Bowen ratio has a significant

Fig. 7. Relationship between convective precipitation rates with (a) latent heat flux and(b) sensible heat flux over Kolkata during 1979–2013.

Fig. 8. Relationship between convective precipitation and surface evaporation rates overKolkata during 1979–2013.

Fig. 10. (a) Comparison between the actual and estimated convective precipitation ratesover Kolkata during 2009–2013. (b) Yearly percentage error as obtained from the actualand predicted convective precipitation rates over Kolkata during 2009–2013.

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dependence on convective precipitation in the pre-monsoon season overtropics. The divergence of surface winds makes Bowen ratio more rele-vant to convection in the tropical atmosphere. The convective rainfallhas gradually increased over the last three decades depending on a num-ber of factors like surface evaporation rate, sea surface temperature andthe temperature at 500 hpa pressure level, in addition to Bowen ratio,in a complex manner. The convection can be basically considered as aresultant process of evaporation. The present study deals with the quan-tification of convective rainfall rate in terms of abovementioned thermo-dynamical parameters over the tropical location of Kolkata.

Sea surface temperature, on the other hand, plays a crucial role incontrolling the global temperature as well as regional climate change.The increase in temperature enhances the surface evaporation ratewhich in turn has caused an increase in convective cloud cover overthe past decade. The supply of moisture influx causes the precipitationto occur due to a pre-mature convection but there is a small variationof potential vorticity over the tropical region during pre-monsoonperiod of the years 1979–2013. A lower level of non-divergence ofsurface winds will cause a more concentrated moisture influx near thesurface which results in an increase in low-level potential vorticity.Thus, there has been an increase in convective precipitation over thetropical region from the pre-mature convective environments. Aninterrelation of the above discussed parameters is very much pertinentto estimate the convective precipitation in a simplistic way. Multiplelinear regression technique has been applied to propose a new index,namely, convective precipitation estimation (CPE) index, with the dataof the period 1979–2008, as a predictive tool to estimate the convec-tive precipitation over the tropical region. The estimated convective

Fig. 9. Linear relationship between convective precipitation rates over Kolkata and CPEIndex during 1979–2008.

precipitation using CPE index has been validated with the subsequent5 years (2009–2013) data. Validation of this indexing shows a goodagreement between the observed andmeasured quantity of convectiveprecipitation with an estimated error within 10%. The predictive modelof convective precipitation rate with the help of convective precipita-tion estimation indexwill be useful in the absence of anymeasurementsof the above mentioned parameters. Further study on this index overother tropical locations will make the indexing method a more usefultool for estimation of convective precipitation.

Acknowledgements

This work has been supported by the grant from Department ofScience and Technology, Government of India under the DST-PURSEprogramme (No. SR/S9/Z-23/2010/15) and Indian Space ResearchOrganisation (ISRO), Bangalore, under the CAWSES India Phase-IIproject “Studies on Solar Control on Indian Summer Rainfall andassociated atmospheric water vapor content and cloud liquid watercontent” (No. B.33015/15/2010-V).

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