Atmospheric water balance over oceanic regions as estimatedfrom satellite, merged, and reanalysis data

Hyo-Jin Park,1 Dong-Bin Shin,1 and Jung-Moon Yoo2

Received 15 November 2012; revised 10 April 2013; accepted 13 April 2013; published 7 May 2013.

[1] The column integrated atmospheric water balance over the ocean was examined usingsatellite-based and merged data sets for the period from 2000 to 2005. The data sets for thecomponents of the atmospheric water balance include evaporation from the HOAPS,GSSTF, and OAFlux and precipitation from the HOAPS, CMAP, and GPCP. The watervapor tendency was derived from water vapor data of HOAPS. The product for water vaporflux convergence estimated using satellite observation data was used. The atmosphericbalance components from the MERRA reanalysis data were also examined. Residuals ofthe atmospheric water balance equation were estimated using nine possible combinationsof the data sets over the ocean between 60�N and 60�S. The results showed that there wasconsiderable disagreement in the residual intensities and distributions from the differentcombinations of the data sets. In particular, the residuals in the estimations of thesatellite-based atmospheric budget appear to be large over the oceanic areas with heavyprecipitation such as the intertropical convergence zone, South Pacific convergence zone,and monsoon regions. The lack of closure of the atmospheric water cycle may be attributedto the uncertainties in the data sets and approximations in the atmospheric water balanceequation. Meanwhile, the anomalies of the residuals from the nine combinations of the datasets are in good agreement with their variability patterns. These results suggest thatsignificant consideration is needed when applying the data sets of water budgetcomponents to quantitative water budget studies, while climate variability analysis basedon the residuals may produce similar results.

Citation: Park, H.-J., D.-B. Shin, and J.-M. Yoo (2013), Atmospheric water balance over oceanic regions as estimatedfrom satellite, merged, and reanalysis data, J. Geophys. Res. Atmos., 118, 3495–3505, doi:10.1002/jgrd.50414.

1. Introduction

[2] The atmospheric water cycle is one of the most impor-tant components of the global water cycle. Large amounts ofwater vapor that are evaporated from the ocean aretransported to the continents through the atmosphere. Thetransported water vapor is converted into precipitation thatprovides vital water for living things on Earth. Precipitationand evaporation over the oceans change the sea surfacesalinity and help to drive the ocean thermohaline circulation.Changes in the phase of water in the atmosphere involvelatent heat exchanges. Latent heat released by condensationis one of the major energy sources driving the general circu-lation of the atmosphere. Knowledge of the atmosphericwater cycle is therefore essential in order to manage waterresources and to understand the Earth’s weather and climate.

[3] The atmospheric water cycle has been investigated inmany regions. The Global Energy and Water Cycle Experi-ment (GEWEX) initiated by the World Climate ResearchProgram is well known for its scientific studies of the watercycle. The GEWEX aims at observing, understanding, andmodeling the hydrological cycle and energy fluxes in orderto predict global and regional climate change. Under themissions of the GEWEX, projects including the RegionalHydroclimate Projects (RHPs) (formerly the ContinentalScale Experiment) were initiated. The focus of the GEWEXwas to solve the problems of closing the balance of waterand energy. In addition, several water cycle studies wereperformed at the atmospheric branch in order to quantifythe regional water balance, including the MackenzieGEWEX Studies [e.g., Stewart et al., 1998 ; Rouse et al.,2003], the Baltic Sea Experiment [e.g., Raschke et al.,2001 ; Ruprecht and Kahl, 2003], the Climate PredictionProgram for the Americas [e.g., Roads et al., 2003], andthe Murray-Darling Basin [e.g., Draper and Mills, 2008].[4] One of the major complications of the atmospheric

water balance study is the selection of appropriate data sets.The atmospheric water balance equation includes watercycle components such as evaporation, precipitation, waterflux convergence, and water tendency. The equation itselfis not complicated, but accurate estimation of each of thewater cycle components is difficult. Water cycle components

1Department of Atmospheric Sciences, Yonsei University, Seoul, SouthKorea.

2Department of Science Education, Ewha Womans University, Seoul,South Korea.

Corresponding author: D.-B. Shin, Department of AtmosphericSciences, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 120-749,South Korea. (dbshin@yonsei.ac.kr)

©2013. American Geophysical Union. All Rights Reserved.2169-897X/13/10.1002/jgrd.50414

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JOURNAL OF GEOPHYSICAL RESEARCH: ATMOSPHERES, VOL. 118, 3495–3505, doi:10.1002/jgrd.50414, 2013

have been acquired from direct measurements, numericalweather prediction (NWP) model-derived products, remotelysensed observations, and residual methods using the atmo-spheric water balance equation. Direct measurements providerelatively reliable data but have limited observation coverage.Earlier water cycle studies were usually performed usingradiosonde data [Rasmusson, 1967, 1968]. Despite its limitedspatial and temporal coverage, radiosonde data is still usedover the regions with dense radiosonde networks [Kanamaruand Salvucci, 2003; Zangvil et al., 2004]. NWP-derived anal-ysis and reanalysis data have been actively employed for thestudy of the water budget [e.g., Roads et al., 2003; Ruprechtand Kahl, 2003; Turato et al., 2004; Draper and Mills,2008], because of their ability to minimize known errors andhigh spatiotemporal resolutions. NWP products, however,are highly dependent on model physics and parameterization.With advancement in satellite instruments and retrieval algo-rithms, more satellite observation data have become available[e.g., Bakan et al., 2000]. Satellite observations, which havebetter coverage than in situ observations particularly over theoceans, have been widely used for a complementary purposeor for comparison with other observations. Many satellite-based or merged data sets for water cycle components havebeen produced using such satellite observations.[5] In this study, the atmospheric water balance is exam-

ined over oceans using various satellite-based and mergeddata sets. Reanalysis data sets are also used for comparisonwith satellite-based data sets for the atmospheric waterbalances over oceanic regions.

2. Data and Methodology

2.1. Atmospheric Water Balance Over the Ocean

[6] The column integrated atmospheric water balance overthe ocean can be expressed as follows [Peixoto and Oort,1992]:

@ W þWcð Þ@t

¼ E � Pð Þ � r � !Q þ!

Qc

� �(1)

where E and P are the evaporation and precipitation, respec-tively. W indicates the column integrated total water vapor,!Q is the horizontal water vapor flux vector, and the subscriptc denotes the condensed phase of water. W+Wc and

!Q þ!

Qc are defined as follows:

W þWc ¼Zpsp0

qþ qcð Þ dpg

(2)

and

!Q þ!

Qc ¼Zpsp0

qþ qcð Þ!v dp

g(3)

where g is the acceleration of gravity, ps is the pressure at thesurface, p0 is the pressure at the top of the atmosphere, q isthe specific humidity, qc is the condensed water mixingratio, and !v is the horizontal wind velocity vector.

[7] The terms @Wc/@ t and!Qc are related to the condensed

phase water and are usually small enough that both the ten-dency of liquid and solid water in clouds and their horizontalflux can be ignored in equation (1). Therefore, by averagingequation (1) in the specified temporal and spatial domain ofinterest, the general atmospheric water balance equation canbe simplified to the following:

@W

@t

�* +¼ �E � �Ph i � r �!Q

�D E(4)

where the bar indicates the time average and the angularbracket denotes the area average. Equation (4) shows thatthe excess of evaporation over precipitation is balanced bythe local rate change of the water vapor contents and bythe horizontal net flux of water vapor.[8] In order to examine the atmospheric water balance, we

calculated the residuals using equation (4) as follows:

R ¼ �E � �Ph i � r �!Q�D E

� @W

@t

�� �(5)

where R represents the residual of the atmospheric waterbalance equation. R was obtained from combinations of thedata sets for the components of the water cycle in equation(5). Section 2.2 describes the data sets used for this study.

2.2. Data Sets

[9] The satellite-based and merged data sets for atmo-spheric water cycle components that are widely used forwater cycle study were selected. Table 1 summarizes thecharacteristics of the data sets for the water cycle compo-nents used in this study. For evaporation (E), the monthlyfields of three data sets were used. The first data set wasthe Hamburg Ocean Atmosphere Parameters and Fluxesfrom Satellite data (HOAPS), and the second data set wasthe Goddard Satellite-based Surface Turbulent Fluxes(GSSTF). The third data set was the Objectively AnalyzedAir-Sea Heat Fluxes (OAFlux) project at the Woods HoleOceanographic Institution. In HOAPS, evaporation datawere obtained from all of the available Special SensorMicrowave Imager (SSM/I) observation data based on the

Table 1. Characteristics of the Data Sets for the Atmospheric Water Balance Componentsa

Data Sets Version Variables Spatial Resolution Temporal Resolution Available Period

OAFlux v3 E 1.0� � 1.0� month 1958–2010GSSTF v2c E 1.0� � 1.0� month 1987–2008GPCP v2.1 P 2.5� � 2.5� month 1979–2010CMAP v1001 P 2.5� � 2.5� month 1979–2009HOAPS v3 E, P, WVT 0.5� � 0.5� month 1987–2005XLT08 v3 WVFC 0.5� � 0.5� month 1999–2008MERRA (GEOS-5.2.0) E, P, WVT, WVFC 0.5� � 2/3� month 1979–2012

aThe components are evaporation (E), precipitation (P), water vapor flux convergence (WVFC), and water vapor tendency (WVT).

PARK ET AL.: COMPARING ATMOSPHERIC WATER BALANCES

3496

Coupled Ocean-atmosphere Response Experiment (COARE)bulk flux algorithm version 2.6a [Bradley et al., 2000; Fairallet al., 1996] for latent heat flux parameterization. The near-surface wind speed and specific air humidity were retrievedfrom the SSM/I brightness temperature, and the sea surfacetemperature data from the Advanced Very High ResolutionRadiometer (AVHRR) measurements were used [Anderssonet al., 2010]. The GSSTF latent heat flux was retrievedbased on the bulk flux model [Chou, 1993], using theSSM/I surface wind, surface air humidity, and near-surfaceair and sea surface temperatures from the National Centersfor Environmental Prediction (NCEP)-National Center forAtmospheric Research (NCAR) reanalysis as the input data[Chou et al., 2003; Shie, 2010]. The OAFlux evaporationdata were derived from the blending of the satelliteretrievals from the SSM/I, the Quick Scatterometer(QuikSCAT), the AVHRR, the Tropical Rain MeasuringMission Microwave Imager, and the Advanced MicrowaveScanning Radiometer Earth Observing System, as well asthe NWP reanalysis outputs from the NCEP (e.g., NCEP/NCAR, NCEP/DOE reanalysis) and European Centre forMedium-Range Weather Forecasts (ECMWF) (e.g.,ERA40) by objective analysis techniques [Yu and Weller,2007; Yu et al., 2008]. The OAFlux products wereconstructed based on the COARE bulk flux algorithmversion 3.0 [Fairall et al., 2003].[10] The following three monthly precipitation (P)

products were used: HOAPS, the Global PrecipitationClimatology Project (GPCP), and the Climate PredictionCenter Merged Analysis of Precipitation (CMAP). TheHOAPS precipitation was retrieved from a neural networkalgorithm that takes the SSM/I brightness temperature andthe precipitation from the ECMWF model as training data[Andersson et al., 2010]. Both the GPCP [Adler et al.,2003; Huffman et al., 2009] and the CMAP [Xie andArkin, 1997] use multiple satellite and rain gauge data setswith some differences in their input data and mergingtechniques [Yin et al., 2004].[11] For water vapor flux convergence (WVFC), the

monthly WVFC estimated by Xie et al. [2008, hereinafterreferred to as XLT08] was used. The XLT08 algorithm

estimates the WVFC based on support vector regression usingthe surface wind vector from the Quick Scatterometer(QuikSCAT), the cloud drift wind vector from the MultiangleImaging Spectroradiometer and the NOAA geostationarysatellites, and the precipitable water from the SSM/I.[12] The water vapor tendency (WVT) data were derived

in this study using the HOAPS twice-daily total columnwater vapor (TPW) data. The HOAPS twice-daily TPWwere averaged over a pentad of days in order to create dailydata (e.g., the 1 January 2005 daily TPW is the averagedvalue of the 30 December 2004 through 3 January 2005

Figure 1. A diagram of the nine residuals estimated frompossible combinations of the data sets for the atmosphericwater cycle components.

2000 2001 2002 2003 2004 2005

Year

2.5

3.0

3.5

4.0

4.5

[mm

/day

]

OAFlux

GSSTFHOAPS

MERRA

2000 2001 2002 2003 2004 2005

Year

2.0

2.5

3.0

3.5

4.0

[mm

/day

]

GPCP MERRA

HOAPS CMAP

2000 2001 2002 2003 2004 2005

Year

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

[mm

/day

]

Xie08 MERRA

2000 2001 2002 2003 2004 2005

Year

-0.10

-0.05

0.00

0.05

0.10

[mm

/day

]

HOAPS MERRA

(a) E

(b) P

(c) WVFC

(d) WVT

Figure 2. Time series of the monthly domain averaged (2)evaporation rates, (b) precipitation rates, (c) water vapor fluxconvergences, and (d) water vapor tendencies for the periodfrom 2000 to 2005. Units are mmd�1.

PARK ET AL.: COMPARING ATMOSPHERIC WATER BALANCES

3497

twice-daily TPW). The monthly WVT was then calculatedusing the following equation:

@W

@t

� �m

¼ Wf �Wi

Δt(6)

where Δt is the 1month time interval, and i and f indicate thefirst and the day of the mth month, respectively.[13] Modern-Era Retrospective analysis for Research and

Applications (MERRA), which is NASA’s new reanalysismethod, was also used for comparison with the satellite-based and merged data sets. The MERRA is generated usingthe Goddard Earth Observing System (GEOS) atmosphericmodel and data assimilation system, version 5.2.0 [Rieneckeret al., 2011]. MERRA provides the various quantities for theatmospheric water cycle components. It shows improved as-pect for representing the atmospheric branch of the hydrolog-ical cycle and provides complete information for budgetstudies as stated by Rienecker et al. [2011].[14] Figure 1 is a diagram of the estimated residuals from

nine possible combinations of satellite and merged datasets for water cycle components. For example, the residual

OGXH indicated that the residual came from the combinationof evaporation for OAFlux, precipitation for GPCP, watervapor flux convergence for XLT08, and water vapor tendencyfor HOAPS. All of the monthly data sets were remapped tohave a 5� by 5� latitude-longitude spatial resolution for theperiod from 2000 to 2005. For each data set, we averagedthe data values at each 5� � 5� grid if the number of themissing value did not exceed 50% of the total number of datapoints. The domain is limited to oceanic regions between60�N and 60�S. Oceanic regions are defined as the areas wherethe MERRA’s ocean fraction is greater than 0.9.

3. Results

3.1. Analyses of Atmospheric Water Cycle Components

3.1.1. Evaporation and Precipitation[15] The time series of the monthly domain averages of the

satellite-based andmerged data sets for four atmospheric watercycle components during the period from 2000 to 2005 areshown in Figure 2. The reanalysis data MERRA is alsodisplayed for comparison. For evaporation (Figure 2a), thedomain averages of the evaporation from GSSTF, HOAPS,

Table 2. Correlation Coefficients for Precipitation Data Sets (the Upper Triangular Part) and for Evaporation Data Sets (the LowerTriangular Part)

GPCP CMAP HOAPS MERRA Precipitation

OAFlux 1.00 1.00 0.88 0.86 0.42 GPCPHOAPS 0.50 1.00 1.00 0.79 0.51 CMAPGSSTF 0.58 0.69 1.00 1.00 0.52 HOAPSMERRA 0.72 0.38 0.29 1.00 1.00 MERRAEvaporation OAFlux HOAPS GSSTF MERRA

(a) E std. Avg. = 0.500 ( 0.230 ~ 1.228)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<[mm/day]

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

(b) E CV Avg. = 0.159 ( 0.053 ~ 0.648)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<[CV]

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75

(c) P std. Avg. = 0.565 ( 0.047 ~ 1.649)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(d) P CV Avg. = 0.278 ( 0.108 ~ 1.051)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

Figure 3. Spatial distributions of the period-mean standard deviations and the coefficients of variation(CVs) between (a, b) three evaporation data sets (OAFlux, HOAPS, and GSSTF) and (c, d) threeprecipitation data sets (GPCP, CMAP, and HOAPS). The values in the upper right corners of each panelindicate domain averages. The minimum and maximum are also indicated in parentheses.

PARK ET AL.: COMPARING ATMOSPHERIC WATER BALANCES

3498

OAFlux, and MERRA are 3.88, 3.82, 3.45, and 3.50mmd�1,respectively. The monthly mean values of evaporation fromthe satellite-based GSSTF and HOAPS are typically greaterthan those from the merged and reanalysis data sets. HOAPSand GSSTF are simply paired due to the similarity in using

the same satellite data from SSM/I, but their estimationmethods are not similar to each other [Chiu et al., 2012].Correlation coefficients between the evaporation data setshave been also investigated (Table 2). Relatively high correla-tion coefficients were found between the OAFlux and

(a) XLT08 DJF Avg. = -0.427 ( -6.294 ~ 8.397)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(b) MERRA DJF Avg. = -0.543 ( -6.537 ~ 5.883)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(c) XLT08 JJA Avg. = -0.441 ( -6.857 ~ 11.865)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(d) MERRA JJA Avg. = -0.562 ( -6.497 ~ 10.836)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<<

[mm/day]-7.2 -6.0 -4.8 -3.6 -2.4 -1.2 0 1.2 2.4 3.6 4.8 6.0 7.2

Figure 4. Mean seasonal distributions of WVFC for XLT08 (a) in winter (December–January–February(DJF)) and (c) in summer (June–July–August (JJA)) and the mean seasonal distributions for MERRA (b)in winter and (d) in summer for the period from 2000 to 2005.

(a) HOAPS DJF Avg. = 0.009 ( -0.274 ~ 0.192)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(b) MERRA DJF Avg. = 0.010 ( -0.269 ~ 0.217)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(c) HOAPS JJA Avg. = -0.001 ( -0.172 ~ 0.238)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(d) MERRA JJA Avg. = 0.001 ( -0.192 ~ 0.275)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<<[mm/day]

-0.18 -0.15 -0.12 -0.09 -0.06 -0.03 0 0.03 0.06 0.09 0.12 0.15 0.18

Figure 5. Mean seasonal distributions ofWVT for HOAPS (a) in winter (DJF) and (c) in summer (JJA) andmean seasonal distributions for MERRA (b) in winter and (d) in summer for the period from 2000 to 2005.

PARK ET AL.: COMPARING ATMOSPHERIC WATER BALANCES

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MERRA data (0.72) and the GSSTF and HOAPS data (0.69),but the correlation coefficients between the HOAPS andMERRA data (0.38) and between the GSSTF and MERRAdata (0.29) were much weaker.[16] The time series of the four precipitation data sets are

shown in Figure 2b. The period-means of precipitation forCMAP, GPCP, HOAPS, and MERRA are 3.14, 3.01, 2.91,and 3.23mmd�1, respectively. The correlations betweenthe satellite-based and merged data sets are generally higherthan those between the reanalysis MERRA and the otherdata sets (Table 2). In particular, relatively high correlationsare found between the GPCP and CMAP (0.88), GPCP andHOAPS (0.86), and HOAPS and CMAP (0.79) data sets.[17] The local variances associated with the various data

sets can be obtained using the following equations:

si ¼ 1

N

XNj¼1

Xj;i � E Xð Þi� ( )0:5

(7a)

sm ¼ 1

M

XMi¼1

si (7b)

where si is the standard deviation of N different data sets ofthe variable X for the ith month and sm is the mean standarddeviation over M months. E(X)i is the average of the X’sestimated from N data sets for the ith month. For three differ-ent evaporation (GSSTF, HOAPS, and OAFlux) and precip-itation (GPCP, CMAP, and HOAPS) data sets, the spatialdistributions of sm were computed for each 5� � 5� grid overthe 72month period between 2000 and 2005 (Figures 3a and3c). Large variances between evaporation data sets existover some of the oceanic dry regions such as the southeast-ern Pacific, the subtropics over the west Pacific, and the partsof the south Atlantic near South Africa. For precipitation,significant variances were found over the regions of theintertropical convergence zone (ITCZ) and the south Pacificconvergence zone (SPCZ) as well as the East China Sea,South China Sea, and Bay of Bengal portions of the Indian

2000 2001 2002 2003 2004 2005Year

-1.5

-1.0

-0.5

0.0

0.5

1.0[m

m/d

ay]

OGXHOCXHOHXH

HGXHHCXHHHXH

GGXHGCXHGHXH

MERRAMERRA(exANA)

2000 2001 2002 2003 2004 2005Year

-1.5

-1.0

-0.5

0.0

0.5

1.0

[mm

/day

]

OGXHOCXHOHXH

HGXHHCXHHHXH

GGXHGCXHGHXH

MERRAMERRA(exANA)

2000 2001 2002 2003 2004 2005Year

-1.5

-1.0

-0.5

0.0

0.5

1.0

[mm

/day

]

Sat.-based MERRAMERRA(exANA)

(a) Resi.

(b) Resi. Anomalies

(c) Resi. Avg. & Std.

Figure 6. Time series of nine monthly domain averaged(a) residuals, (b) residual anomalies, and (c) the averagesof the nine residuals and their standard deviations for theperiod from 2000 to 2005. Residuals from MERRA are alsoillustrated for comparison.

Table 3. Period-Domain Mean Values for Each Component of the Atmospheric Water Cycle and the Corresponding Residuala

E P WVFC WVT Residuals R/E (%) R/P (%)

OGXH 3.450 3.008 �0.456 �0.000 �0.014 0.41 0.47OCXH 3.450 3.135 �0.456 �0.000 �0.141 4.09 4.50OHXH 3.450 2.910 �0.456 �0.000 0.084 2.43 2.89HGXH 3.822 3.008 �0.456 �0.000 0.358 9.37 11.90HCXH 3.822 3.135 �0.456 �0.000 0.231 6.04 7.37HHXH 3.822 2.910 �0.456 �0.000 0.456 11.93 15.67GGXH 3.877 3.008 �0.456 �0.000 0.413 10.65 13.73GCXH 3.877 3.135 �0.456 �0.000 0.286 7.38 9.12GHXH 3.877 2.910 �0.456 �0.000 0.511 13.18 17.56MERRA 3.499 3.235 �0.550 �0.000 b0.005 c�0.286 0.14 0.15

8.17 8.84AVGsat 3.716 3.018 �0.456 �0.000 0.243 (0.224) 6,54 8.05(STDsat) (0.232) (0.113)AVGall (STDall) 3.662 (0.219) 3.072 (0.142) �0.503 �0.000 0.219 (0.224) 5.98 7.13

aUnits are mmd�1. Average of the satellite-based and merged data sets and their standard deviations are denoted as AVGsat and STDsat, respectively.AVGall and STDall also indicate average and standard deviations for all the data sets including the MERRA data set. The ratios of the residual to thecorresponding evaporation and precipitation are denoted as R/E and R/P in percentage.

bMERRA residual including water vapor tendency analysis increment (ANA) term. The value of ANA term is 0.291.cMERRA residual excluding ANA term (i.e., MERRA (exANA)).

PARK ET AL.: COMPARING ATMOSPHERIC WATER BALANCES

3500

Ocean. The difference in the data sets for precipitation wassignificantly lower over the southeastern Pacific Oceanand the Atlantic Ocean. The regions with discrepanciesbetween the data sets for precipitation were distributedover a broader area than those for evaporation. The rangeof sm for precipitation is from 0.05 to 1.65mmd�1, andthe range is from 0.23 to 1.23mmd�1 for evaporation.Coefficient of variation (CV) which is defined as the ratioof the standard deviation to the average (i.e., si/E(Xi)) wasalso computed. The spatial distributions of period meanCVs for evaporation and precipitation data sets are shownin Figures 3b and 3d. Compared with the precipitation, theCVs for evaporation are relatively homogeneous over mostareas of the ocean. For precipitation, the CVs are rela-tively large over oceanic dry regions.3.1.2. Water Vapor Flux Convergence and WaterVapor Tendency[18] Both of the domain mean time series of the XLT08

and MERRA for WVFC (Figure 2c) indicated that the watervapor flux generally diverges over oceanic areas. Theirperiod mean values were negative (�0.46mmd�1 forXLT08 and �0.55mmd�1 for MERRA). For the periodbetween 2000 and 2005, the WVFC of the XLT08 was typ-ically larger than that of the MERRA. The temporal correla-tion coefficient between the XLT08 and MERRA was 0.76.The period mean seasonal spatial distributions of theWVFCs are illustrated in Figure 4. The red colored areas(positive) indicate water vapor flux convergence, and theblue colored areas (negative) indicate water vapor flux diver-gence. The major patterns of the WVFCs and their seasonalvariations were well matched with those of the precipitation

(not shown). We also noted that the XLT08 had relativelyhigher values than the MERRA over the ITCZ and SPCZ.[19] The WVT derived in this study was compared with

the WVT from the MERRA. The WVT of the MERRAincludes the analysis increment tendency of water vapor thatis a nonphysically added value during the assimilation pro-cess in order to adjust it to the observation data. Thedomain averaged time series showed that both of the WVTsare in good agreement (Figure 2d) and have a strong correla-tion (0.90). The domain average estimates of the WVTswere significantly smaller than those of the other compo-nents of the water cycle. The mean seasonal and spatialdistributions of the WVT shown in Figure 5 reveal that thereis a significant seasonal variation between the Northern andSouthern Hemispheres. The distinct negative water vaportendencies are present in the Northern Hemisphere duringthe winter (from December to February), and apparentpositive water vapor tendencies exist in the NorthernHemisphere during the summer (from June to August). Bothof the WVTs have relatively strong positive tendencies overthe oceanic regions around East Asia and the northeasternPacific near Mexico during the boreal summer (Figures 5cand 5d) and strong negative tendencies over the Bay ofBengal during the boreal winter (Figures 5a and 5b).

3.2. Residual Analysis

3.2.1. Domain Averaged Residual Time Series[20] The nine residuals estimated from the combinations

of satellite-based and merged data sets for atmospheric watercycle components were analyzed by taking domain averages(Figure 6). The monthly time series of the domain averaged

(a) OGXH Avg. = -0.014 ( -2.575 ~ 5.328)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(b) OCXH Avg. = -0.141 ( -3.299 ~ 3.923)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(c) OHXH Avg. = 0.084 ( -2.688 ~ 4.170)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(d) HGXH Avg. = 0.358 ( -2.347 ~ 5.059)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(e) HCXH Avg. = 0.231 ( -3.183 ~ 4.422)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(f) HHXH Avg. = 0.456 ( -2.652 ~ 4.669)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(g) GGXH Avg. = 0.413 ( -2.456 ~ 4.698)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(h) GCXH Avg. = 0.286 ( -3.293 ~ 4.593)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(i) GHXH Avg. = 0.511 ( -2.769 ~ 4.841)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<<

[mm/day]

-2.4 -2.0 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2.0 2.4

Figure 7. Mean spatial distributions of the nine residuals for the period between 2000 and 2005.

PARK ET AL.: COMPARING ATMOSPHERIC WATER BALANCES

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residuals (Figure 6a) showed that there is a distinct featurebetween the residuals in combination with the merged evap-oration of the OAFlux and the residuals in combination withthe satellite-based evaporation from HOAPS and GSSTF.OAFlux included residuals that fluctuated between smallpositive and negative values near zero. The period meanvalues of the OGXH, OCXH, and OHXH residuals were�0.01, �0.14, and 0.08mmd�1, respectively. The residualsfrom the HOAPS and GSSTF had relatively high positivevalues between 0.23 and 0.51mmd�1.[21] The residuals of the MERRA were also analyzed in

order to make a comparison. MERRA provides closedatmospheric water budget including two unphysical terms[Bosilovich et al., 2011]. One of the terms is the analysis incre-ment of water vapor (ANA) that makes model predicted statevariable closer to observations. The other term was a negativefilling term (F) in order to ensure positive water vapor content.Since the value of F is small enough to neglect, the MERRAresidual can be obtained using the following equation:

R ¼ �E � �Ph i � r �!Q�D E

� @W

@t

�* +þ ANA (8)

[22] ANA reflects the observation effect on the analysis, andit is an important feature of theMERRA system. The budget ofwater and energy cycles in the model can be studied andevaluated with this quantified term [Robertson et al., 2011;Roberts et al., 2012]. Before defining this term as analysis

increment term, several studies considered this quantity aresidual term [Roads and Betts, 2000; Roads et al., 2002;Roads et al., 2003]. In order to determine the effects of ANAon the atmospheric water budget inMERRA, we also took intoconsideration the residual calculated by excluding ANA inequation (8), and we called this residual MERRA (exANA).While the MERRA residual from equation (8) is close to 0,the MERRA (exANA) residual has relatively large negativevalues (Figure 6a). The period mean values of the MERRAand MERRA (exANA) residuals are 0.01 and�0.29mmd�1,respectively. The anomalies with respect to the long-termmean of each time series for the nine estimated residuals seemto be in good agreement with each other (Figure 6b).Relatively high correlations exist between the residuals fromidentical evaporation and precipitation data sets exceptbetween OGXH-GHXH (0.80). The highest correlation canbe found between GCXH-GGXH (0.92). The correlationsbetween the nine estimated residuals are stronger than the cor-relations with the MERRA residual except for OHXH-HCXH(0.25) and OHXH-GCXH (0.29). The MERRA (exANA)residual anomaly time series seems to have no relationshipwith the others. The averaged values of the nine estimatedresiduals and their standard deviations (error bars) are alsoshown in Figure 6c.[23] The period-domain means for each atmospheric water

budget components and associated residuals are also sum-marized in Table 3. The relative magnitudes of the residualscompared to corresponding evaporation and precipitation arealso calculated in percentage and denoted as R/E and R/P inTable 3. For period-domain mean fields, the relative magni-tude of OGXH residual is smaller than other estimated resid-uals except MERRA residual. The magnitude of OGXHresidual is 0.41% of evaporation from OAFlux and 0.47%of precipitation from GPCP.3.2.2. Period Mean Residual Distribution[24] The nine estimated residuals show disagreements in

their intensities and patterns for the period mean spatialdistributions between 2000 and 2005 (Figure 7). Positive re-siduals (from green to red colored) indicate that the magni-tudes of the source terms (E, WVFC) for water vapor inrespect to the atmosphere are larger than the magnitudes ofthe sink term (P). Negative residuals (from blue to violetcolored) indicate the sink terms are larger than the sourceterms. The residuals from the combinations that includeHOAPS and GSSTF evaporation have more positive regionsthan the residuals that include the OAFlux evaporation. Mostof the residuals have positive values due to larger WVFC oversome portions of the ITCZ where P is generally larger than Ewith the exception of that for OHXH. Some of the residualshave widely spread positive values over the southeasternPacific except the residuals that include OAflux evaporation.Over the SPCZ, there are distinct negative residuals especiallyin the residuals that included CMAP precipitation. Yin et al.[2004] noted that the CMAP precipitation is often larger thanthe GPCP over SPCZ regions due to involvement of atollgauge data. The regions where differences between the nineestimated residuals exist can also be determined using equa-tion (7). The distribution of the large variances in theresiduals coincides with those of evaporation and precipitation(Figure 10a).[25] The relative magnitudes of residuals to the terms in the

water budget were also investigated for each grid with the ratio

(a) OGXH/OAFlux Avg. = 27.242 (0.002 ~ 348.573)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(b) OGXH/GPCP Avg. = 51.441 (0.001 ~2063.328)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<

[%]0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200

Figure 8. Spatial distributions of the ratios of period-meanOGXH residual (a) to period-mean evaporation fromOAFlux and (b) to period-mean precipitation from GPCP.The period is from 2000 to 2005. Units are %.

PARK ET AL.: COMPARING ATMOSPHERIC WATER BALANCES

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of period-mean residuals to period-mean values for evapora-tion and period-mean values for precipitation. As an example,the case of OGXH is included in Figure 8. Over most of theoceanic areas, the period-mean relative magnitudes of OGXHresiduals to evaporation from OAFlux are less than about50%. Near coastline and around 60�S, however, the valuesbecome higher (Figure 8a). It is also found that the residualscompared to precipitation from GPCP are usually large overthe dry oceanic regions (Figure 8b).[26] The mean spatial distribution of the ANA of MERRA

(Figure 9b) had strong negative values over the oceanicregions near Peru. Strong positive values exist over the WestPacific, the Bay of Bengal, subtropical regions over the EastPacific, and inter-American seas. A major feature of theANA period mean distribution is analogous to ANA clima-tological mean map represented by Robertson et al. [2011].

The residual MERRA (exANA) had identical patterns withopposite signs as the ANA in its period mean spatial distri-bution (Figure 9a). The period mean of the MERRA(exANA) residual ranged from �2.64 to 2.69mmd�1. TheMERRA residual derived by taking the ANA into consider-ation had relatively small values between �0.07 and0.06mmd�1 (Figure 9c).[27] A large quantity of the residual indicates an imbal-

ance in the atmospheric water budget. In order to determinethe regions where large imbalances would appear, the meanabsolute errors were calculated from the nine estimatedresiduals for each grid box as follows:

MAEi ¼ 1

9

X9j¼1

Ri;j � 0 (9a)

and

MAEm ¼ 1

72

X72i¼1

MAEi (9b)

where MAEi is the mean absolute error from the nineestimated residuals, Ri,j is the jth estimated residual fromthe satellite-based and merged data sets at month i, andMAEm is the period mean absolute error. Figure 10b shows

(a) Resi std. Avg. = 0.718 ( 0.271 ~ 1.510)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<[mm/day]

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5

(b) Resi MAE Avg. = 1.540 ( 0.722 ~ 4.714)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<[mm/day]

0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0

Figure 10. Spatial distributions of (a) the standard devia-tions and (b) the mean absolute errors from the nine esti-mated residuals.

(a) MERRA(exANA) Avg. = -0.286 ( -2.644 ~ 2.692)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(b) WVT(ANA) Avg. = 0.291 ( -2.737 ~ 2.668)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

(c) MERRA Avg. = 0.005 ( -0.067 ~ 0.061)

60S

30S

0

30N

60N

0E 60E 120E 180 120W 60W 0W

<<[mm/day]

-2.4 -2.0 -1.6 -1.2 -0.8 -0.4 0 0.4 0.8 1.2 1.6 2.0 2.4

Figure 9. Mean spatial distributions of (a) the residualexcluding the ANA term and (b) the ANA for water vapor aswell as (c) the residual including the ANA term for MERRA.

PARK ET AL.: COMPARING ATMOSPHERIC WATER BALANCES

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the spatial distribution of MAEm. Relatively large magni-tudes of residuals appeared around some of the coastal areasand over the Arabian Sea. The imbalances were also gener-ally large over the ITCZ, SPCZ, and monsoon area whereheavy precipitation occurs.

4. Summary and Conclusions

[28] This study examined column integrated atmosphericwater balances based on the analysis of residuals from variouscombinations of satellite-based and merged data sets for atmo-spheric water cycle components. Satellite-based data sets forevaporation such as HOAPS and GSSTF were used as wellas the satellite-NWP reanalysis merged evaporation data setOAFlux. For precipitation, the satellite-gauge merged GPCPand CMAP data sets as well as the satellite-based HOAPSwere used. The water vapor flux convergence by XLT08 andthe water vapor tendency derived from the HOAPS TPWwerealso used. The residuals of the MERRA in regard to analysisincrements were also analyzed for comparison.[29] The mean spatial distribution analysis for the period

between 2000 and 2005 over oceanic regions (60�N–60�S)showed that the satellite-based residual distribution and theirmagnitudes varied with the data sets. The residuals fromcombinations including HOAPS and GSSTF evaporationhad relatively large positive values over the midlatitude oce-anic regions due to the relatively high evaporation values ofthe HOAPS and GSSTF over these areas. The values of theperiod mean standard deviations between the residuals weresignificantly larger over the ITCZ, SPCZ, and monsoonregions, and their magnitudes ranged from 0.27 to 1.5mmd�1.The magnitude of the imbalance in the atmospheric waterbudget estimated from the satellite-based and merged data setswas also generally larger over the oceanic areas with heavyprecipitation such as the ITCZ, SPCZ, and monsoon regionsand had values ranging from 0.72 to 4.71mmd�1 with adomain average value of 1.54mmd�1. The larger residualsover the ocean may be attributed to errors in the data setsand the approximation of the water budget equation withoutthe condensed phase water component. Meanwhile, theMERRA has closed atmospheric water budget requiringartificially added nonphysical analysis increment term for thewater vapor tendency.[30] Analysis of the residuals from various combinations

of data sets in this study indicated that challenges remainin order to obtain an accurate atmospheric water budget.The errors in the individual data sets may be attributed totheir own methodologies and algorithms. Therefore, werecommend that careful consideration be used when apply-ing data sets for water budget components to water budgetstudies. However, similar residual anomalies suggest thatclimate variability analysis based on the residuals may notbe greatly affected by a specific data set.

[31] Acknowledgments. This work was funded by the Korea Meteo-rological Administration Research and Development Program under GrantCATER 2012–2063.

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