JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. D3, PAGES 7341-7358, MARCH 20, 1996 Balancing the atmospheric hydrologic budget Shyh-ChinChen, Charles L. Norris, and JohnO. Roads ClimateResearch Division, Scripps Institution of Oceanography, University of CaliforniaSanDiego, La Jolla Abstract. The atmospheric hydrologic budget in an idealized general circulation modelis diffi- cultto balance, especially if samples aretoo infrequent, mainlybecause of an inaccurately deter- mined moisture flux divergence. Although theclimatology canbe reasonably derived by consider- ing longer time averages, thealiased anomalous moisture divergences dueto insufficient sampling are intrinsic and cannot be removed; the effect is noticeable and detrimental out to seasonaltimes- cales. Increased temporal resolution or even continuous accumulations arereallyrequired. Lack of temporal resolution also affects forecast skill aswell astheperceived importance of theprecipi- table water tendency. Current atmospheric hydrologic analyses of moisture fluxes andevensatellite precipitation observations mayhave similar sampling problems. We recommend thatmodern analyses should provide more frequently sampled or even continuously accumulated hydrologic quantities, just asprecipitation is currently provided. 1. Introduction There are problems in trying to accurately descri!•e the at- mospheric moisture flux. Previously, radiosonde measure- ments were used [Starr and Peixoto, 1958; Starr et al., 1965, 1969; Rastnusson, 1967, 1968, 1971; Rosen et al., 1979; Peixoto et al., 1981; Savijarvi, 1988]. Along with the intrin- sic problems associated with accurately measuring winds and humidity as the radiosondesascendfrom the surface to the stratosphere, radiosonde measurements are only made at coarsely and irregularly spacedland locations. More recently, atmospheric moisturefluxes have been de- rived from four-dimensional data assimilation products [Trenberth, 1991; Roads et al., 1992a, 1994; Chen and Pfaendtner,1993; Trenberth atut Guillemot, 1995; Wang and Paegle, this issue; E.M. Rasmusson, and K. Mo, Large-scale atmospheric water vapor transport as evaluated t¾omNMC analysis, submitted to J. Climate, 1995, hereinafter referred to as Rasmusson and Mo, submitted manuscript, 1995]. These analyses, which more effectively combine, interpolate, and extrapolate diverse measurements to a regular global grid, are still not perfect. Potential problelns range fi'om lack of obser- vations to imperfections in the underlying model [e.g., Tren- berth and Olson, 1988; Hoskins et al., 1989; Trenberth and Guillemot, 1995]. Analyses also sufferfrom low horizontal as well as vertical resolution.In the past it has been common to provide analyses only on mandatory pressure surfaces. Manda- tory pressure surfaces do not adequately describethe boundary layer wheremost of the atmospheric moisture resides [Mo and Rasmusson, 1990]. Suspicious imperfections do show up in the moisture fluxes derived from National Meteorological Center (NMC) global pressure analyses. For example, over a sufficiently long time there shouldbe a balancebetweenthe net influx of water by the atmospheric motions and the net outflow by the surface streams (as well as underground flow). Roads et al. l1994] used Copyright 1996 bythe American Geophysical Union. Paper number95JD01746. 0148-0227/96/95 JD-01746505.00 this presumedbalance to correct the annual average of the moisture flux for basins in the conterminous United States. Even with this correction there were still noticeable crrors in quantities derived from these fluxes,such as evaporation. For example, close to the coast, evaporation was larger during the winter thanduring the summer; this seasonal variation was at odds with theevaporation derived from pan evaporation meas- urements. In certain areas, the derived annual evaporation was even negative. (See also Roadset al. [1992a, 1995b]). Although some of these suspicious characteristics couldcer- tainly be attributed to ourinability to adequately measure pre- cipitation, we were quite worried about our ability to adequately describe the fluxes with NMC's global pressure analyses. Roads et al. [1995] subsequently showed that NMC's pressure analyses hada bias in therelative humidity overlarge parts of the UnitedStates. The 12 UTC or early morningrelative hu- midities were toolow.Thisreduction could affect the perceived convergence. Another potentialerror was the inability of the mandatory pressure surfaces to adequately resolve the low-level jet. At 1000 mbar the surfacewinds usedin the calculations of the moisture divergence were too strong,but aloft the winds were too weak. Analysis products arecertainly improving. NMC's analyses on model's sigma levels have been available since March 1990 at the National Center for Atmospheric Research (NCAR). This analysis has 1-deghorizontal resolution (as opposed to the previous 2.5-deg resolution). The vertical resolution is also much higher, especially in the moistboundary layer. As dis- cussed by Kanamitsu [1989], since the sigma-level analyses betterresolve andmodel the atmospheric boundary layer, the final sigma-level analysis should betterreflect the true state of the near-surface atmosphere than the subsequent reinterpola- tionto mandatory pressure levels and the subsequent interpola- tion to standard pressure levels as was previously done in de- riving verticalintegrals from the pressure-level analyses [see Roads et al., 1992a, 1994]. Evenhigher spatial resolution than is currently possible with this global analysis system is probably still needed for adequately describing the atmospheric hydrologic parameters overland.Higher resolution analysis is needed to provide in- formation about hydrologic climates strongly influenced by 7341
Transcript
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 101, NO. D3, PAGES 7341-7358, MARCH 20, 1996
Balancing the atmospheric hydrologic budget
Shyh-Chin Chen, Charles L. Norris, and John O. Roads Climate Research Division, Scripps Institution of Oceanography, University of California San Diego, La Jolla
Abstract. The atmospheric hydrologic budget in an idealized general circulation model is diffi- cult to balance, especially if samples are too infrequent, mainly because of an inaccurately deter- mined moisture flux divergence. Although the climatology can be reasonably derived by consider- ing longer time averages, the aliased anomalous moisture divergences due to insufficient sampling are intrinsic and cannot be removed; the effect is noticeable and detrimental out to seasonal times- cales. Increased temporal resolution or even continuous accumulations are really required. Lack of temporal resolution also affects forecast skill as well as the perceived importance of the precipi- table water tendency. Current atmospheric hydrologic analyses of moisture fluxes and even satellite precipitation observations may have similar sampling problems. We recommend that modern analyses should provide more frequently sampled or even continuously accumulated hydrologic quantities, just as precipitation is currently provided.
1. Introduction
There are problems in trying to accurately descri!•e the at- mospheric moisture flux. Previously, radiosonde measure- ments were used [Starr and Peixoto, 1958; Starr et al., 1965, 1969; Rastnusson, 1967, 1968, 1971; Rosen et al., 1979; Peixoto et al., 1981; Savijarvi, 1988]. Along with the intrin- sic problems associated with accurately measuring winds and humidity as the radiosondes ascend from the surface to the stratosphere, radiosonde measurements are only made at coarsely and irregularly spaced land locations.
More recently, atmospheric moisture fluxes have been de- rived from four-dimensional data assimilation products [Trenberth, 1991; Roads et al., 1992a, 1994; Chen and Pfaendtner, 1993; Trenberth atut Guillemot, 1995; Wang and Paegle, this issue; E.M. Rasmusson, and K. Mo, Large-scale atmospheric water vapor transport as evaluated t¾om NMC analysis, submitted to J. Climate, 1995, hereinafter referred to as Rasmusson and Mo, submitted manuscript, 1995]. These analyses, which more effectively combine, interpolate, and extrapolate diverse measurements to a regular global grid, are still not perfect. Potential problelns range fi'om lack of obser- vations to imperfections in the underlying model [e.g., Tren- berth and Olson, 1988; Hoskins et al., 1989; Trenberth and
Guillemot, 1995]. Analyses also suffer from low horizontal as well as vertical resolution. In the past it has been common to provide analyses only on mandatory pressure surfaces. Manda- tory pressure surfaces do not adequately describe the boundary layer where most of the atmospheric moisture resides [Mo and Rasmusson, 1990].
Suspicious imperfections do show up in the moisture fluxes derived from National Meteorological Center (NMC) global pressure analyses. For example, over a sufficiently long time there should be a balance between the net influx of water by the atmospheric motions and the net outflow by the surface streams (as well as underground flow). Roads et al. l1994] used
Copyright 1996 by the American Geophysical Union.
Paper number 95JD01746. 0148-0227/96/95 JD-01746505.00
this presumed balance to correct the annual average of the moisture flux for basins in the conterminous United States.
Even with this correction there were still noticeable crrors in
quantities derived from these fluxes, such as evaporation. For example, close to the coast, evaporation was larger during the winter than during the summer; this seasonal variation was at odds with the evaporation derived from pan evaporation meas- urements. In certain areas, the derived annual evaporation was even negative. (See also Roads et al. [1992a, 1995b]).
Although some of these suspicious characteristics could cer- tainly be attributed to our inability to adequately measure pre- cipitation, we were quite worried about our ability to adequately describe the fluxes with NMC's global pressure analyses. Roads et al. [1995] subsequently showed that NMC's pressure analyses had a bias in the relative humidity over large parts of the United States. The 12 UTC or early morning relative hu- midities were too low. This reduction could affect the perceived convergence. Another potential error was the inability of the mandatory pressure surfaces to adequately resolve the low-level jet. At 1000 mbar the surface winds used in the calculations of the moisture divergence were too strong, but aloft the winds were too weak.
Analysis products are certainly improving. NMC's analyses on model's sigma levels have been available since March 1990 at the National Center for Atmospheric Research (NCAR). This analysis has 1-deg horizontal resolution (as opposed to the previous 2.5-deg resolution). The vertical resolution is also much higher, especially in the moist boundary layer. As dis- cussed by Kanamitsu [1989], since the sigma-level analyses better resolve and model the atmospheric boundary layer, the final sigma-level analysis should better reflect the true state of the near-surface atmosphere than the subsequent reinterpola- tion to mandatory pressure levels and the subsequent interpola- tion to standard pressure levels as was previously done in de- riving vertical integrals from the pressure-level analyses [see Roads et al., 1992a, 1994].
Even higher spatial resolution than is currently possible with this global analysis system is probably still needed for adequately describing the atmospheric hydrologic parameters over land. Higher resolution analysis is needed to provide in- formation about hydrologic climates strongly influenced by
7341
7342 CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET
NMC 84-91 Q DJF CLIM. CI = 10 Kg m -• x10 •
5
3
1
NMC 84-91 DJF DIV(VQ) C•__M.o.25 v,-4 Kg m -a s -• x10 -•
lO
5
o
Figure 1. December-January-February (DJF) clilnatology of National Meteorological Center (NMC) T40 pressure level analyses (1984-1991). Mass-weighted ,•ertical integrals of (a) precipitable water {q} and (b) moisture flux divergence Vo{qV}. Only areas with positive divergence are shaded in Figure lb. In this and sub- sequent figures, contour intervals and units are noted in the upper right hand corner of each panel; shading in- tervals are noted by the gray-scale bars on the right.
small-scale topographic features. Achieving sufficiently high global resolution is not possible, though, within the near term. An interim solution, for particular small-scale regions, is to use a mesoscale model, with mesoscale topography, forced at the boundary and initialized with large-scale co•di- tions from a general circulation model (GCM) or the analysis [Dickinson et al., 1989; Giorgi, 1990; Roads et al., 1992b; Berbery et al., 1994].
Is the amount of available analysis (and reanalysis [see Kalnay and Jenne, 1991]) data, that is growing almost expo- nentially as we begin to move toward higher vertical and hori- zontal resolution, really going to be adequate? How accurately can we ultimately predict variations in the hydrologic cycle. How accui'ately can we determine budgets'? The ultimate answer to these questions will depend upon comparison of new analy- sis products with new measurements made as part of the Global Energy and Water Cycle Experiment (GEWEX) Continental Scale International Project (GCIP) and other GEWEX pro- grams. However, in preparation for analyzing tl•e v•ealth of
data to be realized by the GEWEX programs, we attempted to answer these questions in a more idealized setting. For exam- ple, just how accurately can we predict the atmospheric hydro- logic cycle in a simplified GCM. The major simplifications are the lack of diurnal and seasonal cycles. The surface hydrology is also simplified. However, the model does provide a reason- able atmospheric hydrologic cycle and the simplifications al- lowed us to generate very long time series about which we can have statistical certainty.
Initially, we were interested in trying to understand just !•ow well we could predict the moisture flux convergence. We had previously showed that the moisture flux convergence was im- perfectly related to observed precipitation [Roads et al. 1994] but were uncertain how strong the relationship actually was. We felt that, in reality, it would be easier to verify moisture convergence than it would precipitation since the moisture convergence can be deduced from analysis. Unlike precipita- tion, moisture convergence can be both positive and negative, and this linear nature suggests that moisture convergence may
CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET 7343
R•O MODEL JAN. CLIM. DIV(V(•t =(•.• E-4 Kg m-Zs -• x10 -•
lO
5
o
Figure 2. As in Figure 1, except shown here are the simplified GCM climatologies of {q} and Vo{qV}.
be easier to quantify the prediction skills. We were also aware of the intrinsic difficulties caused by the small-scale nature of precipitation. We also felt that precipitation forecasts may be too dependent upon the model parameterizations and that it might be better to concentrate forecast studies upon an alterna- tive relevant quantity like moisture convergence. Finally, we were aware that moisture divergence really measures the differ- ence between evaporation and precipitation and thus predic- tions of this variable might be more relevant to surface hy- drology.
Most of these preconceptions were incorrect. As discussed by Nghiem [1991] and as discussed in this paper, moisture convergence, as it is presently archived, has many potential problems. Within the confines of our idealized experiment, it was actually much easier to predict and specify precipitation. The basic reason is that precipitation is accumulated whereas moisture convergence is sampled. Inadequate sampling of quantities that should really be accumulated cannot be compen- sated for by developing long sample periods. It is more impor- tant to either accumulate or sample more frequently than we
have been able to in the past with the available twice-daily analyses. We also show that as we increase the accuracy of the moisture convergence calculation, by increasing sample tYe- quency, that the importance of the precipitable water tendency becomes more apparent.
The diurnal cycle may create additional problems. Again, we should not simply sample moisture fluxes at 0 and 12 • and then expect an exact comparison with the precipitation accu- mulated over the same 24-hour time period; this precipitation will be dependent upon the accumulated convergence as well as accumulated evaporation and integral precipitable water ten- dency. Even analyses 4 times a day may not be sufficient. Phil- lips et al. [ 1992] point out that some model variables, convec- tive precipitation and land evaporation in particular, have characteristic timescales shorter than a quarter day. Thus we are now fairly certain that when we are trying to develop hydro- logic budgets that past analysis archives are limited by inade- quate temporal resolution as well as horizontal and vertical resolution. We now believe that in order to achieve balanced
hydrologic budgets, it will be necessary to continuously accu-
7344 CHEN ET AL.: BALANCING 'FHE ATMOSP}IERIC HYDROLOGIC BUDGET
Figure 3. As in Figure 1, except shown here are the simplified GCM climatologies of (a) evaporation and (b) precipitation.
mulate moisture convergence as well as precipitation and then make these accumulated flux fields available along with the al- ready available instantaneously sampled data.
In section 2, we describe the data used for this investiga- tion. We mainly investigate the atmospheric hydrologic budget in a simplified GCM, but we also point out that similar temporal resolution problems may occur in NMC's analysis and satellite measurements of liquid water. Climatology inter- comparisons and budgets are shown in section 3. RMS vari- ability and short term budgets are shown in section 4. Predict- ability characteristics are shown in section 5. Conclusions are provided in section 6.
2. Data
2.1. Global Model Output
The moist primitive equation global GCM used for this study is described by Chen et al. [1993] and Chen cazd Cayan [1994]. The model, which is a simplified version of NMC's GCM [Sela, 1982] has relatively low resolution with four ver- tical sigma layers and a spectral truncation' oi' t'homboldal 20.
The model has no diurnal cycle and the hydrologic parameteri- zations include large-scale condensation, Kuo's convective parameterization, and bulk aerodynamic evaporation. Surface sensible heating and surface friction are similarly parameter- ized. The model overlies a climatological ocean with January climatological sea surface temperatures. The model is forced by empirically derived temperature and streamfunction for- cings designed to produce a reasonable climatology, (see Chen et al. [ 1993] for a discussion of how the forcings were derived). Gratifyingly, unforced internal variability is also reasonable in comparison to the observations.
Although the model only approximates nature, we can at least use it to obtain a very accurate budget. The model mois- ture budget can be written as
c•{qJ+v.{qV}-KV2{q}= E-P , (1) where q denotes the specific humidity, V the horizontal wind, E the surface evaporation, and P the precipitation. A%-"2{q} is the moders diffusion parameterization for small-scale, unre- solved terms. For the budgets discussed in the paper, it had
CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET 7345
Figure 4. (a) Special sensor microwave imager (SSM/!) derived DJF liquid water climatology (December 1987 to February 1991). (b) Total number of measurements at each grid box.
only a small influence and henceforth will often be ignore•l. The braces represent the mass weighted vertical integral
{...} = I...•/p/g , 0
t,2)
where Ps is the surface pressure and g is the gravitational con- stant. All other symbols are conventional. The vertical inte- grals described in (2) could be calculated simply by summing the sigma layers. However, for the divergence of the vertically integrated moisture flux, V-{qV}, we summed the advection terms (including the vertical advection). Since the advection form is the explicit form for the moders equations, this pro- vided a more consistent and numerically accurate model budget. Once all products were ultimately truncated to the model R20 resolution, differences resulting from use of the flux or diver- gent form were quite small. It is generally not easy to show that GCM output satisfies, to high accuracy, exact budgets. As errors emerge, we usually resort to trying to identically emu- late model calculations (like the above advection fmmulation)
in order to convince ourselves that we really do have an accu- rate budget.
A model perpetual January control run was carried out for 1700 days, but only the last statistically stationary 1600 days were considered for these budget calculations. From this basic time series, three ensembles of daily values for {q}, Vo{qV}, and E were constructed and compared to daily precipitation ac- cumulations. The first ensemble of daily values was con- structed from instantaneous samples one day apart. A daily av- erage was approximated by the average of the sample at the end of each day and the sample at the beginning of each day or equivalently at the end of the previous day. Itenceforth, this ensemble will be denoted as the IX ensemble. The second or
2X ensemble included an extra sample in the middle of each model day; a trapezoidal integration applied to the three sam- ple points provided a more accurate daily average than the av- erage of the end points. The third or 4X ensemble included two additional samples; each quarter day is sampled and added to the daily trapezoidal integral over five points. Moisture tendency, •{q}/•t, is simply evaluated as the difference between the be- ginning of the day and the end of the day and is the same Ibr al I
7346 CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET
-.0000a806 TO .000035a5
-.00000584 TO .00001033
R20 JAN. CLIM. (4X)RESIDI•__L o.• E-4 Kg rn-as -' x10-5
6
Figure 5. Climatological budget residuals for (a) IX and (b) 4X ensembles.
ensembles. Precipitation is accumulated from each time step of the model and is also the same for all three ensembles. Only moisture convergence and evaporation are affected by sam- pling frequency.
We shall also deal with running window lengths of 1-60 days for all (1X, 2X, and 3X) ensembles. It might be a priori assumed that longer averaging lengths would mitigate the minimal sample ensembles. As shall be show, minimal sample effects are still noticeable even for very large window aver- ages.
To evaluate the variability of the moisture budget, we com- pute root-mean-square (RMS) for each terms in (l) as well as the residual (imbalance) of the equation. We consider two RMS quantities, anomalous RMS (ARMS)and total RMS (TRMS). These quantities are derived by first separating all hydrologic variables
A(x,t)={A}+A (x)+A'(x,t) , (3)
where A(x,t) is a function of space and time, (..) stands for long term mean, { } denotes the global mean, and ( )* and ( )' represent the spatial and the temporal deviation. Thus global
mean ARMS and TRMS are respectively defined as
{A' 2'• • - )2 • and {(A-{A} }
2.2. NMC Data
Vertically integrated atmospheric hydrological variables, {q} and Vo{qV}, were derived from NMC's global pressure analysis for the period January 1984 through December 1991 [see Roads et al., 1992a, 1994]. •'he giobal pressure 'analysia archives were available twice daily at I1 mandatory pressure levels on a regular 2.5øx2.5 ø horizontal grid. These variables were interpolated to a higher resolution vertical grid of 50 mbar before the vertical integration was carried out from the surface to the top of the atmosphere. Surface pressure interpo- lated from geopotential height and orography was also used to weight the column mass; this provided slightly better looking fields than using the original surface pressure provided with the analysis. After vertical sums were calculated, all fields were transformed from the original 2.5 ø grid to T40 spherical har- monics. This spectral representation provided a convenient way to evaluate derivatives as well as economically store data.
CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET 7347
(a) ARMS OF DQ/DT+DIV+DIFFUci(__l•!25 E-4 Kg m-2s -x x10 -4 .....7•-- - '"""':::':"":" •. I
(b) ARMS 0F E-P (1X) CI = 0.25 E-4 Kg m -2 s-' x 10 -4
1
.0000135 TO .0003150
Figure 6. Anomalous root-mean-square (ARMS) variations for the (a) left-hand side and (b) right-hand side of the moisture budget equation (I), from the IX ensemble.
A divergent correction to the winds [Trenberth, 1991] was also incorporated in order to provide more accurate vertically inte- grated mass and moisture flux divergence.
Again, as was done for the model data, IX and 2X ensembles were derived from twice daily archives of {q} and Vo{qV}. Use of twice daily data is even more critical here than it was for the model because of the diurnal cycle. Another critical difference is that the analyses have seasonal variations. A 31-day run- ning-mean annual climatology from eight analysis years was constructed. Daily anomalies for each ensemble were then de- rived by removing this running-mean climatology fi'om daily values. Seasonal variations in the analysis are potentially more problematical than the kinds of variations found in the
perpetual January GCM output. For comparison with perpetual January GCM output, we ultimately used only December, Janu- ary, and February (DJF) analyses.
We found it more convenient here to quality control the ul- timate hydrologic sums rather than the original .global analy- sis data (see also RoarIs et al. [1995]). In particular, we used a 4-sigma filter to identify apparently erroneous analyses. Al- though some spurious spikes of the global-mean RMS were
found, none of these occurred during our DJF seasons. Poten- tially spurious values tend to be more of a problem in June, July, and August. Another noticeable effect occurred in June 1991, when a new analysis method called spectral statistical interpolation (SSI)was incorporated into the NMC analysis [Derbet et al., 1991; Parrish and ,)erber, 1992]. This change produced a reduction in the daily variance in tropics which would have been noticeable if we included December 1991. Al-
though this new analysis is presumably better than previous analyses, we decided for consistency not to use December 1991 analyses.
2.3. SSM/I Liquid Water
The special sensor microwave imager (SSM/I) is a passive microwave imaging instrument carried aboard the Defense Me- teorological Satellite Program (DMSP) series of spacecraft [Hollinger et al., 1987]. SSM/I has been quite useful for sens- ing atmospheric water, both in the liquid and vapor phases [Wentz, 1986; Schluessel and Emery, 1990; Berg and Chase, 1992]. The SSM/I measures microwave radiances at 19.35,
7348 CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET
(at) ARMS OF DQ/DT+DIV+DIFFUci(•!25 E-4 Kg m-2s -I x10 -4
4
3
2
1
-I x 10 -4
4
3
1
ß 0000188 TO .0003170
Figure 7. As in Figure 6, except shown here are the ARMS variations from the 2X ensemble.
22.235, 37.0, and 85.5 GHz. The 19.35-, 22.235-, and 37.0- GHz channels report radiances in both horizontal and vertical polarizations, while the 22.235-GHz channel reports only the vertical polarization. Several DMSP spacecraft carrying SSM/I instruments are currently in operation (the data used in this study are taken from the DMSP F8 spacecraft, which is in a cir- cular, Sun-synchronous, near-polar orbit with an instrument swath width of 1400 km).
Over the oceans, SSM/I is capable of measuring column- integrated water vapor (precipitable water) as well as liquid wa- ter (associated with clouds). Precipitation rates can then be re- lated to liquid water [e.g., Went•, 1992], but the details of how precipitation should best be determined are a subject of ongo- ing study. We avoid this research issue to some extent by working only with atmospheric liquid water. However, the variability of any precipitation algorithm derived fi'Oln liquid water amounts should still ultimately correlate with the m•der- lying liquid water field.
From a 4-year (1987-1991) liquid water SSM/! data set [Wentz, 1989], we binned all liquid water data into 2.5 by 2.5- deg grid boxes. Since satellite flight-paths do not pass a p•r- ticular point at the same time each day, we grouped all incas-
urements between 0 and 12 UTC and between 12 and 24 LrlC to
roughly represent IX- and 2X-daily ensembles as NMC analy- sis and model output. Again, we used only DJF data, but a 31- day running climatology was used to deduce the daily anomaly.
There are many data gaps in the SSM/I tithe series; this is due to the nature of polar orbiting satellite measurements. Al- though the SSM/I gives nearly full globe coverage each day, diamond-shaped data gaps occur in lhe tropics; these transient gaps proceeds toward the east with each successive day. A point on the surface which happens to fall within one of these data gaps may not see another SSM/I overflight ll.}r periods as long as 4 days, until the gap has moved past. Also, small, cir- cular, permanent data gaps are found at the north and south poles, but these are small and do not impact our analysis. As a result of the pattern of data gaps, the total number of data sam- pies varies from the tropics to the poles. For example, in 13 months of twice daily time series, the total number of samples or counts per grid point used for the climatology computation of liquid water is shown in Figure 4b. In the tropics, there are only about 175 counts (averaging less thm• one measurement every other day)out of a possible 780. High I,•ti:udcs have relatively more frequent measurements.
CHEN ET AL.: BALANCING THE ATMOSPHERIC 1tYDROLOGIC BUDGET 7349
(&) ARMS OF DQ/DT+DIV+DIFFUci(__4)•!aa E-4 Kg m-es -• xlO -4
1
ß 0000146 TO .000:3152•
(b) ARMS OF E-P (4X) cI = 0.25 E-4 Kg m-2s -• ox10 -4
(.?....--:.,.:•
1
ß 0000138 TO .0003173
Figure 8. As in Figure 6, except shown here are the ARMS variations from the 4X ensemble.
3. Climatology
The DJF climatologics of prccipliable water {q} ,,:•d mois- ture divergence V-{qV} fi'om twice daily NMC analysis for the period 1984 to 1991 are shown in Figure I. Fhc analysis pre- cipitable water (Figure l a) is similar to that l•rcscnted previ- ously by Roads et al. [1992a], which included only 1987 through 1989. Areas with high values occur over the Amazon, equatorial Indian Ocean, western Pacific warm pool region, and South Pacific Convergent Zone (SPCZ). A moisture laden band extends from the warm pool to the equatorial eastern Pacific and continues across the Atlantic. This moist band coincides
well with the Inter-Tropical Convergent Zone (ITCZ). Dry ar- eas are mainly over major continents except for tro?ical Africa and South America.
The 4X climatology of {q} from the GCM is shown in Fig- ure 2a. As might be expected, the GCM {q} is greatest over the tropical oceans. Minimum values occur over regions of high topography, such as the Himalayans and Rocky mountains. As was noted for other GCMs [e.g., Roads et al., 1992a, Marshall and Oglesby, 1994; Roads et al., this issue] the overall amount of precipitable water is low. This model does not have a severe
temperature bias [Chen et al., 1993}; the low pre½ipitable wa- ter is due to the model's coarse vertical resolution which does
not adequately resolve boundary layer humidity. Wet Amazon features are also not evident, perhaps due to lack of a land sur- face hydrology in the model.
In Figure lb, NMC's analysis shows that there is large moisture convergence (dashed lines indicate negative diver- gence or convergence) over the Indian Ocean, SPCZ, ITCZ, and South America. Again, even with four more winters included, the divergent patterns shown here are quite similar to that shown previously by Roads et al. [ 1992a]. Despite the model's deficient precipitable water as well as the omission of the nar- row ITCZ in the eastern Pacific, the model's Vo{qV}, shown in Figure 2b, captures most of the convergent and divergent fea- tures in the analysis. Features such as the SPCZ and subtropical divergent source regions are reproduced quite well.
GCM evaporation and precipitation fields are shown in Fig- ures 3a and 3b, respectively. Evaporation is especially strong over the tropical and subtropical Indian, Pacific and Atlantic Oceans. Land evaporation is not included in this model (The negligible amounts evident in Figures 3a are due to spectral spillage from the ocean areas, since all fields wc•c filtered to
7350 CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET
(a) ARMS OF RESIDUAL (1X•i = 0.25 E-4 Kg m -2 s -t ...... . •..?.. ;.-•,:_.':-"•-'ø.-.,•..•:' , - ........ =..:•....:::.,•:...
.0000186 TO .0004215
ß 00000213 TO .00003108
Figure 9. Residual ARMS for (a) IX and (b) 4X ensembles.
x10 -4
4
x10 -5
R20 resolution). Major precipitation patterns are found over the'tropical Indian and Pacific Oceans as well as over two pro- nounced storm tracks in the northern Pacific and Atlantic.
Consistent with the moisture flux convergence, the major defi- ciency of'these precipitation patterns in comparison to the observed wintertime precipitation climatology [e.g., Legates and Willmott, 1990], are the lack of narrow heavy ITCZ pre- cipitation regions in the eastern tropical Pacific and Atlantic. Similar to the low precipitable water, the model also failed to produce heavy precipitation over the Amazon.
The wintertime climatology of the SSM/I liquid water, which can be related to precipitation, is shown in Figure 42. (The SSM/I algorithms used hem to diagnose liquid water are' most useful over ocean; hence land areas are •nasked.) l'wo identifiable maximums occur in the vicinity of the north Pa- cific and Atlantic ocean storm tracks. The SPCZ is not particu- larly strong. There is an intense narrow band of liquid water in the eastern tropical Pacific. There are also some spurious high values over coastal Asia which may be due to signal contami- nation from islands and continents. Despite the tropical differ- ences, the midlatitude liquid water features are similar to model and analysis flux convergences as well as model prccipitatlon.
To summarize, there are still many problems that arise as we continue to try to describe regional details of the global hydro- logic cycle. Individual fields from observations and models can be compared with each other but given the still large dis- crepancies it is difficult to attempt to deduce fields that cannot be directly measured from these diverse measurements. How- ever, a complete budget can be analyzed within the confines of the model output.
Figure 5b shows the difference or residual between the left- and right-hand side of (1) using the 4X model ensemble. smallness of the residual indicates that the climatological budget in (1) is almost balanced. The maximum residual value barely exceeds 10 -5 kg m-2s •. From this balanced budget, we are confident that we have developed the numerical tools to ac- curately describe the atmospheric GCM's hydrologic budget. Note that the error is a bit larger for more infrequent samples. For the ensemble sampled only once per day (Figure 52), there are some noticeable errors in the eastern Pacific and midlati-
tude to high-latitude region of the southern hemisphere. Accu- rate climatological budgets may require more than long time samples; they may also require more frequent sampling than has heretofore been attempted.
CHEN ET AL.: BALANCING THE ATMOSPHERIC 11YDROLOGIC BUDGET 7351
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Figure 10. (a) Global mean residual total root-mean-square (TRMS) for the 1X, 2X, and 4X ensembles. The RMS of E-P is also shown by the thick solid curve. (b) Normalized global mean residual TRMS for the IX, 2X, and 4X ensembles. (c) Normalized global mean residual ARMS for the IX, 2X, and 4X ensembles.
4. Variability
As shown previously by Nghiem [1991], balanced budgets are even more difficult to achieve on a day-to-day basis. For example, the daily variability on each side of the budget equa- tion (1) should be completely balanced. It is not. Figure 6 shows the ARMS of the anomalous left-hand side and the right- hand side of (1) for the 1X ensemble. The sum on the left-hand side will be referred to as effective divergence in section 5. The ARMS is calculated after the corresponding time-mean value from each ensemble is removed. As may be clearly seen, the variability of the left-hand side terms are substantially larger than the variability of the right-hand side terms everywhere.
The maximum disagreement corresponds to the Indian Ocean, SPCZ, and especially over the midlatitude oceanic storm tracks.
The imbalance, as shown in Figure 7, can be reduced by sampling twice a day (2X ensemble). However, over the mid- latitudinal oceanic storm tracks regions, the imbalance is still quite noticeable. As shown in Figure 8, a better balance is ob- tained by sampling 4 times a day (4X ensemble). Note also that the ARMS of the right-hand side changes little from the 1X to the 4X ensemble. Since precipitation is continuously accumulated, whereas E is sampled at the same rate as the di- vergence, any change due to sampling frequency is solely be- cause of sampling of E, and this is small in the r,•odel. Also,
7352 CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET
(a) NMC 84-91 DJF q ARMS (iX) CI = •.0 Kg m -a
NMC 84-91 DJF Q ARMS (2X) CI = 2.0 Kg m -a
12
8
4
Figure 11. NMC analysis DJF precipitable walel, {q}, ARMS: (a) IX and (b) 2X ensembles.
since diffusion is negligible and •){q}/Ot is identical for all en- sembles, we must conclude that it is really only the divergence
that is strongly affected by the frequency at which samples are taken.
As shown in Figure 9, imbalances in the budget due to insuf- ficient sampling can be as large, if not larger, than the diver- gence itself. This imbalance occurs primarily over regions where the background variance is relatively high such as over the midlatitude storm tracks. Tropical regions, despite high variance, appear slightly less affected by the sampling fre- quency.
A common misperception is that a suitably long running mean will mitigate minimal sample error. This is true only for describing the climatology rather than a low-frequency anom- aly as shown in Figure 10. Figure 10a shows the global mean residual TRMS of the three ensembles along with the TRMS (with climatology included) of 4X E-P as a function of the run- ning mean window length (see section 2.! for a definition of window average). The residual TRMS normalized by the TRMS of E-P is shown in Figure 10b. The IX ensemble residual is larger than that of E-P for window lengths shorter than a month; 2X and 4X daily residuals are s•naller than the E-P for all window length. The normalized residuals show daily imbal-
ances of 180%, 60%, and 20% and am noticeably improved as the window length increases, especially lbr 1X ensemble. In fact, if all three curves in Figure 10b were extended to 1600 days window length, which represents the global-mean clima- tology residuals, the corresponding normalized residual TRMS are 18% and 9% for IX and 4X ensembles respcctively.
However, the reduction of normalized residuals as the win-
dow length increases is not e¾ident in the anomalous (climatology removed) budget. The residual ARMS of all three ensembles decreases with increasing window length at roughly the same rate that the RMS of E-P decreases. As shown in Fig- ure 10c, all three curves approach constant values. Running means are effective in reducing budget discrepancies only for the first few days. Apparently, the imbalance due to insuffi- cient sampling frequency is an intrinsic aliased feature that cannot be substantially compensated simply by taking longer averages. Accuracy in budget calculations comes mainly from increased frequency of sampling (or continuous accumulation) rather than from increased duration of poorly sampled ensem- bles. Representativeness, of course, does require increased du- ration.
Sampling frequencies have less impact on the other hydro- logic variables. For example, the ARMS magniludcs of {q} for
CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET 7353
Figure 12. As in Figure 11, except shown here is NMC's flux divergence Vo{qV}.
the 4X and 1X ensembles (not shown) are comparable, and, un- like divergence, the ARMS magnitude of {q} is much smaller than the climatology {q}. The magnitude of the relative ARMS of each term in (1) can be ordered as V-{qV}, P, O{q}/Ot and then E. However, since we use a simplified model which has evaporation only available over ocean, the evaporation over land and its strong annual and diurnal cycle [e.g., Roads et al., 1994] is not really simulated. It may ultimately be necessary to accumulate evaporation the same way we accumulate precipi- tation.
It is more difficult to discern whether or not we have a sam-
pling problem with NMC pressure analyses because there is no budget to balance. There is a budget associated with tl•c sigma analyses and as shown bv Rasmusson and M o (submitted manuscript, 1995), there is an unexplained imbal- ance. To at least check whether a substantial reduction occurs
in the pressure analysis with increasing sample size, we con- sider lX and 2X analyses. As might be expecled and similar to model results, the daily ARMS of {q} is not sensitive to sam- pling frequency (Figure 11). Here we use the mean value of two consecutive 00Z analyses to represem a daily value il• the 1X ensemble. The 1X ensemble that included the 12Z analysis alone did not show significant differences, even in the summer
hemisphere and over the continents where the variability is highest. As shown in Figure 12, there is a noticeable impact on the perceived moisture convergence. ARMS amplitudes are reduced almost everywhere when the 2X ensemble is used. As shown previously for the simplified GCM, areas most affected by sampling frequency are the midlatitude oceanic storm track regions and the SPCZ.
Satellite measurements also have a sampling problem. Fig- ure 13a shows the ARMS when the daily anomalies are evalu- ated using measurements only from the 1200-2400 hour time period. Separate consideration of the ARMS from the 0000- 1200 hour time period gives similar features (not shown). Es- sentially, large variations can be found over midlatitude and high latitudes, as well as the ITCZ and SPCZ. Figure 13b is similar to Figure 13a, except all available observations are in- cluded; however, because of the nature of satellite measure-
ments, we really only have 2X or more data in middle latitudes. This has an impact upon the perceived variance reduction asso- ciated with more frequent samples. For example, the RMS of the 2X ensemble is reduced only over the oceanic storm track regions. Because of lack of samples, tropical RMS values show only slight reductions.
It should be pointed out here that despite the lack of sam-
7354 CHEN ET AL.: BALANCING rI'ttE ATMOSPHERIC I IYDROLOGIC BUDGET
Figure 13. SSM/I DJF liquid water ARMS. (a) 1200-2400 hour measurement only and (b) 24 hours averaged if both 0000-1200 and 1200-2400 hour measurement can be found; otherwise, use whatever is available.
pies, SSM/I measurements do show that there are large tropical variations as well as large variations in high-latitude storm track regions. This is consistent with the model characteris- tics. NMC's analysis characteristics, however, do not have the strong tropical variations shown here for SSM/I measurement as well as for the GCM simulations. This scant evidence sug- gests that NMC's pressure-level analysis may be unable to de- pict the intensity and variation of tropical features.
5. Specification and Prediction
As discussed in the previous section, the error variance is reduced by considering quantities that are more frequently sam- pled or even accumulated. Here we investigate the impact of this sampling error on the perceived prediction skill of the hy- drologic cycle. In particular, we show how well we can predict precipitation as well as E-P using moisture divergence. As de- scribed by Chen et al. [ 1993], we had previously developed a set of predictability experiments l¾om the control run de- scribed here. Starting off from initial conditions extracted from the control run, but with initial error added at small
scales, a set of twenty-six 60-day forecasts was made every 60
days. The initial error was introduced into the initial condi- tions by spectrally truncating all R20 prognostic varipbles at R15. This truncation represented, in an idealized fashion, ob- servational error. On the average, this truncation introduces an initial relative RMS error of about 2.5% in the height field. Output from the predictability experiment was saved 4 times daily, and three ensembles; i.e., IX, 2X, and 4X were again constructed.
In order to interpret the predictability curves, it is helpful to first examine the specification skill of time-averages as indi- cated by anomaly pattern correlations. By time-averaged specification we mean 5-day averages specifying 5-day aver- ages, 10-day averages specifying 10-day averages, and so on. The pattern correlation between two variables a' and b' is given by
{a'b'}
p(a,b) = {a' 2 }•A {b' 2 }•A (4) where a' and b' have the climatological mean as well as the spa- tial mean removed. Brackets indicate an average over space. We average all pattern correlat'ions within the ensemblc'.'to de- velop the ultimate ensemble mean pattern correlati,,ns.
CHEN ET AL.: BALANCING THE ATMOSPHERIC I IYDROLOGIC BUDGET 7355
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Figure 14. Time average specification skill for (a) evaporation minus precipitation E-P and (b) precipitation P. The 4X', 2X', and 1X' curves denote ensembles using only divergence, Vo{qV}. The 4X, 2X, and 1X curves denote ensembles using effective divergence, 3{q}/Ot + Vo{qV}.
Figure 14a demonstrates the skill, as represented by the pat- tern correlation, of specifying E-P using the flux divergence (dashed curves IX', 2X', and 4X'). Sampling divergence once per day (1X') yields correlations less than 0.6 for all time aver- ages. The 2X' and 4X' ensembles show better skill but only reach correlations of 0.9 for monthly means.
The precipitable water tendency term has a notable impact upon this perceived skill. The skill at specifying E-P using the sum of the divergence and the tendency, 3{q}/Ot + Vo{qV}, which we denote effective divergence, is also shown in Figure 14a for the 1 X, 2X, and 4X ensembles (solid curves). The addi- tion of the tendency term substantially increases the correla- tion for time averages a tEw days in duration. Thus we cannot ignore the precipitable water tendency in short-term balances and prediction. In fact, if the tendency terms are omitted, the specification skill of the 4X ensemble is no longer superior to the 2X specification. The tendency terms have a smaller im- pact on the 1X ensemble, presumably due to the large imbal- ances still remaining in this aliased ensemble.
Specification of P by the divergence and effective diver- gence (Figure 14b) show sinfilar but slightly smaller skill. Again. 4X and 2X ensembles are much more skillful than IX
ensembles throughout the entire 60-day period. The precipi- table water tendency is also important for the 2X and 4X en- sembles. Similar but much lower skills, correlations of 0.2'5 to
0.4 (initially), occur for divergence and effective divergence predicting evaporation (not shown). Thus the moisture flux convergence and precipitable water tendencies are useful but imperfect predictors for P and E, so long as the flux conver- gence can be sampled sufficiently often, or even accmnulated.
Figure 15 shows how well time averages of divergence and effective divergence predict the time averages of E-P and P. The skill of the three ensembles are compared to the forecast skill if forecast E-P is used to predict E-P and forecast P is used to predict P. Similar to Figures 14a and 14b, sampling once per day (1X')provides the smallest forecast skills. By contrast, the forecast skill of the effective divergence 4X ensemble ap- proaches that of E-P as well as P. The forecast skill using di- vergence alone, namely 4X', 2X', and IX', is lower initially, but similar to specification, increases at longer timescales. However, all prediction skills asymptotically move toward each other and zero as the initial et for growq.
Figure 16 compares the tomcast skill in tropical and mid- latitude regions. Tropical skill characteristics are similar to
7356 CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDROLOGIC BUDGET
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Figure 15. As in Figure 14, except shown here is time average prediction skill. The prediction skill using the model E-P and P are also plotted as solid thick curves in the corresponding panel. Predictions are made at zero lag for various time averages (abscissa).
the global skill characteristics shown previously in Figure 15. Apparently, the global skill is heavily weighted toward the tropical regions which has the largest variance of precipita- tion and moisture flux divergence. As was shown previously, these areas are sufficiently sampled with the 2X ensemble. Sampling more often (4X ensemble) is more important in mid- dle latitudes, especially if the tendency term is included.
It should be noted that the skills shown in these experi- ments are highly idealized cases. In reality, prediction skill of rainfall is very low; large error occurs after first lbw hours of integration due to spin up or spin down problem as well as many defects of the model and observing network. Sampling error in short-term forecast may be small colnpar•z;J to these other errors.
6. Conclusions
In the available public archives of atmospheric analyses, atmospheric moisture and winds are archived a few times a day and from these infrequent samples we have attempted, in the past, to relate the moisture flux convergence to precipitation measurements as well as to derive a residual evaporation. Some of these precipitation measurements come from accumulations
in sparsely distributed rain gauges; other measurements are de- rived from relationships of satellite brightness temperature in microwave frequencies. Other imperfect observations will soon come on line and will have to be integrated into the over- all observing system. Will we be able to ultimately show from these archives that we can adequately describe and predict the atmospheric moisture budget?
In this paper, we asked a simpler question. Itow accurately can we determine the atmospheric moisture budget terms if we could perfectly measure individual components? We then at- tempted to determine the climatology, variability and predict- ability of components of the atmospheric hydroibgic cycle in a simplified global general circulation model. Even with rea- sonable approximations, it was quite difficult to achieve a bal- anced budget for any averaging length. The residual budget er- ror can be as large as the divergence of the moisture flux. The major problem here lay in our methodology of deriving at- mospheric moisture flux divergence from only a tbw samples per day. Sampling once per day may be marginally useful for describing the large-scale time-incan atmospheric hydrologic cycle. To describe shorter term (even •nonthly scale) and smaller spatial scales of model variability and predictability, samples many more times a day are necessary.
CItEN ET AL.: BALANCING TIlE ATMOSPHERIC 1 tYDROLOGIC BUDGET 7357
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Figure 16. Time average prediction skill for P i• (a) tropics (between 15øN and 15ø51) and (b) NH midlatitudes (60øN and 30øS). Xs and X's mark the prediction curves using effective divergence and divergence, respectively.
This aliased feature of atmospheric moisture fluxes cannot be removed simply by considering longer time averages; the effect is noticeable and detrimental out to seasonal timcscales.
However, the impact is geographically dependent. Midlatitude storm track regions are most severely affected; t•opical re- gions are also affected. Subtropical regions are affectcd least. It is not unreasonable to suspect that higher resolution models with a diurnal cycle and land hydro!ogy as well as archived analyses may have even more severe problends. I• this regard, we showed that the moisture flux derived fi'o n NMC pressure analysis and liquid water derived from SSM/I measurement do have similar sampling characteristics.
Lack of temporal resolution also affects perceived forecast skill. Flux convergence and precipitable watcr tendency are not useful for predicting precipitation and evaporation if the flux is not sufficiently sampled. We found that the precipitable water tendency term was important at short time scales, espe- cially if we could get a useful approximation to the divergence with sufficient samples. The tendency term may also be impor- tant in developing observed budgets but because of all the other errors may not have been given its proper due in the past. Another dreaded possibility is that analysis products may have an even larger tendency due to the imperfections i• the
underlying analysis model (M. Kanamitsu, personal communi- cation, 1995). That is, the analysis model clinmfe i• certainly different from the analysis climate. This adjustment or drift to this climate could potentially be just as important as the ten- dency due to internal variations examined here.
Temporal resolution is certainly increasing in the new analysis products. In NMC's sigma-level analysis. which has been archived at NCAR since 1990, analyses are available 4 times a day. Although the observing frequency of available rawinsonde observations might be limited to only a few per day, there is no reason that the corresponding output has to have the same limits. In the Eta model (Mesinger et al., 1990; Black, 1994) GCIP archives, the assimilated regional analysis will be available 8 times a day. Again, even this kind of reso- lution may be inadequate and just as precipitation is accumu- lated, so should other corresponding hydrologic quantities. This means that atmospheric moisture fluxes need to be accu- mulated during the model forecast and along with the instanta- neous samples, these data should also be provid•,d as part of the analyses or reanalyses. The initial guess file that currently provides the precipitation should also be expanded to provide the tendency terms as well as accumulated moisture Ilux. Only by developing confidence in our ability to provide balanced
73 58 CHEN ET AL.: BALANCING THE ATMOSPHERIC HYDI',OLOGIC BUDGET
model and analyses budgets will we be able to have confidence in our ability to infer less well sampled and less well observed natural budgets.
Acknowledgements. This research was supported by NOAA grants NA36GP0377 and NA37GP0372, NSF grant ATM89-22733, NASA grant NAG 5-2238, and a grant from the University of California Insti- tutional Collaborative Research Program. Comments by J. Paegle and two anonymous reviewers were quite helpful in improving the presenta- tion of the results.
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(Received January 19, 1995; revised April 27, 1995; accepted May 22, 1995.)
