Evaluation of Methllds to Estimate the Surface Downwelling Longwave Flux During Arctic Winter

306 J 0 11 K N A I. 0 I- 4 P I' I. I I. I) hl I.. 1' I' 0 K 0 I. 0 C; Y vcit I hll 1 I

Evaluation of Methllds to Estimate the Surface Downwelling Longwave Flux during Arctic Winter

(Manuwript ricched ?I March 2001. in linal form R August 2001)

ABSTRACI

Surface lonpuiive radiation fluxc\ doininate the energy budget olnighttime polar regions. yet little I\ known about the relati\e a( curacy of exisling satellite-based techniques to estimate this parameter. We compare eight methods to estimate the downwellinp longwave radiation flux and to validate their performance with measure- menth from two fielcl programs in thc Arctic: the Coordinated Eastern Arctic Experiment (CEAREX ) conducted in the Barents Sea curing the aiituniii and winter of 19XX. and the Lead Erpcrirneni performed in the Heaulort Sea in the spring of 1092. Five of thc eight methods fiere developed for satellite-derived quantities. and three are simple parainetc ritations bared 1111 surface observations. All of the algorithms require information ahout cloud fraction. which i\ provided from the NASA-NOAA Televition and Infrared Observation Sarellite (TIROS) Operational Vertical Sounder (TOVS) polar pathtinder data\et (Path-P): some techniques ingest temperature and moisture profile3 (a1 .o frnm Path-PI: tme-half of the methods wsiime that clouds itre opaque and have ;I con\tant geometric thickness of 50 hPa. and three include no thichncrs information whatsoever. With a somewhiit limited \alidation datawt. tie following priin;irq conclusions result: I ) all methods exhibit approximately the sumc correlations with mtasurements and rms differences. hut the hiares range from -34 W m (16% ot'the mean) to nearly 0: 2) the t rror analysis dcwihed here indicates that the assumpticin of a SO-hPa cloud thicknes\ 13 too thin hy a factor tmf 2 on average in! 1~1)I;iinighttime conditions: 3)cloud-overlap techniques. which eflecti\ely increase mean clou~lthickness. \igiiilicsiitly improve the rcsulLr: 4) simple Arctic-specific paranietcriratiom pertcirrncd poorly. r rnbahty hecauw they wcrc devclopcd with wrface-observed cloud fraction\ H hciritr the ed here used s;rtellite-dciivcd effective cloud fractions: and 5)the \ingle algorithm that include3 an cloud th ckncs< exhihit* ihe snialleat differenccs Iron1 obrervaticins.

1. Introduction tion.;. including a long-term dataset (or studies of var- In this investigation we cxtend the uork of Key et iability and change and use as forcing fields for mod- al. (1996) and evaluate the ability of several existing eling studies. We also extend the work of Key et al. methods to estimate the surface downwelling flux of ll997) in evaluating the sensitivity of DLF to pertur- longwave radiation (DLI:) cwer snow- mid ice-covered bations in various atmospheric parameters with the in- surfaces, particularly at night. The algorithnis examined tent of identifying variables thitt require improved re- by Key et al. (1996) arc a 1 simple parameteriLntions trieval accuracy. empirically derived from si riace measurements in the Polar regions are notoriously problematic for global Arctic; here we also evalu itc several techniques that surface radiation budget (SRB ) algorithms based on sat- ingest retrievals from satell te data. Our goal is to de- ellite data. because several factors coniplicaie the re- termine which method(s) should be used in computing trieval process and few validation data are available. DLF from wtellite retricva s for a variety ol' itpplica- Rccause the high latitudes are recognixed as climatically senaitive areas. there is a strong dcniand from the sci- entific community for reliable. long-term surface radi- Ctirrr\poiidriix urtrhor uddt-t,,u: Dr. Jcnniter l+.mcis. htituts 111 Marine and Coastal Sciences. Kuigcr\ Univzr\ity. 71 Dtidlcy Rtl.. ation datasets for the polar regions. We employ a com- New Rrunswick. NJ OXYOI-Xfi?l. bination of satellite retrievals from the National Aero- E-mail: fraiicis(~'inics.rutg~rs.cdu nautics and Space Administration (NASA)-National _Ice_---

.\ MARC" ?ON)? ('HIACCHIO ET AI-. 307

Oceanographic and Atmosp ieric Administration Schweiger 2000). The TOVS insti-ument, which has (NOAA) Television and Inti-are 1 Observation Satellite flown on NOAA polar-orbiting sensors since 1978. com- Operational Vertical Sounder (1OVS) pcilar pathtinder prises the High-Resolution Infrared Radiation Sounder (hereinafter, Path-P) dataset (F'riincis and Schwciger (HIRS). the Microwave Sounding Unit (MSU), and the 2000) with surface observations from radiometers. ceil- Stratospheric Sounding Unit (SSU). Data from SSU are ometers, and surface observers to evaluate the perfor- not used to create the Path-P dataset. HIRS measures mance of several existing algorithins to estimate surface radiances in 20 channels from the visible to infrared longwave fluxes in the Arctic. wavelengths with a resolution of 17 km at nadir, and *. Longwave radiation doniinstey the Arctic surface en- MSU has four channels in the oxygen absorption band ergy budget for almost one-half of the year when in- near 50 GHz. The Path-P dataset was produced using solation is absent or weak. During the polar winter, tur- the improved initialiration inversion (31) processing 91- bulent fluxes are small in sca-ii.e-covered regions, ex- prithni for TOVS radiances. developed by the Atmo- cept over cracks in the ice when vertical air-ocean teni- spheric Radiation Analysis Group at the Laboratoire de perature and moisture gradients are large. In contrast to MetCorologie Dynmique in Palaiseau. France (ChCdin lower latitudes, 31 which low-le\ el temperature and wa- ct al. 1985). The 21 algorithin was modified to improve ter vapor content largely go\wri the DLF. clouds play retrieval accuracy over sea ice and snow [Francis the most importnnt role in polnr regions. Sensitivity (lY94); Scott et al. (19YY)I. Path-P products are pro- studies by Key et al. (19971. Fiouin et al. (1988). and vided daily on a (100 km): grid and include temperature Chiacchio (2001) show that DI,F is most sensitive to and moisture profiles, surface skin temperature, cloud cloud traction. cloud thickness (or liquid water path). fraction and height. and a variety of other parameters. and cloud-base height. Of thcse xiranieters. passive sat- The 31 algorithm has at its core ii comprehensive library ellite sensors can be used to cstiriate only cloud fraction of global atmospheric profiles (.- I8(K)) that provides and cloud-top height during pol;ir night conditions. and the tirst guess to this physical-statistical technique and even these have much larger uiicertainties than do es- consequently is able to capture the strong surface-based timates from other parts ol' thc globe. Algorithms to and elevated temperature inversions that are nearly ubiq- detect clouds and to diagnose their properties often tail uitous in all seasons hut summer in the Arctic region. over snow- and ice-covered miis because cd frequent Validation of surface and 900-hPa temperatures with surface-based tcinpcrature inver-;ions that confound sat- radiosonde data reveals small mean errors ( 1.4 and 2.5 ellite cloud-detection algorithm.; and introduce unccr- K). Retrieved inversion strength, however, is often less tainty into satellite-retrieved temperature profiles. Short- than radiosonde values owing to the coarse vertical rcs- wave channels, especially ncw misors that measure ra- olution of the temperature profile. ilnd the cap may be diances in the I .6-pm wavelen;:th region. add consid- misplaced in the vertical by il few lens of hectopascals. erable inforniation, but historica \ isible data iire limited The cloud fraction variable (labclcd FCLD in the Path- by the lack of contrast between clouds and snow. Efforts P dataset) is an y[pc.riiv cloud fraction A, E. which is are underway to infer polor cloud characteristics beyond the product of the fraction A* of Ihe sky covered by fraction and cloud-top height. but they are still exper- cloud and the cloud emissivity E. Cloud emissivity rang- imental. es between 0 an I: therefore A, E is always less than or Several algorithm and paramcterizations exist for es- equal to A,, which is the quantity reported by human timating DLF from satellite-dcrib*edintormation. hut in- observers. This distinction is significant in polar regions tercomparisons and validation for polar-night conditions because optically thin clouds-ven in the infrared- have not been performed. The ahjective of this inves- are common, especially in winter. Hereinafter we ab- tigation is to conipnrc DLF valuer. computed with eight breviate effective cloud fraction as A,, . and "cloud frac- different methods quantitatilcly to validate result5 with tion" denotes the fraction of the sky covered by cloud measurements from surface-bas XI instruments and hu- (A,). See Schweiger et al. (2001) for additional infor- man observers. to identify prob;.ble causes for errors in mation and validation results for the Path-P data. each method, iind to niakr rcc,onrnendations ;IS to which algorithni(s) provides the bot ehnates of DLF in the h. Vtrlicltiiiori c1atri.vcJt.v Arctic night. A significant problem in studying cloud or surface characteristics in this region is the paucity of measure- 2. Data sources and tools ments. especially in winter when DLF is the dominant

, (1. Sriirllitc,-(l~).iI'Pnprocliic'i.\ component of the surface energy budget. Observations from two tield experiments are used in this study. The Several of the methods undt r investigation require tirst is the drift phase of the Coordinated Eastern Arctic temperature protiles. humidity r rofiles, surface teinper- Experinient (CEAREX: CEAREX Drift Group 1990). ature, cloud tinction. and/or cloud height. For this study, which was conducted in the eastern Arctic Basin from atmospheric state inforniation is obtained froin the September of 1988 through January of I989 (Fig. I). NASA-NOAA TOVS Path-P dataset (Francis and The experiment included two research vessels and an 308 _I 0 II I< N A I. 0 I- ,\ I' P I. I E I> M k I 1: 0 K 0 I 0 (i Y VOI I'htl 41

westward from 24 March 1992 until 2.5 April I992 (Fig. I ). The main objectives of the experiment were to study the cracklike openings (leads) in sea ice formed by the ice deformation and to understand the effects of leads on the polar ocean and atmosphere. In addition to radiation measurements. we use cloud-base height retrievals from a lidar ceilometer to compare with Path-P- derived values. The vertical resolution of the ceilometer retrievals was 30 111. and the instrument could observe cloud bases up to 8 kni. These ceilometer estimates are not considered to be reliable for absolute validation. however, owing to reported problems in detecting thin. low-level, ice clouds (0.Persson 1999, personal com- munication). Thirty-second ceilometer values are averaged over 24 h to be consistent with Path-P products.

c. Rudiutiw trirrtsjrr tttodrl Sensitivity tests and calculations of surface fluxes are performed using a forward radiative transfer model called Streamer, which wx assenihled hy J. Key and A. Schweigcr (Key and Schweiger 1998). Streamer is a array of surface canips at which a variety of nieteoro- publicly available, highly flexible package that can be logical and oceanographic measurements were made. In used to calculate shortwave and longwave radiances and this study we use data obtained aboard the R/V fo- fluxes for a wide variety of atmospheric and surface Inrbjiirn. which include downward infrared fluxes (be- conditions. Absorption and scattering by gases is pa- tween 4 and SO pm) from an Eppley Laboratory. Inc., rameterized for 24 shortwave and 105 longwave bands. pyrgeometer. which has a nominal instrument error of Built-in data include water and ice cloud optical prop- 5 W In (CEAREX Drift Group 1990). Owing to the erties. aerosol profiles. iind seven standard-atmosphere lack of solar radiation during CEAHEX. as well as the profiles. or users ciin provide their own. Each scene can low sun angles and large cloud fractions during the 1992 include up to IO cloud types, up to ID overlapping cloud Beaufort Sea Ixad Experiment (LeadEx). we assume sets of up to 10 clouds each. and up to three surface errors in radiometer measurements resulting from solar types. Also. spectral albedos for various surface con- contamination are small. The radiometer domes required ditions are included. The number of streams used in the cleaning hourly to remove frost and precipitation; only calculation can be varied; two are used in this study. measurements follhwing a cleaning were used to com- Modeled fluxes for standard atmospheres were compute daily-average flux vnlues, which we compare with pared with calculations by approximately 37 other mod- daily-average satellite-derived DLFs. The differing els presented in the report of the lntercomparison of space scales 01 Palh-P data and surface point nieasure- Radiation Codes in Clirnatc Models pro.@ (Ellingson ments is a possihle source of error. Schweiger et al. et al. 199 I ). Streamer-computed fluxes were within 5% (200 1 ) analyzed correlations between time-averaged (I standard deviation) ofthe mean of all models (Francis point measurements of cloud fraction and spatially av- 1997). eraged satellite vnlues and found that correlations werc low for timescale4 shorter than 2 days and peak at X 3. Sensitivity of DLF to atmospheric parameters days. Because clouds are the dominant factor in determining DLF in the Arctic winter, we wsume these cor- Sensitivity studies are performed to determine the relations also apply to DLE They speculate that the lack likely errors in DLF resulting froin uncertainty in cloud of strong correlation at short timescales may be caused parameters and from published uncertainties in Path-P by the differing perspectives of satellite versus surface products. DLF is calculated using Strcamer for typical observations (view from above or below). Another proh- winter and summer Arctic conditions and with expected able cause is that smaller variations occur at short time- rim errors (in parentheses) for each of the following scales, which may cause this signal to be lost in noise, state variables under clear conditions: surface skin tem- . whereas large variations may occur at long timescales perature (23 K). temperature profile ( 2.3 K at all lev- and so are more detectable above the noise. els), and moisture protile (230%at all levels). In ad- Data from LeadEx (LeadEx Group 1993) are also dition. we estimate the sensitivity of DLF to varying used to validate DLF computed from each of the eight bulk cloud properties: fraction, thickness, base height. algorithms. This tield program was conducted in the liquid water content (LWC). and effective droplet radius Beaufort Sea ;it ii camp on the pack ice that drifted r, . Each calculation includes omnc amounts for a stan- E 20 uV

dard subarctic winter protile, and the carhon dioxide -20 concentration is fixed at 340 ppmv. Clouds in these tests are composed of spherical water droplets with a nominal cloud thickness of SO hPa. an LWC of 0.20 g rn ', and ;I typical r, of 8 pm (Curry and Ehert 1991). We feel justified in considering only water clouds, because liquid water was detected in over one-half of the clouds during the Surface Heat Budget of the Arctic (SHEBA) experiment in every month except December (lntrieri et at. 1001 ) and because phase alone has a ncgligihle etfcct on DLF (Francis 1999). Result> of sensitivity tests for temperatures and water vapor are shown in Fig. 3 and are summarized in Table I. These results iirc consistent with those of' Key et at. ( 1997) and show that errors in DLF arising Croni doc- c,4 -10 ...... 1 umented uncertainties in satellite-derived temperature 3 and moisture protile\ will be well within the 10 W ni 9 -20-1-7 threshold that has been suggested by the World Climate I Rcsearcli Progratiime (WCRP) ;is thc target accuracy -mLdfor surface Hux estimates (Raschke et at. 1990).Wc also -6 -4 -2 0 2 4 6 use Streamer to test the sensitivity of DLF to uncertainties in TOVS-retrieved surface-based inversions. We Pmrtwbotbn to Sfc. r.mp.mtur. (K) calculate DLF for ii typical winter surfacc-hased inversion (13 K difference between the surface and top of I the inversion at 900 hPa) and for a temperature profile with the inversion smeared out and ;I positive lapsc rate throughout. A typical SO-hPa-thick water cloud is placed with its top at 900 hPa (top of the inversion). The difference in DLF hctwc.cn these two model runs is less than 3 W 111 (inversion run is smaller). Because this scenario is likely a worst case. we conclude that any errors in TOVS-retrieved invewion strength, height. or even existence would not result in the niagnitude of DLF deticiencies we ohserve in many of the algorithms. Figure 3 shows the computed sensitivity of DLF to cloud fraction and geometric thickness. A 30% error in low-cloud fraction would result in DLF errors in excess of the WCRP threshold. but DLF is less sensitive to uncertainties in high-cloud fractions. DLF is highly scn- sitive to cloud thickness-more so for low clouds: an error of IO W rn : could arise from iissuming a cloud is only 30 hPa thicker than its actual value. This is an important point in our later discussion of the assumption in some ;tlpithnis that clouds are a constant SO hPa thick. Figure 1 shows the sensitivity of' DLF to cloud LWC for varying droplet effectivc radii and cloud-base heights, with and without a surface-hased teniperature 0.00 0.05 0.10 0.15 0.20 0.0 0.2 0.4 0.6 0.8 1.0 Le[9rn+l Cloud &action

c! 6

0.00 0.05 0.10 0.15 L* Ism7

0 20 40 0 80 100 80 Cloud thickness [mbl 2.-860 mb e------a FIG. 3. Senhitivity 01 ULF to perturbation\ in (a) clwd frwtiun and (hl cloud thickneir. with cloud-hose heights at XIWI and 400 hPa in typical Apr ci)nditii)m in the central Arctic. Cloud.\ are coinpored of hphcrical ~aterdroplet?. with o nonliniil cloud rhickiwb of 50 hPa. an LN'C' 01 0.20 g rn '. and a typicill equivalent radius r, 01 X pm. inversion. We use temperature and water vapor profiles typical for April. and LWC is varied from 0.0 to 0.2 g m '. In each of these experiments. it is apparent that the DLF is extremely sensitive to the LWC in thin. high E. clouds that contain less than 0.02 g m ' of water and 0 ----.--...---- in low clouds with less than 0.05 g m I. For thicker clouds. DLF ih no longer sensitive to LWC: that is, the cloud is optically thick in the infrared. Cloud droplet cffcctive radius in this size range, however. has a negligible effect on DLE This result is consistent with results by Francis (1999) that show little sensitivity of infrared cloud radiative forcing by water clouds (rv = 10 pni) versus ice clouds (r, = 50 pm). Figure 4b shows below the cap of a surface-based temperature inversion. that DLF is more sensitive to the LWC of low clouds The results of these sensitivity tests for bulk cloud pa- than of high clouds and that. for optically thick clouds, rameters are also generally consistent with those of Key an error of IO W m-: would rcsult from an error in et al. (1997). although we test some different variables cloud-hasc height of approximately I SO hPa. Figure 4c and, in some cases, over ii more widely varying range illuhtrates thc effect of a cloud base lying above and of values. We are interested only in the sensitivity of DLF to individual variiihles, givc n thai part 01' our goal GEWEX SRH and CERES projects ohtained from re- is to identify which satellite-relrieved quantities lack analysis datasets (either the European Centre for Me- sufficient accuracy for DLF ciilcu alions. For an analysis dium-Range Weather Forecasts or NASA's Data Assim- of the overall uncertainty in DIJ see Key et ill. (1997). ilation Oftice). In this sttidy. we instead use the Path-P From the results of these te\ts, ue conclude that DLF products. hecause they iire helicvcd to be more accurate is mosl sensitive to errors in cli~uJ fraction and to LWC in Arctic conditions (Francis 1994). The primary as- in thin clouds and that IILI-' is rc.l;itiwly insenhitive to suniptions of the Gupta ( 1989) technique are that clouds droplet size. Known uncertai tit ic s in satel I itc-retrieved exist in ;I single. SO-hPa-thick layer nnd they are opaque. temperature and water vapor profiles result in IILF cr- The method parameteri7es DLF ;is rors within 10 W ti1 2. For lurthcr details on rcncitivity DLF = DLFL,,(I - A ) + DLF<,,,,A,, (1) tests, see Chiacchio (2001 ). where DLF,,, is the downwitrd longwave flux for clear 4. Methodology sky, DLFL,!, is the downward Hux for cloudy sky. and A, is the cloud fraction. for which we use .4cLfrom Path- We evaluate the ability of sc'vetiil methods to estimate P. This equation is then simplified a< DLF by comparing daily-mean-t alculated viilues from a (100 km)' grid hox to surl';icc,-tiieasured DLF from D1.F = C, + (-,A,.,. (2) two tield experiments in the Arctic. Some of the algo- where C, = DLF,,, and C': = (DLF,,,, - DLFL,,).that rithms. such as those of Gupt;~( 1989) ;ind Frouin et al. is. the therrnnl emission from the cloud base. The C,is (1988). are being used globally. and we compare their parameterized in terms of the effective emitting tem- performance with Arctic-specif : algorithms. such as perature T, of the atmosphere (estimated from the sui-- that of Francis ( 1997). We iilso evalunte thrce simple lace and lower tropospheric temperatures) and the sur- empirical parameterimticins tlevc~lopctllor Arctic con- frtce-to-7OO-hPa water vapor hurdeii W, (mm): ditions: Marshunova ( 1966).%ill naii ( 1972). and May- kut and Church ( 1973). Thcse par;uneteri/;itions are c, = .ji w,)7;.. (3) among the longwave flux method5 cxaniined hy Key et where .r i\ empirically dctermined to he 3.7. Further. al. (IY96). yet we do not coiisitler the Schmctz et al. f( W,) is exprcssed ;IS ( 1986) method. bccausc it WIS developed for daylight conditions. In this section we deszribe each mcthod and the required input data. A suiiirn;iry ol' the assumptions where V = In(U',) and the As are regression coefticients. and required informetion for cat:h mcthod i> given in Equation (4) is then fit to fluxes and meteorological Table 2. profiles from tive sites in the United States to obtain the regression cod'licients A,, = 1.70 X 10 '. A = (I. C'Lcpt~r I IYXO) 2.093 X 10 '.A, = -3.748 X IO '. and A, = 1.184 x 10 &'. This algorithm was used to ;ciieriite a global 8-yr The p:iramctcrization of c', contains the terms TI, SRB dataset (Gupta ct al. IWVI and also is included (clnud-hase tc.mprr;iture) and W, (w;iter vapor below the among other algorithms in hotti the Clouds and the cloud). To determine TLl3,the cloud-hasc hcight must hc Earth's Radiant Energy Systern (CERES, and the calculated from the sutcllite-retrieved cloud-top height. WCRP-Global Energy and CVa er Cycle Experiment assuming ;I cloud thickness of SO hPa and ii positive (GEWEX) SRB projects. This riethod requires inputs atmospheric lapse rate. Radiosonde d;it;i and a forward for water vapor and temperature Imtiles. cloud fraction, radiative transler model are used to determinc the re- and cloud-top pressure. which (iupta ( 1989) obtained lalionship between and TLb: from NOAA operationid TOV S retrievals. and the C, region (F,,. F ,,,. and F,for high. middle, and low): 4) c, = (5) compute the probabiliiies (C,,,, ) for each cloud type (B,, + R,W< 4- B:W' 8,W,')' , - using the following equations: Tests by Gupta et al. (1991) using products from the Intrrnational Satellite Cloud Climatology Project C,, = F,,ll. (7) (ISCCP) dataset show that (5)works well except when c C, IFh,/( I - F,,)I, and (8) P, - P,.h5 200 hPa (P,is the surface pressure, and Pch is the pressure of the cloud base), which is a significant C,, F, /( I - F,, - F,,,): (9) problem in the Arctic where low. thin clouds predom- inate. -5) calculate clear-sky probabilities (e.g., 1 - C,, for high clouds); 6) calculate fractional values for combinations of conditions (clear. high alone, high over middle, high h. Froirin rf c~l.I IYXXI over low, high over middle over low. etc.); 7) calculate This algorithm comprises two techniques (hereinafter fluxes fur each case (DLF,) with appropriate cloud-buse FI and F2) for determining DLF during nighttime. The height (SO-hPa thickness assumption) and A,, using FI method requires temperature profiles, water vapor Streamer; and 8) multiply fluxes for each case by their protiles. and cloud properties (cloud-top height and corresponding fractional values C,: cloud fraction), which we obtain from the Path-P dataset DLF*,,,,,= DLF,C, + DLF,C, -I- . . . + DLF,C,. (10) (Frouin et at. (198X) used operational NOAA TOVS retrievals]. In this algorithm. clouds are assumed to exist where DLF,,,,, is the new Hux valuc from the cloud- in one opaque layer that is SO hPa thick. The temperature overlap method. and water vapor protiles (from Path-P) are input to Streamer io compute the clear-sky DLE To estimate the c. FrctrrcYs (1997) cloudy-sky flux, we use the Path-P cloud effective fruc- tion and cloud-top height and assign a cloud-base height The only assumptions in this method are that clouds that is SO hPa lower than thc cloud-top height. Using exist in one layer and that cloud fraction is always 100%. the Path-P temperature protile. the cloud-base height is with all the variability in A,., occurring in \he emissivity. matched with the level of the corresponding temperature Clouds may be optically thin and may have varying level to obtain the cloud-base temperature. This infor- geometric thicknesses. This technique ingests Path-P at- mation is input to Streamer to calculate the cloudy-sky mospheric temperature and moisture protiles, effective DI,E The cleiir-sky and cloudy-hky fluxes are combined cloud fraction. cloud-top height. and surface tempera- according to ( I ). ture. Differences between brightness temperatures (TB) tn F2. DLF is pararneterixd as a function afthe clear- in several pairs of HlRS channels are used to estimate sky flux DLF,,,: cloud type (positive or negative internal lapse rate). phase, thickness, and LWC of Arctic clouds. Cloud DLF = DLF<,,+ <.A,, (6) phase is inferred by sohtracting TBs in two pairs of which is colculated iis for F1. Again, we use A,,cin placc channels: HlRS 10 (8.3 pm) and HIRS 8 ( I I. I pm). of cloud fraction. The coefficient c depends on latitude. and HlRS 18 (4.0 pm) and HlRS 15, (3.7 pm). For season, an3 cloud typc, which is determined by Frouin exaniple, in the first pair. the absorption coefficients k;,,, et al. ( 1988) by siinulating DLF in varying cloud con- for water and ice are different. At 8.3 ,urn. k,,, is similar Jitions using the Stephens ( 1978) model. A value at' 66 for wafer and ice, hut at I I. I pm the difterence in k,,,, W rn is selected for this study. which corresponds IO is large. thereby differentiating ice and water clouds. subarctic winter conditions and liquid water clouds. Cloud thickness is estimated using TB differences in Polar clouds rarely exist as a single layer (e.g.. two pairs of channels: HlRS 6 (13.7 pm) - HlRS 15 Schweiger and Key 1992): thus. we investigate the ef- (3.46 pm). and HlRS 14 (4.52 Gm) - HIRS 7 (13.7 fects of multilayeriiig by applying il cloud-overlap tech- pm). The first pair is for mid- and high clouds (top nique to the FI method using TOVS Path-P data as height >750 hPa), and the second pair is used for low input. This random-overlap technique is adopted from clouds. Because the weighting function peak of HIRS Tian and Curry ( 1989) and is heing ksted at the NASA h is at a lower altitude than that of HIRS 15. its TB is Langley Research Ccnter for the WCRP-GEWEX SRB warmer in B cloud-free sky. When a thin cloud is present. program. the difference in TB decreases. To determine the cloud The overlap method comprises thc following steps: thickness from the differences in TB, the base fraction, 1) obtain cloud-top height and A,,, for each satellite re- a value between 0 and I, is determined by setting end- trieval in ;I 2.5" x 2.5" region; 2) categorize the cloud point thresholds and interpolating linearly between them type for each retrieval hased on the ISCCP cloud-height by matching calculated DLFs to ohserved quantities. definitions (high: top pressurc below 440 hPa, middle: The liquid or ice water content (IWC) is estiniaced between 440 and 680 hPa. and low: greater than 680 using empirical relationships between mean cloud tem- hPa): 3) dcterniinc the fraction of each cloud type in a perature and LWC or IWC for water or ice clouds. All this informiition is input to Streinier to compute DLF tion 3 and listed in Table 2. Fluxes calculated from daily- See Francis ( 1997) for further di.tails of this ;iIgorithin average input data are compared to daily-average mea- The following three algorithras are simple. enipiri- sured fluxes from the CEAREX and LeadEx held pro- cally derived parameteri;lation\. For this study the P;rth- grams. Scatterplots that illustrate direct comparisons of P effective cloud fraction is useG in pl:ice ofc.loud frac- the computed and measured fluxes are shown in Fig. 5. . tion in the relationships. iind ;I summary ot the comparison statistics is presented in Table 3. The rms differences and correlation coefticients are d. Murshitnocci ( 1966) remarkably similar for all eight methods; hence. they This mcthod is an empirical y derived parameteri- are listed in decreasing accuracy according to bias. All zation to estimate DLF had on surface temperature. the methods exhihit negative bias, that is. calculated near-surface vapor pressure. and cloud fraction. A sini- fluxes are too small. although it is negligihle for the ple cloud factor is defined th;it i icludes the cloud frac- Francis ( 1997) algorithm. which is one ofthe four spe- tion and a coefficient: cifically designed for polar conditions. The cloud-overlap niethtd applied to FI clearly improves the results: DLF = Dl,F,,,(I t xA, ). (11) the bias is reduced froin -34 (16%) to - I1 (5%) W where m :. Results from the other three Arctic-specific mcthods IMarshunova (1966): iMaykut and Church (1972): DLF,,, = trT30.67 i 0.OSe"'). (12) Zillman ( I972)I. although only simple parameterim- .r is a coefticient derived usin: time-varying surface tions. are disappointing. These same three paranieteri- temperatures T,, and P is nc;ir-! urface vapor pressure. ziitions were evaluated by Key et al. ( 1996) using wl- In this study .r = 0.26 afrer an ;iniJysis by Jacohs ( 1978). idation data from two land stations: Resolute, Northwest Effective cloud fractions and sk 11 temperatures are ob- Territories, Caniida. and Barrow. Alaska. When coni- tained from Path-P data. and (' i i calculated I'rom Path- pard with Key et al. (1996). the Maykut and Church P moisture profiles. (1973) algorithm exhibited ii bias one-half as large iis in our study. probably because it was developed with data fi-om Barrow. Alaska. The Zillrnan ( 1972) parain- e. Zillrriiitr ( 19721 etcridon. developed with data from the Southern This parameterization is a function of both the cloud Ocean was. not surprisingly. the least accurate of the amount and the near-surface air temperature. The Path- three in both evnluotions. Our results yielded ;I larger P surface skin temperatures are used in this \tudy. be- negative hias for the Marshunova (1966) method. again cause our analysis of CEAREX measurements reveals probably because the parameterization was developed that the surface skin temperalure rarely differ< from thc using diitii from Arctic coastal stations such as Resolute 2-in air temperature hy morc ttiiii 2 K except in pro- and Barrow rather. than observations from within the longed clear winter conditioris. Arctic Ocean.

DLF - DLF,,, + [trTf0.96(1 - 9.2 X 10 '*T;)A,1, ( 13) h. Sources of' error where DLFL,,= rrTi (9.2 X IO "Tt). This rclationship was derived hy Zillman ( 1973) fiom nieasurciiients over 1 ) AT\IIOSP)tEKI(' PROFII.ES Antarctic sea ice obtained from Pease ( I975 ). The reported bias in Path-P temperature profiles is approximately I K (Schweiger el al. 2001 1. which mans- ,f: Mtrxkur titid Clrurch (I97.J) lates to an error in DLF of about 3 W in in summer and 1.5 W m in winter. The bias in water vapor pro- The relationship was developt:d with year-round sur- lilcs, as compared with r;idiosonde data from the SHE- face temperature and cloud fra-tion data collected in BA tield program. is about 10%. which would produce Barrow. Alask;i. over a 5-yr period, during which the an error in DLF of approximatcly 3 W in :. Wc con- surface temperature ranged froni to 277 K. The DLF 144 sequently conclude that errors in satellite-retrieved tein- is paruneteri;led as perature and water vapor profiles do riot contribute sig- DLF = DLFJ I -t 0.22~275). (14) nificitntly to the apparent biases in computed DLF. where DLF,,, = 0.7855crT:. 2) Cl.OU0 PKACfION 5. Results and discussion Because all of these algorithms rcquire infomiation about cloud fractii)n and because DLF in polur regions u. Perfiit-niut~c.c~of DLF d,yoririltt1.s is sensitive to cloud traction. this variable may xcotint Downwiird longwave fluxes ;it the surfact: ;ire coni- for much of the error in computed DLE As already puted using each of the cight mithods descrihed in sec- mentioned. the Path-P product used in the analy\es is 314 J 0 1' I< N A 1. 0 F A PPI. I ED M ET EO K 0 1. 0 Ci Y

Gupta l19891 Frouin et at. r19881 #l

Frouin et at. [1988] #1 w/OL Frouin et 01. [ 19881 #2

x 1 200 200 0 rn 30 51500 , - 0 0 0 E V 100 ' 100 100 150 200 250 300 100 150 200 250 300 Ueosured nux [wmJ] Msmursd Flux [Wm-) Francis 19971 Marshunova r 19661

,0 100 150 200 250 300 100 150 200 250 300 Measured Flux [Wm-'1 Ueosured Flux [Wm-q Maykut and Church [1973]

x G1M

loot4 . J loo 150 200 250 300 100 150 200 250 300 uworurod nux [Wm4J uoosured nux [Wmq 3) CI.U~I)-HASI:itcic;in-

Cloud-base height in three of the algorithms is determined by assuming it is SO hPa lower than the Path- Francir (1997) IY 0.77 P-retrieved cloud-top height. Thus there ;ire two com- Frouin et :iI. (10x8). FI with iiverliip 19 0.76 - ponents oi this variable to consider: First is thc accuracy Frrwin et ill. (IYXX). F2 19 0.77 Marshunriva 1 IYhh) 20 0.73 of cloud-top height in the Path-P dataset and how it Maykut and Church f 1973) 20 0.72 differs from heights estimated using 'lidnr ceilometers. Gupta ( 19x9) IY 0.7.5 The cloud top can be difficult to defne. because cloud Zillrnan (1972) 21 0.72 boundaries are often ephemeral and partially transparent Frouin et ;iI. (1088). FI 31 073 to infrared radiation. A compsrison of surface-based. * Here r is correlation cotllicient. lidar-radar-retrieved cloud-top heights with thosc from Path-P during SHEBA. for examplc. shows that cloud tops are generally higher in lidar-radar rctrievals than those from Path-P (Schweiger et ai. ZOO1 ). This behav- the ejjkiive cloud fraction, whit.h is the product of the ior is expected because of inherent differences in the cloud emissivity and the cloud fraction. Four of the two observing techniques: the lidar-radar systeiii is sen- algorithms we evaluate assume that clouds are black sitive to the small. sparse ice particles that frequently (i,e.. opaque) and 50 hPa thick. These separate as- compose high-latitude cloud tops. whereas Path-P re- sumptions will contribute to er vrs of different signs. trieves a value corresponding to the effective radiating Clouds with emissivities less [ha 1 unity (nonhlack) have height. that is the height from which the hulk of the been observed in the Arctic tCuiry et ai. 1996). In these radiation is emitted from the cloud lop. Although no cases, which theoretically would yield a retrieved A,, conclusion ciin be drawn at this time regarding the ve- that is smaller than the surface-cbserved cloud fraction, racity of Path-P cloud-top height retrievals. we do know the opaque assumption will caiise an oivre.ht~tm~in that to contribute to negative biases in computed DLF. DLF because a black cloud \.vi11 emit more infrared ra- the retrieved cloud tops would haw to be conaistcntly diation. all other characteristic: heing equal. The ils- too high, which is not what Schweiger ai. (3001) sumption of a 50-hPa-thick clqutl. on the other hand. show. an ir,itlere,stitrzcitic,,I 0.: will cause 1)l-F if the cloud base The second issue is the assumption of ;I constant. 50- is actually lower. ' hPa cloud thickness. as in Gupta (IY8Y). FI. FI with To produce a'DLF that is hiased by -30 W m >, the overlap. and F2. We compare ceilometer-obser~eii cloud fraction would have til bt too small by .approxi- cloud-base heights from LeadEx to those estimatcd us- mately 60% for low clouds an1 even larger for high ing the Path-P retrieved cloud-top heights assumihg a clouds, according to our semiti\ ity tests. A compnrison 50-hPa thickness (Fig. ha). Cloud-base height observed of cloud climatological descriptions from nine different hy the ceilometer is markedly lower thiui that obtained sources lseven based on human libservers and two from assuming a 50-hPa thickness (bias = 1200 in). which satellites (Chiacchio 2001 )I shovfsthat mean Path-P val- can be explained either by retrieved cloud tops that are ues for April (48%) fall in the middle of the range of too high or thicknesses that are too thin. Whichever the values [ 29% (Vowinckel and Or\ ig 1970)to 8Y% (Barry cause, this positive bias results in surface tluxcs bcing et ai. 1987)l. Excluding (includirig) the single large out- much lower than observed and is the most likely source lier. the mean is 46% (5I %-) an( the standard deviation of error in the calculated DLFs. Furthermorc. if Path-P is 8.5% (16.5%). cloud-top heights are generally lower than the iictual In addition. we compare ceilometer-derived cloud values. as suggested by the SHEBA comporiwu. the SO- fractions from the LeadEx field program to those from hPa assumption may be even less realistic than these Path-P (Fig. 6). Although the day-to-day variability is results indicate. Including the cloud-overlap technique lower in Path-P retrievals. the!. appear to he slightly in FI makes n considerable itnpro\enient (Fig. 6b) by /nr,qrr than the ceilometer vaIui:s. As previously men- representing multiple cloud layers and effectively low- tioned, however, the ceilometer iften did not sense thin ering the cloud base. low clouds, which probably con!ributes to the large dis- Our sensitivity calculations show that if ;i low-cloud crepancies near year days 89, 09, and 106-109 when base were 50 hPa (about SO0 m) too high. the DLF the ceilometer retrievals werc cl Jar (Fig. 6c). Data from would he about 20 W rn too smull with a typical winter the SHEBA tield project aniilyied by Schwcigrr et al. Arctic temperature profile. The algorithms that assume (200 1 ) did not exhibit this behavior. however; lidar- a SO-hPa-thick cloud exhihit an average bias of ap- derived cloud fractions were sy ;tcmatically larger than proximately this amount. We therefore conclude. based those reported by human (her\ers. Based on these re- on these results. that the 50-hPa cloud thickness as- sults, we conclude that errors ;n Path-P A,, retrievals sumption is unsuitable for Arctic winter conditions id are not responsible for the largc negative biases exhib- that a more realistic value would he approximately 2 ited by most of the DLF alpriihins. times as thick. 3 16 J 0 II K N ?\ I. OF h PPI, I E D M ET fiO K 01. 0 ti Y

50 mb - LaadEx bios=lZOB m RYSD: 973 m 0

b (50 mb (ornrbp)) - LdEx bbs-659 m RYSD 957 m . r- - - __ - -___ - __ -2

(TOVS - Lex) 100 bios: 12% RUSO 30% C

-40 w m I n m II .D mi sa .I Y m a w a n ~rnl~ii~~~~~irn(~i~~i~i~iioi~i -o*. FK;.6. Differences brrwceii iihsri \rd and retrieved cluud-ba>rhrighl c\tiinated using Psrh-P cloud-tup height and aswiiiing la) a SO-hPa thickncss: (b) cloud-hahc height ils in (a). but with random-cloud-overlap method spplied: and [c) dil'l'erence in cloud fraction. Observed cloud-hasc heights and tractions arc trim ttic LcadEx ctiliiiiirtrr; rrtrie\als ;ire l'roiii Path-I?

4) OTHER SOLIKC'1:S OF ERROR fective cloud fraction are rejected (Francis 1997). Errors may also result from differences in perspectives by sur- The poor results exhibited by the Mushunova ( 1966). face observers and satellites for both cloud height and Zillman (1972). and Maykut and Church (1973) param- cloud fraction. A surface observer has a bottom-up view, eterinations are somewhat surprising. given that they whereas satellites look down on the cloud top. Surface were developed for polar conditions. Because they are observations of cloud fraction are usually larger than so simple, it is difficult to ascertain the cause of the those derived from satellites owing to differences in errors. but it is likely that they arise because the param- view angles and the field of view (Schweiger and eterizations were developed using human-observed sky Key 1992; Chiacchio 2001). cloud fractions rather than values derived from remote sensing instruments. Apparent errors in all methods may arise because of 6. Summary and conclusions the inherent differences in comparing daily averaged, point-flux measurements with values computed from The dominant component of the Arctic surface energy (I00 km)? retrieved atmospheric parameters. In addi- budget during almost one-half of the year is longwave tion. a negative (clear sky) bias may be introduced be- radiation; however, its spatial and temporal scales of cause TOVS retricval boxeh with greater than 908 ef- variability are not known well, and a reliable, basinwide dataset is not available. A long-term dataset id surface hPa-thickness assumption should not he iipplied during radiation is needed for a variety of applications in oli- polar winter conditions and thot. if a constant could Inate research. A number of' rnethrxki with v;irying tic- thickness is required, it value approximately 2 times as grecs of complexity exist for estinrrrting DLF from sat- large should be used. This conclusion is further sup- ellite and surface nieawrerIIent5 and, atrhough surface ported by the results of applying a randoni-cloud-over- parameterization schemes WCI'C tntrrcnmpared and evnl- lap method, which effectively lowcrs the mean cloud uated thnroughly by Key et at. (19%). thew h little hnse, and by the lack of a DLF bias in the one method information about the perform;ince of wtellite-based that ingests the cloud-top height but attempts to eslimatl: techniques in polar nighttinic ccditions. In this study cloud-hast. heights from dirterences in satellite-ob- we attempt to evaluate several nl' these methuds and to served brightness temperatures. identify reasons for their apparent shortcomings. Our detailed conclusions are presented below. In dry polar conditions, cloud properties priinarify govern DLE In particular. our sewitivity tests shcrw that I ) All eight methods exhibited wrying degrees of ne&- DLF is most sensitive to uncciza7nLiesin cloud fraction, ative bias, rnnging from - I (0.5%)to -34 W m LWC. and thickness while hcin:! insensitive IO droplet ( 16%) as compared with surfiiut measurements of IILF; rins errors and correlation coefficients did not radiuh. All of the techniques W: tested require an estimate of cloud l'riiction as inpul. wnic requirc temprr- vary signiticantly. nture and moisture information. and one ingests satellile 2) The assumption of a constant. WhPa cloud thick- brightness temperatures directly. Four of the mcthods ness is the most likely cause of negative DLF biases. assume that clouds are a constmt SO-hPa thick. threc Rased on our analysis, we suggest that if a constant is contain no thickness inforination whatsoever, and iill cloud thickness used for Arctic winter ccmditions, algorithms but one assume clotrds exist in cine layer. it should he dnuhled to IOU hPa, We note, however, that the sample size for this analysis is no{ large (7H Only one algorithm allows for 5 nrying cloud thickness and emissivity. Using satellite-derived Path-P products total collocaiions from CEAREX and LeadEx) and as input for thu eight DLF riretiiods. we found that all validrttion data cover only one aufuiiin-winter season the region northeast of Spitsberpen one spring techniques except one exhibit I large (>IO W IN '1 in and sewon the Beaufor1 Sea. negative bias as compared with tneasurenients from LWO in field programs in the Arctic win er and spring. The rins 3) Application of a techniyue to simulate random cloud errors and correlation coefiiciei ts do not vary signiti- overlapping reduces the bias by the Fi method from canrly among the methods. howver, hugposting thar -34 to - 1 1 W m >.This improvement is believed cluud fraction. the same data foi which are iogested by to be the result of effectively lowering the mean all methods. probably accounts for much of the vari- cloud base. ability. Our efforts. consequcntiy. focused on identify- 4)'The most accurate DLF algorithm nray be Francis ing the cause(s) of the consi\teiir negative biases. (1997). which exhibits a bias of -I W m when Errors in atmospheric tempei alurc and water vapor compared with surface ineasureinents. This method protiles from the Path-P dataset were diminatcd an pmh- is specifically developed for Arctic conditicms. al- able sotirces of deticient DLFs. i cause reported biases lows for clouds within inversicin laycrs, differentiates in the Path-P profiles could ;tcccun( for only about 4 W ice and water clouds, and does iiof assume cloud m (2%of mean DLF). Path-P t ffective cloud fractions thickness to be constant. We recommend its use for were also dismissed :is a likclj source. because com- Arctic autumn, winter. and spring conditions. Its per- parisons with surface ohservatioiis (both by hurnsrrs and formance in the sumnier has not been evaluated yet. active reniote sensing instruinerifs) reveal ii xmsll~~1.~-5) The FT, method outperforms ~lreFI algorilhm be- itiw bias in cloud fracrion. which would rosult in a cause the coefficient in the formulation depends on p,si~iwhias in DL,E Severti1 ot rhr methods require a location. season. and cloud type. cloud-top height estimate. for H hich we used the Path- 6) Simple parameterizations designed spccitically for P pmduc!. 'I'his is a difficult v;iriablr to verify ctwing pilar conditions IMaykut and Church (1973); Zill- to inherent differences among ribserving mcthads. hut man ( 1972); Marshunova ( 1966)j did not perform it is likely that Path-Pcloud-top heights are biased sorne- well, probably because they were formulated using whal negatively, which would agsin result in cloud ba- surface-observed cloud fractions from land stations. ses that were t~ warm and DLFs tha! were IOO large. whereas we used satellite-retrieved effective cloud Thus errors in cloud-top height retrievals probably do fractions. not account lor thc negativuiy biased calculated DLF 7) Errors in satellite-retrieved temperature and water values. The most likely source (4 error. therefore. is the vapir protiles dn not contribute higniticantly to the assumption by one-hali of the algorithnts that clouds negative biases exhihired hy calculated DLFs. are SO hPa thick. Model calculat ons show that ifa cluud Y) Coniparisoiis of Path-P effective cloud fraction with layer were SO hPa too thin, the DLF would he approx- ceilometer-retrieved values indicate ;t slight pnsiriw inrately 20 W m too sm;ill. Having eliminated the bias. which would contribute to a positive bias in other likely sources of crrur. w : conclude tlut the 50- DLE We therelore rule out error5 in cloud fraction 318 JOURNAL. OF APPI.IED METEOROI.OGY VOI ii~r,41

as the source of consistent negative biases in cal- -. 1997: A method to dcrive dnwnwelling longwave fluxes at thc culated DLFs. Arctic \iirf;ice from TOVS data. J. Grophy.,. Res.. 102. 1705- 1806. 9) Attempts to validate Path-P cloud-top heights sug- -, 1999: Cloud radiative forcing over Arctic surface$. Preprint\. gest they may be too low, which would also con- Fifli Coit/: oil Polar Meteorology und Ocrotiograplrv. D:tllas. tribute to a positive DLF bias. We therefore dismiss TX. Amer. Meteor. Soc.. 221-276. this variable as a source of negative DLF biases. -. and A. 1. Schwciger, 2000: A new window opens on the Arctic. ECIJ.Trum Aiiier. tieopliy. Union. 81, 77-83. IO) DLF in the winter Arctic is most sensitive to cloud Frouin, R.. C. Gautier. and 1.-J. Morcrette. 19x8: Downward longwave fraction, LWC. and cloud thickness; cloud droplet irradiance at the ocean surface from satellite data: Methodology size has a negligible effect on DLE and in bitu validation. 1. Grriphw Res.. 93, 507-619. Gupta. S. K.. 1989: A paranietcrisation for longwave surfacc radidion from sun-synchronous satellite data. J. Cliintrre. 2, 305-320 In summary, we have presented quantitative analyses __ . W. I>. Darnell. and A. C. Wilber, 1992: A parameteriratton tor of the sensitivity of downwelling longwave fluxes to Ionpwavc surface radiation from satcllitc data: Recent improve- realistic uncertainties in satellite-derived atmospheric ments. J. Appl. Mi,tror.. 31. 136I-l367. --. N. A. Ritchey. A. C. Wilber. and C. H. Whitlock. 1999: A parameters in typical Arctic winter conditions. The most climatology 01' surlace radiation budget derived from \atellite complex of the algorithms we tested, which includes a data. J. Cliiiiure. 12, 269 1-27 IO. technique to estimate cloud-base height and emissivity. lntricri. J. M.. M. D.Shupe. T. Uttrl. and B. 1. McCarty, 2001: An produces DLFs that are closest to measured fluxes in annual cycle of Arctic cloud characteristics observed by radar and lidar at SHEBA. J. G~oiphys.Res.. in press. these conditions. We found that simpler algorithms that Jacobs, J. I).. 197X: Radiation climate of Broughton Island. t'rrrrxr. assume clouds have a constant thickness and have unit Rudgrt .71iidir.\ iii Rrlcition rn Fasi-lw Rrc~~kupProc.r.w,.r iri emissivity perform poorly in the Arctic, but biases in Dovi.~Sfrctir. R. G. Barry and J. D. Jacob\, Etls.. Paper 26. their results are significantly improved by doubling the INSTARR. Unirersity of Colorado, 105-120. assumed cloud thickness. This analysis should be ex- Key. J.. and A. J. Schweiger. 1998: Tools for atmospheric radiative transfer: Streamer and FluxNet. Cnniput. Geosri.. 24, 443-45 I. tended to include all seasons. perhaps using measure- , R. S Silcox. and R. S. Stone. 1996: Evaluation of wrface ments from the SHEBA experiment and more locations radiative flux pararneterizations for use in sea ice models. J. representative of polar conditions. cefll~/~'h?..s.R~.L101, 3839-3849, -. A. J. Schweiger. and R. S. Stone. 1997: Expected uncertainty in atellite-derived estimates of the high-latitude surface radia- Acknowiedgmmt.~.We thank the reviewers, particu- tion budget. J. Geophvs. Rrs.. 102, IS 837- I5 847. larly J. Key, for their careful reading of the manuscript LeadEx Group. 1993: The Lead Experiment. G1.v. Trutt$.Amcv. Gee- and helpful comments. We are also grateful to Dr. Shashi phys. L'tiioii, 393-397. Gupta for valuable discussions regarding his radiative Marshunova. M. S.. 1966: Principal characteristics of the radiation. transfer model and for general comments. Funding for balance til the underlying surface. Soviet data on the Arctic heat budget and it\ climate influence, Rep. R. 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