Estimation of downward longwave radiation for clear sky conditions
during the cold season in eastern Siberia* Yoshihiro Iijima 1, Hironori Yabuki 1, Tetsuo Ohata1(1: Institute of Observational Research for Global Change, JAMSTEC)* Institute of Observational Research for Global Change, JAMSTEC, 236-0001, Showa-machi,
Kanazawa-ku, Yokohama, Japan. e-mail: yiijima@jamstec.go.jp
Abstract
Downward longwave radiation (DLR) is an important incoming radiation in high latitude area, especially during winterand snowmelt season. In eastern Siberia, DLR during winter (from October to next April) is strongly affected by the surface
temperature inversion layer which is developed in conjunction with remarkable air temperature decrease on the inlandsurface. Few estimation schemes for the DLR at land surface represent the effect of strong surface inversion as appeared ineastern Siberia. In the present study, an estimation of DLR for clear sky conditions during winter based on the relationshipbetween DLR and surface temperature inversion was examined using observed DLR data and upper air data in 2000 (duringGAME-Siberia experiments) in Yakutsk. Generally DLR is estimated based on Stefan-Boltzmann radiation law using
atmospheric emissivity associated with accumulated water vapor content and air temperature at screen height as effectivetemperature. In the present study, the effect of surface inversion layer (dTe) is added to the surface air temperature. A
difference between surface air temperature and mean temperature in inversion layer is highly correlated with dTe. In
addition, this inversion temperature difference has liner relationship with surface air temperature below -10˚C. Theestimation in the present study shows good agreement with the estimation used in the dataset of the International Satellite
Land Surface Climatology Project (ISLSCP) with a RMS difference of 5.1Wm-2.
Keyword: Downward longwave radiation, inversion layer, accumulated water content, cold season, Siberia

1. Introduction
During the cold season in Siberia, air temperature near
the surface has severe decrease corresponding withremarkably developed surface inversion layer aloft.
Downward longwave radiation (DLR) substantiallyaffected by this characteristic temperature profile is mostimportant component as accounting for the surface energy
budget during the cold season in Siberia. In general, DLR
at a site without direct observation used to estimate using
air temperature and water vapor pressure at screen height.
However, as the case during winter in Siberia, conventional
estimation of DLR using surface parameters is mostly
unsuitable without taking account of the effects ofinversion.
In the present study, DLR estimation under clear sky wasimproved for the cold season in Siberia based on theestimation of Kondo (1994) which is often used in Japan.
In addition, the efficiency was compared with otherestimation applied in other polar sites for the cold region.

2. Data
Observational meteorological data in Yakutsk of eastern
Siberia was used for the present study. Duration of useddata was in April and from October to December, 2000.
Direct observation of DLR was measured by a ventilated
pyrgeometer (MS-202, EKO INSTRUMENTS Ltd.) at thetop of a larch forest tower (32m above the surface) near
Yakutsk. Observed DLR was corrected using thetemperature difference between dome and sensor (Shiobaraand Asano 1992). Vertical profiles of air temperature andwater vapor content were from upper air data observed atYakutsk observatory (62.01 °N, 129.43 °E) every 0:00

UTC compiled by ADP (an abbreviation for AutomatedData Processing) Global Upper Air Observation Subsets(DS353.4: radio sonde data). Precipitable water in the
National Centers for Environmental Prediction /National
Center for Atmospheric Research (NCEP/NCAR)
Reanalysis set (Kistler et al. 2001) was used for thecomparison. In addition, surface meteorological elements
at Yakutsk observatory were used from Baseline
Meteorological Data in Siberia (BMDS) Version 3.

3. Methods
Reference value of DLR for clear sky conditions wascalculated by radiation chart (Yamamoto 1952) using upper
air data. An accuracy of DLR from the radiation chart was±5 Wm-2 (Kondo 1994). We confirmed the accuracy
compared with multiple model predictions of DLR derived
from typical profiles of five climate zones inIntercomparison of Radiation Codes Used in Climate
Model (ICRCCM; Ellingson et al. 1991). As a result,
Estimated DLR by radiation chart was within a standard
deviation of model predictions (±5 Wm-2).
According to Kondo (1994), DLR under clear sky
condition (Ldf) at surface is estimated as follows:

Ldf = ε ' σ T 4e(1)ε ' = 0.59 + 0.038 ln (ω *) + 0.011 (ln (ω *))2(2)where Te is air temperature at the height near the surface(from 0 to 1 km) referred as effective temperature, ε’ isemissivity of atmosphere, ω* (1mm<ω*<80mm) is
effective accumulated water vapor content within a column

W m -2300

hPa200(a) downward longwave radiation− Ld at Spa skayapad● Ld calculated by radiation c hart

25025 Nov. 2000

300200150

400

100℃

15(b) difference from effective temperature (dTe)

500

10600

50700-5℃(c) air temperature (Ta)0800-10900-20-301000-40-50

OctoberNovem ber

DecemberFig. 1: Time series in meteorological components
concerning downward longwave radiation fromOctober to December 2000
a: observed and estimated DLR, b: effective
temperature by inversion layer (dTe), c: screen height
air temperature (Ta)Fig. 2: An example of inversion layer index (dTsum)on 25 November 2000℃
15(3)Using upper air data at Yakutsk during April and from
October to December, DLR for clear sky was estimated byradiation chart, and dTe was calculated backward fromDLR, ω* and Ta (Fig. 1).
In order to examine relationship between dTe anddevelopment of inversion layer, inversion layer index(dTsum) was defined; that is, average temperature of upper
air with more than Ta (Fig. 2).
As shown in Fig. 3, this index (dTsum) shows highcorrelation with dTe. Liner approximation between dTsum
and dTe is as follows:dTe = 1.16 dTsum−0.84(R 2 = 0.944)(4)

If we have only surface observation data, dTsum can be
estimated by those surface data. Surface air temperature
with less than -10 °C (263K) has good liner correlation
with dTsum (Fig. 4) as follows:

dTsum = −0.382 Ta + 99.3

(R 2 = 0.786)(but Ta < 263.15 [K] (-10 °C))(5)dTe (Te-Ta)of atmosphere of unit area. Generally, in the case of
absence of upper air data, daily averaged air temperature isused as Te.
However, under conditions of remarkable establishmentof inversion layer during the cold season in Siberia, using
only air temperature exceedingly underestimates DLR.
Thus, Te with the effect of inversion layer (dTe) is newly
defined as follows:

Te = Ta + dTe℃

-40
-20
02040
temperature difference from Ta

105℃0-5051015dT s u m-5Fig. 3 Relationship between inversion layer index(dTsum) and dTe
Data were from 1 to 30 April and from 1 October to31 December, 2000
Using equation 3 to 5, effective temperature Te during thecold season with less than -10 °C of surface air temperature
can be estimated as follows:

Te = 0.557 Ta + 114.35(6)

It should be noted, however, that temperature profiles
during April and early October when surface airtemperature ranges from -10 to 0 °C demonstrateun-developed and developed inversion layer, respectively.
Thus, further evaluation is needed for the estimation ofDLR during the turn of the seasons.
In order to estimate accumulated water content (ω*),
comparison was made among precipitable water by upper
air observation, by NCEP/NCAR Reanalysis data, and byLdf = (A0 + A1 V + A2 V 2 + A3 V 3 ) Te3.7(7)where V = ln PW , PW is the precipitable water (mm),Te is the effective temperature, A0 (=1.791×10-7), A1(=2.093×10-8), A2 (=-2.748×10-9), and A3 (=1.184×10-9) areregression coefficients. Te was represented as a weighted
sum of upper air temperatures:

Te = k s Ts + k1 T1 + k 2 T2(8)where Ts is the surface temperature, T1 and T2 are thetemperatures of the first (surface to 800hPa) and second(800 to 680hPa) atmospheric layers. The values ofcoefficients are ks=0.60, k1=0.35, and k2=0.05.
Comparing with the estimation of König-Langlo andAugstein (1994), the result shows much better relationshipwith our estimation (Fig. 6) with a RMS difference of
5.1Wm-2. Gupta et al. (1992) examined careful comparison
between the estimation and the detailed radiation models
using 330 soundings covered global meteorologicalconditions from pole to pole; surface temperature ranged
from 239 to 317K and confirmed precision for their15℃○2000/4/1-30＋2000/10/1-14
2000/10/15-12/31●1050-50℃-40-30-20-10Ta (surface air temp)

05Fig. 4: Relationship between Ta and dTsum(a)mm

precipitable water (sonde)

40

30

2010mm00102030

40

precipitable water (NCEP/NCAR)40

pre cip itable water (sonde)

4. Comparison with other estimations
DLR for clear sky computed with the modified
estimation in the present study was compared with othertwo estimation models. A set of 122 days sampled fromupper air and surface data at Yakutsk observatory for April
and from October to December, 2000, was used for thiscomparison.
König-Langlo and Augstein (1994) represented thesimplest estimation of DLR for clear sky: that is,emissivity of atmosphere (ε’) is fixed as 0.765. They madethis estimation using dataset at coastal sites in polar region.
As shown in Fig. 6, however, DLR estimation using theirestimation shows larger radiation with a RMS difference of22.1 Wm-2. This deviation is likely due to not only
difference in temperature and water vapor profiles, but alsoin aerosols, haze, ice crystals even in a cloudlessatmosphere between coastal and inland sites.
Another estimation takes account of temperature profile.
Gupta et al. (1992) made the estimation model using datafrom the International Satellite Cloud Climatology Project(ISCCP). This estimation is used for the DLR dataset in theInternational Satellite Land Surface Climatology Project(ISLSCP). The parameterized equation was expressed as:

dTsum (mean inversion temp)

estimation using surface dew temperature (Kondo 1994).
As shown in Fig. 5, precipitable water of upper air and theReanalysis data has high correlation, especially during coldseason with less than 10mm of precipitable water with aroot-mean square (RMS) difference of ±0.53mm. Althoughrelationship with estimated precipitable water by surface
dew temperature largely scattered during warm season,
high correlation appeared during cold season with a RMS
difference of ±1.13mm. The season with less than 10mm ofprecipitable water is from October to next April, namely
the accumulated water content during cold season, can be
estimated adequately even if only surface observation.

(b)

mm30201000mm

10203040

precipitable water (Kondo)
Fig. 5: Comparison of precipitable water at Yakutsk
a: nearest grid data of NCEP/NCAR Reanalysis data
and upper air data, b: estimation by surface dew
temperature data and upper air data
Dots and crosses denote less or more than 10mm ofprecipitable water calculated using upper air
observation at Yakutsk, respectively.

W m -2

estimated Ldf (other model)

300○ König-Langlo and Augstein (1994)of Kondo (1994).
(2) This inversion temperature difference has liner
relationship with surface air temperature below -10˚Cat Yakutsk observatory.
(3) The accumulated water content during cold season
can be estimated by using only surface water vapor
pressure on daily basis.
(4) Estimation in the present study shows good
agreement with the estimation used in the dataset of theInternational Satellite Land Surface Climatology
Project (ISLSCP) with a RMS difference of 5.1Wm-2.

250

200150● Gupta et al. (1992)

100100W m -2150

200

250

300

estimated Ldf (present study)

Fig. 6:Comparison of downward longwave
radiation for clear sky conditions between
estimations of the present study and others.
estimation. Therefore, the good agreement with theirestimation can be concluded that modified estimation in
the present study can be used as a concise estimation for
DLR for clear sky conditions during the cold season.

5. Conclusions
In the present study, we conducted an estimation of DLR
under clear sky during winter in eastern Siberia based on
the relationship between DLR and surface temperature
inversion and intercomparison with different estimation
models. Conclusions are summarized that:(1) A difference between surface air temperature andmean temperature in inversion layer is adequate
measure for the effect of surface inversion layer on anestimation of DLR for clear sky based on the estimation

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