Theoretical and Applied Climatology

, Volume 107, Issue 3–4, pp 461–477 | Cite as

Calculating downward longwave radiation under clear and cloudy conditions over a tropical lowland forest site: an evaluation of model schemes for hourly data

  • Toby R. MarthewsEmail author
  • Yadvinder Malhi
  • Hiroki Iwata
Original Paper


Field measurements of radiation fluxes—notably downwelling longwave radiation flux (LW flux)—are as yet rare or nonexistent outside a very select number of sites in the tropics. Data gaps can only be filled through the use of estimation schemes based on measurements of other meteorological variables, and there is a need for recommendations on best practice in this area. We selected 18 contrasting semi-empirical estimation schemes for downward longwave radiation, based on air emissivities, combined with six different sky cover estimation schemes and compared the expected longwave flux with hourly observations from a flux tower at Caxiuanã in Brazil. Of all schemes tested, the Dilley–Kimball emissivity scheme combined with Kasten and Czeplak’s sky cover scheme during the day and Dilley and O’Brien’s model B scheme at night proved to be the most reliable, yielding estimates of LW flux generally within 20 W/m2 of measurements across all time points.


Emissivity Diffuse Fraction Flux Tower Lowland Tropical Forest Downward Longwave Radiation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was supported by Microsoft Research and the Oxford University John Fell Fund. We thank I. Perzia for all her extremely patient support and the staff of the Environmental Change Institute, University of Oxford, as well as C. Delire, A. Friend, P. Żelazowski, L. Cowley, P. Palmer, M. Allen, D. Andrews, H. Pumphrey, J. Wang, K. Halladay, P. Stier and two anonymous reviewers for useful comments during development of the text.


  1. Allen RG, Pereira LS, Raes D, Smith M (1998) Crop evapotranspiration Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56, FAO, Rome, Italy. Accessed 7 May 2011
  2. Anderson ER (1954) Energy-budget studies. USGS Prof Pap 269:71–119Google Scholar
  3. Ångström A (1915) A study of the radiation of the atmosphere. Smithsonian Miscellaneous Collections 65(3)Google Scholar
  4. Ångström A (1924) Solar and terrestrial radiation. Q J Roy Meteor Soc 50:121–126CrossRefGoogle Scholar
  5. Aragão LEOC, Malhi Y, Metcalfe DB, Silva-Espejo JE, Jiménez E, Navarrete D, Almeida S, Costa ACL, Salinas N, Phillips OL, Anderson LO, Alvarez E, Baker TR, Goncalvez PH, Huamán-Ovalle J, Mamani-Solórzano M, Meir P, Monteagudo A, Patiño S, Peñuela MC, Prieto A, Quesada CA, Rozas-Dávila A, Rudas A, Silva JA, Vásquez R (2009) Above- and below-ground net primary productivity across ten Amazonian forests on contrasting soils. Biogeosciences 6:2759–2778CrossRefGoogle Scholar
  6. Avissar R, Nobre CA (2002) Preface to special issue on the Large-Scale Biosphere–Atmosphere Experiment in Amazonia (LBA). J Geophys Res D 107(D20):8034(LBA1)Google Scholar
  7. Baldocchi D, Falge E, Gu LH, Olson R, Hollinger D, Running S, Anthoni P, Bernhofer C, Davis K, Evans R, Fuentes J, Goldstein A, Katul G, Law B, Lee XH, Malhi Y, Meyers T, Munger W, Oechel W, Paw UKT, Pilegaard K, Schmid HP, Valentini R, Verma S, Vesala T, Wilson K, Wofsy S (2001) FLUXNET: a new tool to study the temporal and spatial variability of ecosystem-scale carbon dioxide, water vapor, and energy flux densities. Bull Am Meteorol Soc 82:2415–2434CrossRefGoogle Scholar
  8. Berberan-Santos MN, Bodunov EN, Pogliani L (1997) On the barometric formula. Am J Phys 65:404–412CrossRefGoogle Scholar
  9. Bindi M, Miglietta F, Zipoli G (1992) Different methods for separating diffuse and direct components of solar radiation and their application in crop growth models. Clim Res 2:47–54CrossRefGoogle Scholar
  10. Bisht G, Bras RL (2010) Estimation of net radiation from the MODIS data under all sky conditions: Southern Great Plains case study. Remote Sens Environ 114:1522–1534CrossRefGoogle Scholar
  11. Black JN (1956) The distribution of solar radiation over the Earth’s surface. Arch Meteor Geophy B 7:165–189CrossRefGoogle Scholar
  12. Brunt D (1932) Notes on radiation in the atmosphere I. Q J Roy Meteor Soc 58:389–420CrossRefGoogle Scholar
  13. Brutsaert W (1975) On a derivable formula for long-wave radiation from clear skies. Water Resour Res 11:742–744CrossRefGoogle Scholar
  14. Brutsaert W (1982) Evaporation into the atmosphere. D. Reidel, DordrechtGoogle Scholar
  15. Butt N, New M, Lizcano G, Malhi Y (2009) Spatial patterns and recent trends in cloud fraction and cloud-related diffuse radiation in Amazonia. J Geophys Res D 114:D21104CrossRefGoogle Scholar
  16. Campbell GS (1985) Soil physics with BASIC. Elsevier, AmsterdamGoogle Scholar
  17. Campbell GS, Norman JM (1998) An introduction to environmental biophysics, 2nd edn. Springer, New YorkCrossRefGoogle Scholar
  18. Carswell FE, Costa AL, Palheta M, Malhi Y, Meir P, Costa JDR, Ruivo MD, Leal LDM, Costa JMN, Clement RJ, Grace J (2002) Seasonality in CO2 and H2O flux at an eastern Amazonian rain forest. J Geophys Res D 107:D8076CrossRefGoogle Scholar
  19. Chang J (1968) Climate and agriculture. Aldine, ChicagoGoogle Scholar
  20. Chapman CA, Gautier-Hion A, Oates JF, Onderdonk DA (1999) African primate communities: determinants of structure and threats to survival. In: Fleagle JG, Janson CH, Reed KE (eds) Primate communities. CUP, Cambridge, UK, pp. 1–37CrossRefGoogle Scholar
  21. Crawford TM, Duchon CE (1999) An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling longwave radiation. J Appl Meteorol 38:474–480CrossRefGoogle Scholar
  22. R Development Core Team (2011) R: a language and environment for statistical computing, version 2.12.1. R Foundation for Statistical Computing, Vienna. Accessed 7 May 2011
  23. Dilley AC, O’Brien DM (1998) Estimating downward clear sky long-wave irradiance at the surface from screen temperature and precipitable water. Q J Roy Meteor Soc 124:1391–1401CrossRefGoogle Scholar
  24. Doorenbos J, Pruitt WO (1977) Crop water requirements. FAO Irrigation and Drainage Paper 24, FAO, Rome, ItalyGoogle Scholar
  25. Dubayah R, Rich PM (1995) Topographic solar radiation models for GIS. Int J Geogr Inf Syst 9:405–419CrossRefGoogle Scholar
  26. Dunne T, Leopold LB (1978) Water in environmental planning. W.H. Freeman, New YorkGoogle Scholar
  27. Ellingson RG (1995) Surface longwave fluxes from satellite observations: a critical review. Remote Sens Environ 51:89–97CrossRefGoogle Scholar
  28. Falge E, Baldocchi D, Olson R, Anthoni P, Aubinet M, Bernhofer C, Burba G, Ceulemans R, Clement R, Dolman H, Granier A, Gross P, Grünwald T, Hollinger D, Jensen N, Katul G, Keronen P, Kowalski A, Lai CT, Law BE, Meyers T, Moncrieff J, Moors E, Munger JW, Pilegaard K, Rannik Ü, Rebmann C, Sukyer A, Tenhunen J, Tu K, Verma S, Vesala T, Wilson K, Wofsy S (2001) Gap filling strategies for defensible annual sums of net ecosystem exchange. Agr For Meteorol 107:43–69CrossRefGoogle Scholar
  29. Flerchinger GN, Xaio W, Marks D, Sauer TJ, Yu Q (2009) Comparison of algorithms for incoming atmospheric long-wave radiation. Water Resour Res 45:W03423CrossRefGoogle Scholar
  30. Friend AD (1998) Parameterisation of a global daily weather generator for terrestrial ecosystem modelling. Ecol Model 109:121–140CrossRefGoogle Scholar
  31. Friend AD (2001) Modelling canopy CO2 fluxes: are ‘big-leaf’ simplifications justified? Glob Ecol Biogeogr 10:603–619CrossRefGoogle Scholar
  32. Friend AD, Stevens AK, Knox RG, Cannell MGR (1997) A process-based, terrestrial biosphere model of ecosystem dynamics (Hybrid v3.0). Ecol Model 95:249–287CrossRefGoogle Scholar
  33. Friend AD, Geider RJ, Behrenfeld MJ, Still CJ (2009) Photosynthesis in global-scale models. In: Laisk A, Nedbal L, Govindjee (eds) Photosynthesis in silico: understanding complexity from molecules to ecosystems. Springer, Dordrecht, pp 465–497Google Scholar
  34. Gabathuler M, Marty CA, Hanselmann KW (2001) Parameterization of incoming longwave radiation in high-mountain environments. Phys Geogr 22:99–114Google Scholar
  35. Gates DM (1980) Biophysical ecology. Springer, New YorkCrossRefGoogle Scholar
  36. Ghazoul J, Sheil D (2010) Tropical rain forest ecology, diversity, and conservation. Oxford University Press, OxfordGoogle Scholar
  37. Goudriaan J (1977) Crop micrometeorology: a simulation study. Pudoc, WageningenGoogle Scholar
  38. Hellwege K, Madelung O (1988) Landolt–Börnstein numerical data and functional relationships in science and technology, volume V/4b: physical and chemical properties of the air. Springer, BerlinGoogle Scholar
  39. Idso SB (1981) A set of equations for full spectrum and 8- to 14-μm and 10.5- to 12.5-μm thermal radiation from cloudless skies. Water Resour Res 17:295–304CrossRefGoogle Scholar
  40. Idso SB, Jackson RD (1969) Thermal radiation from the atmosphere. J Geophys Res 74:5397–5403CrossRefGoogle Scholar
  41. Ineichen P, Perez R (1999) Derivation of cloud index from geostationary satellites and application to the production of solar irradiance and daylight illuminance data. Theor Appl Climatol 64:119–130CrossRefGoogle Scholar
  42. Ineichen P, Perez R (2002) A new airmass independent formulation for the Linke turbidity coefficient. Sol Energy 73:151–157CrossRefGoogle Scholar
  43. Intergovernmental Panel on Climate Change (2007) Climate Change 2007: the Fourth IPCC Assessment Report. Cambridge University Press, CambridgeGoogle Scholar
  44. Iqbal M (1983) An introduction to solar radiation. Academic, TorontoGoogle Scholar
  45. Ivanov VY, Bras RL, Curtis DC (2007) A weather generator for hydrological, ecological, and agricultural applications. Water Resour Res 43:W10406CrossRefGoogle Scholar
  46. Iwata H, Malhi Y, von Randow C (2005) Gap-filling measurements of carbon dioxide storage in tropical rainforest canopy airspace. Agr For Meteorol 132:305–314CrossRefGoogle Scholar
  47. Iziomon MG, Mayer H, Matzarakis A (2003) Downward atmospheric longwave irradiance under clear and cloudy skies: measurement and parameterization. J Atmos Sol-Terr Phy 65:1107–1116CrossRefGoogle Scholar
  48. Jegede OO, Ogolo EO, Aregbesola TO (2006) Estimating net radiation using routine meteorological data at a tropical location in Nigeria. Int J Sustain Energy 25:107–115CrossRefGoogle Scholar
  49. Jones HG, Archer N, Rotenberg E (2004) Thermal radiation, canopy temperature and evaporation from forest canopies. In: Mencuccini M, Grace J, Moncrieff J, McNaughton KG (eds) Forests at the land–atmosphere interface. CABI Publishing, Wallingford, pp 123–144CrossRefGoogle Scholar
  50. Kanniah KD, Beringer J, Tapper NJ, Long CN (2010) Aerosols and their influence on radiation partitioning and savanna productivity in northern Australia. Theor Appl Climatol 100:423–438CrossRefGoogle Scholar
  51. Kasten F, Czeplak G (1980) Solar and terrestrial radiation dependent on the amount and type of cloud. Sol Energy 24:177–189CrossRefGoogle Scholar
  52. Killeen TJ (2007) A perfect storm in the Amazon wilderness. Advances in Applied Biodiversity Science 7. Accessed 7 May 2011
  53. Kimball BA, Idso SB, Aase JK (1982) A model of thermal radiation from partly cloudy and overcast skies. Water Resour Res 18:931–936CrossRefGoogle Scholar
  54. Konzelmann T, van de Wal RSW, Greuell W, Bintanja R, Henneken EAC, Abe-Ouchi A (1994) Parameterization of global and longwave incoming radiation for the Greenland Ice Sheet. Glob Planet Chang 9:143–164CrossRefGoogle Scholar
  55. Kotarba AZ (2010) Estimation of fractional cloud cover for moderate resolution imaging spectroradiometer/Terra cloud mask classes with high-resolution over ocean ASTER observations. J Geophys Res D 115:D22210CrossRefGoogle Scholar
  56. Landsberg J, Sands P (2011) Physiological ecology of forest production. Academic, AmsterdamGoogle Scholar
  57. Leigh EG (1999) Tropical climates. In: Leigh EG (ed) Tropical forest ecology: a view from Barro Colorado Island. Oxford University Press, New York, pp 46–66Google Scholar
  58. Lewis SL, Lloyd J, Sitch S, Mitchard ETA, Laurance WF (2009) Changing ecology of tropical forests: evidence and drivers. Annu Rev Ecol Evol S 40:529–549CrossRefGoogle Scholar
  59. Lhomme JP, Vacher JJ, Rocheteau A (2007) Estimating downward long-wave radiation on the Andean Altiplano. Agr For Meteorol 145:139–148CrossRefGoogle Scholar
  60. Lin JC, Matsui T, Pielke RA, Kummerow C (2006) Effects of biomass-burning-derived aerosols on precipitation and clouds in the Amazon Basin: a satellite-based empirical study. J Geophys Res D 111:D19204CrossRefGoogle Scholar
  61. Lisboa PLB (1997) A Estação Científica Ferreira Penna/ECFPn. In: Lisboa PLB (ed), Caxiuanã, Museu Paraense Emílio Goeldi, Belém, Brazil, pp 20–49Google Scholar
  62. Liu BYH, Jordan RC (1960) The interrelationship and characteristic distribution of direct, diffuse, and total solar radiation. Sol Energy 4:1–19CrossRefGoogle Scholar
  63. Malhi Y (2010) The carbon balance of tropical forest regions, 1990–2005. Curr Opin Environ Sustain 2:237–244CrossRefGoogle Scholar
  64. Malhi Y, Wright J (2004) Spatial patterns and recent trends in the climate of tropical rainforest regions. Philos Trans R Soc B 359:311–329CrossRefGoogle Scholar
  65. Malhi Y, Meir P, Brown S (2002a) Forests, carbon and global climate. Philos Trans R Soc A 360:1567–1591CrossRefGoogle Scholar
  66. Malhi Y, Pegoraro E, Nobre AD, Pereira MGP, Grace J, Culf AD, Clement R (2002b) Energy and water dynamics of a central Amazonian rain forest. J Geophys Res 107(D20):LBA45CrossRefGoogle Scholar
  67. Malhi Y, Aragão LEOC, Metcalfe DB, Paiva R, Quesada CA, Almeida S, Anderson L, Brando P, Chambers JQ, da Costa ACL, Hutyra LR, Oliveira P, Patiño S, Pyle EH, Robertson AL, Teixeira LM (2009) Comprehensive assessment of carbon productivity, allocation and storage in three Amazonian forests. Glob Chang Biol 15:1255–1274CrossRefGoogle Scholar
  68. Martínez-Lozano JA, Tena F, Onrubia JE, de la Rubia J (1984) The historical evolution of the Ångström formula and its modifications: review and bibliography. Agr For Meteorol 33:109–128CrossRefGoogle Scholar
  69. Mercado LM, Huntingford C, Gash JHC, Cox PM, Jogireddy V (2007) Improving the representation of radiation interception and photosynthesis for climate model applications. Tellus B 59:553–565CrossRefGoogle Scholar
  70. Mercado LM, Bellouin N, Sitch S, Boucher O, Huntingford C, Wild M, Cox PM (2009) Impact of changes in diffuse radiation on the global land carbon sink. Nature 458:1014–1018CrossRefGoogle Scholar
  71. Mokhov II, Akperov MG (2006) Tropospheric lapse rate and its relation to surface temperature from reanalysis data. Izvestiya Atmos Ocean Phys 42:430–438CrossRefGoogle Scholar
  72. Monteith JL, Unsworth MH (1990) Principles of environmental physics, 2nd edn. Butterworth, OxfordGoogle Scholar
  73. Muneer T, Gueymard C, Kambezidis H (2004) Solar radiation and daylight models, 2nd edn. Elsevier Butterworth-Heinemann, OxfordGoogle Scholar
  74. Niemelä S, Räisänen P, Savijärvi H (2001) Comparison of surface radiative flux parameterizations. Part I: Longwave radiation. Atmos Res 58:1–18CrossRefGoogle Scholar
  75. Okogbue EC, Adedokun JA, Holmgren B (2009) Hourly and daily clearness index and diffuse fraction at a tropical station, Ile-Ife, Nigeria. Int J Climatol 29:1035–1047CrossRefGoogle Scholar
  76. Peel MC, Finlayson BL, McMahon TA (2007) Updated world map of the Köppen–Geiger climate classification. Hydrol Earth Syst Sc 11:1633–1644CrossRefGoogle Scholar
  77. Penman HL (1948) Natural evaporation from open water, bare soil and grass. P Roy Soc Lond A 193:120–146CrossRefGoogle Scholar
  78. Perez R, Ineichen P, Seals R, Zelenka A (1990) Making full use of the clearness index for parameterizing hourly insolation conditions. Sol Energy 45:111–114CrossRefGoogle Scholar
  79. Pirazzini R, Nardino M, Orsini A, Calzolari F, Georgiadis T, Levizzani V (2000) Parameterization of the downward longwave radiation from clear and cloudy skies at Ny Ålesund (Svalbard). In: Smith WL, Timofeyev YM (eds) International Radiation Symposium (IRS) July 2000, St Petersburg, Russia: Current Problems in Atmospheric Radiation. Deepak Publishing, Hampton, Virginia, pp 559–562Google Scholar
  80. Prata AJ (1996) A new long-wave formula for estimating downward clear-sky radiation at the surface. Q J Roy Meteor Soc 122:1127–1151CrossRefGoogle Scholar
  81. Prentice IC, Bondeau A, Cramer W, Harrison SP, Hickler T, Lucht W, Sitch S, Smith B, Sykes MT (2007) Dynamic global vegetation modeling: quantifying terrestrial ecosystem responses to large-scale environmental change. In: Canadell JG, Pataki DE, Pitelka LF (eds) Terrestrial ecosystems in a changing world. Springer, Berlin, pp 175–192CrossRefGoogle Scholar
  82. Rose F, Charlock T, Wielicki B, Doelling D, Zentz S (2006) CERES synoptic gridded diurnaly resolved radiative transfer. Proceedings of the 12th Conference on Atmospheric Radiation, Madison, WI, USA, 10–14 July. Accessed 7 May 2011
  83. Ross J (1975) Radiative transfer in plant communities. In: Monteith JL (ed) Vegetation and the atmosphere (vol. I). Academic, London, pp 13–55Google Scholar
  84. Rossow WB, Schiffer RA (1991) ISCCP cloud data products. Bull Am Meteorol Soc 72:2–20CrossRefGoogle Scholar
  85. Rossow WB, Mosher F, Kinsella E, Arking A, Desbois M, Harrison E, Minnis P, Ruprecht E, Seze G, Simmer C, Smith E (1985) ISCCP cloud algorithm intercomparison. J Clim Appl Meteorol 24:877–903CrossRefGoogle Scholar
  86. Rymes M (1998) The SolPos algorithm. National Renewable Energy Laboratory, USA. Accessed 7 May 2011
  87. Şen Z (2008) Solar energy fundamentals and modeling techniques. Springer, LondonGoogle Scholar
  88. Spitters CJT, Toussaint HAJM, Goudriaan J (1986) Separating the diffuse and direct component of global radiation and its implications for modeling canopy photosynthesis. Part I. Components of incoming radiation. Agr For Meteorol 38:217–229CrossRefGoogle Scholar
  89. Stöckli R (2007) LBA-MIP driver data gap filling algorithms. Unpublished. Accessed 7 May 2011
  90. Suits GH (1972) The calculation of the directional reflectance of a vegetative canopy. Remote Sens Environ 2:117–125CrossRefGoogle Scholar
  91. Swinbank WC (1963) Long-wave radiation from clear skies. Q J Roy Meteor Soc 89:339–348CrossRefGoogle Scholar
  92. Walsh RPD (1996) Climate. In: Richards PW, Walsh RPD, Baillie IC, Greig-Smith P (eds) The tropical rain forest, 2nd edn. Cambridge University Press, Cambridge, pp 159–205, 503–540Google Scholar
  93. Weishampel JF, Urban DL (1996) Coupling a spatially-explicit forest gap model with a 3-D solar routine to simulate latitudinal effects. Ecol Model 86:101–111CrossRefGoogle Scholar
  94. Wild M (2008) Short-wave and long-wave surface radiation budgets in GCMs: a review based on the IPCC-AR4/CMIP3 models. Tellus A 60:932–945CrossRefGoogle Scholar
  95. Wright SJ (2005) The El Niño Southern Oscillation influences tree performance in tropical rainforests. In: Bermingham E, Dick CW, Moritz C (eds) Tropical rainforests: past, present, and future. University of Chicago Press, Chicago, pp 295–310, 611–713Google Scholar
  96. Xing Z, Bourque CP, Meng F, Cox RM, Swift DE, Zha T, Chow L (2008) A process-based model designed for filling of large data gaps in tower-based measurements of net ecosystem productivity. Ecol Model 213:165–179CrossRefGoogle Scholar
  97. Zelazowski P, Malhi Y, Huntingford C, Sitch S, Fisher JB (2011) Changes in the potential distribution of humid tropical forests on a warmer planet. Philos Tr R Soc A 369:137–160CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • Toby R. Marthews
    • 1
    Email author
  • Yadvinder Malhi
    • 1
  • Hiroki Iwata
    • 2
  1. 1.Environmental Change Institute, School of Geography and the EnvironmentUniversity of OxfordOxfordUK
  2. 2.International Arctic Research CenterUniversity of Alaska FairbanksFairbanksUSA

Personalised recommendations