The Surface Energy Budget

The Surface Energy Budget

The radiation (R) budget Shortwave (solar) Radiation Longwave Radiation R SW R SW α α = surface albedo R LW εσt 4 ε = emissivity σ = Stefan-Boltzman constant T = temperature Subsurface Column (variously soil, rock, ice, water) R NET = R SW (1- α ) + R LW + εσt 4 Fluxes are positive when directed toward the surface

The non-radiative terms Sensible Heat (S) Latent Heat (L) Melt (M) Conduction (C) Subsurface Column (variously soil, rock, ice, water) R NET = S + L + M + C Non radiative terms positive when directed away from the surface

Components of the budget

Spectral irradiance for a black body at 5900K, Incoming solar radiation at sea level assuming no absorbtion, and observed solar radiation at the earth s surface. Note the various atmospheric absorbtion bands due primarily to ozone, diatomic oxygen, water vapor and carbon dioxide. http://stlab.iis.u-tokyo.ac.jp/~wataru/lecture/rsgis/rsnote/cp1/cp1-10.htm

Mean monthly downwelling solar radiation at the surface (R SW, Wm -2 ) for March through October, based on ISCCP-D satellite data [courtesy of J. Key, NOAA, Madison, WI]. The surface flux depends on TOA solar flux, clear-sky absorbtion and scattering, and absorbtion and scattering by clouds.

These two MODIS composites serve to emphasize two points: (1) The Arctic is typically cloudy, meaning that much of the TOA solar flux is scattered back to space (clouds have a high albedo); 2) surface albedo, while typically quite high in the Arctic, is also highly variable both spatially and temporally MODIS mosiac, April 30,2010 MODIS mosiac, July 17, 2011 http://lance.nasa.gov/imagery/rapid-response/

From Serreze and Barry, 2005

Albedo of snow Direct beam spectral reflectance for a semi-infinite snowpack as a function of wavelength for grain radii from 50 to 1000 µm and for a solar zenith angle of 60 [from Wiscombe and Warren, 1980, by permission of AMS]. The key points are that the spectral reflectance of a snowpack is higher for short wavelengths (visible band) and small grain sizes. Albedo is the integrated spectral reflectance over the solar spectrum.

Effect of solar zenith angle The albedo of snow tends to increase with an increasing solar zenith angle (the angle between zenith an the sun). This is understood from the forward-scattering nature of snow particles. For a large zenith angle (sun near the horizon) there is a high likelihood that a photon will be scattered upwards and out of the snowpack. For a small zenith angle (sun close to overhead) there will be more interactions between a photon and snow grains, and a greater likelihood of absorbtion. http://www.instesre.org/temperatecli mate/temperateclimate.htm

Cloud cover tends to increase the albedo of snow relative to clear skies 1) Clouds preferentially absorb longer wavelengths, so that the incoming radiation at the surface is relatively enriched in the short wavelengths for which the snow albedo is highest. This is augmented by stronger multiple scattering between the surface and cloud base. 2) Clouds increase the ratio of diffuse (scattered) to direct-beam radiation. The effective solar zenith angle under overcast skies is 50. Hence: --- if the true solar zenith angle is >50 o, the effect of cloud is to decrease the effective solar zenith angle and reduce the albedo --- if the true solar zenith angle is <50 o, the effect of cloud is to increase the effective solar zenith angle and increase the albedo However, enrichment of the incident flux in she shorter wavelengths normally outweighs the effect of cloud cover on the effective solar zenith angle, such that cloud cover has an overall effect of increasing the albedo

Effect of sastrugi aligned snow drifts Albedo can be several percent lower when the solar zenith angle is normal to sastrugi in the snow cover (causing shadows) compared to when it is parallel to sastrugi. http://nsidc.org/snow/gallery/sastrugi1.html

Albedo of snow: summary High Albedo Shorter wavelengths High zenith angle Small grain size Fresh snow Uniform layer Cloudy skies Low Albedo Longer wavelengths Low zenith angle Large grain size Old snow (grain size and pollution particles) Drift patterns Clear skies

Sea ice albedo quite variable, both temporally (snow cover aging, meltpond formation, fresh snowfall events), and spatially (regional differences in temperature, snow depth, snow characteristics and sea ice concentration) Courtesy D. Perovich, USA CRREL

Seasonal cycle of surface albedo over the central Arctic Ocean based on SHEBA data for 1997. The coloring, from left to right, breaks to time series into, respectively, pre-melt, initial melt, rapid melt, summer, and autumn freezeup (courtesy D. Perovich, USA CRREL).

Mean monthly surface albedo across the Arctic for April through September, based on APP-x satellite data [courtesy of J. Key, NOAA/NESDIS, Madison, WI]. Spring values over snow covered sea ice can exceed 0.80. Values over open water are less than 0.10. The albedo of the cold, snow covered central Greenland ice sheet stays high year round

Mean monthly downwelling longwave radiation at the surface (R LW, Wm -2 ) for the four mid-season months based on ISCCP-D data [courtesy of J. Key, NOAA, Madison, WI]. The flux depends on temperature, water vapor content and cloud cover, the latter two which affect the atmospheric emissivity. Clouds radiate approximately as blackbodies.

Mean monthly net longwave radiation at the surface (Wm -2 ) for the four mid-season months based on ISCCP-D data [courtesy of J. Key, NOAA, Madison, WI]. Note that the fluxes are all negative (emitted longwave radiation exceeds to downward longwave flux). The net longwave flux depends strongly on cloud cover.

Mean monthly net allwave radiation at the surface (Wm-2) for the four mid-season months based on ISCCP-D data [courtesy of J. Key, NOAA, Madison, WI].

Cloud radiative forcing (CRF) The radiative impact of clouds at the surface or top of the atmosphere CRF = (SW average - SW clear ) + (LW average - LW clear ) Shortwave Forcing Longwave Forcing (-30 W/m 2 in Arctic) (+55 W/m 2 in Arctic) CRF > 0 : Clouds are a warming mechanism CRF < 0 : Clouds are a cooling mechanism

Modeled annual cycle of (a) the surface and (b) top of atmosphere cloud radiative forcing (net shortwave, net longwave and net allwave) at 80 N [from Curry and Ebert, 1992, by permission of AMS]. The competing effects of cloud shortwave forcing (clouds reduce the downward solar flux) and cloud longwave forcing (clouds increase the downward longwave flux) are most pronounced at the surface. Averaged over the year, surface net allwave (longwave plus shortwave) cloud radiative forcing is positive (cloud cover increases the net allwave flux, i.e., it warms the surface). Net allwave surface forcing is negative (clouds cool the surface) only for a short time during summer. The shortwave cloud forcing at the surface is very sensitive to surface albedo. The negative net allwave forcing at the top of the atmosphere in summer is primarily due to the high albedo of clouds.

Mean monthly total (allwave) cloud radiative forcing at the surface (Wm -2 ) for the four mid-season months based on ISCCP-D data [courtesy of J. Key, NOAA, Madison, WI]. Only the July field shows negative values.

Observed surface cloud radiative forcing: Barrow, AK x axis = month, y axis = cloud fraction (f) Courtesy J. Walsh, Univ. IL Urbana Champaign

Monthly radiation balance components (W m -2 ) for the central Arctic Ocean from the SHEBA (Surface Heat Budget of the Arctic Ocean) experiment. Shown are (a) net radiation (heavy lines) and albedo (thin lines); (b) incoming shortwave radiation; (c) incoming longwave radiation. In each panel, results from the SHEBA experiment are shown along with those from other studies [adapted from Persson et al., 2002, by permission of AGU].

Monthly non-radiative energy balance components (W m -2 ) for the Central Arctic Ocean from the SHEBA effort. Shown are (a) sensible heat flux; (b) latent heat flux; (c) conductive heat flux. In each panel, results from the SHEBA experiment are shown along with those from other studies [adapted from Persson et al., 2002, by permission of AGU]. Note the smallness of these terms compared to the radiative fluxes (previous slide).

Arctic temperature inversions

Mean temperature profiles for February 1987 from 6 stations located around the periphery of the Arctic Ocean: 1) Krenkel (81 N, 58 E), 2) Chelyuskin (78 N,104 E), 3) Kotelny (76 N, 138 E), 4) Barrow (71 N, 86 W), 5) Mould Bay (76 N, 119 W) and Eureka (80 N, 86 W) [from Overland et al., 1997, by permission of AMS]. The surface-based temperature inversion at each site, to a first order, can be viewed in terms of longwave radiative equilibrium.

Longwave radiative equilibrium The atmosphere has a lower emissivity than the surface. If the system is in longwave equilibrium, the atmopshere must be radiating at a higher physical temperature than the surface. Atmosphere (ε a < 1) ε s σt s 4 = ε a σt a 4 but ε s σt s 4 ε a σt a 4 ε s > ε a hence T a > T s Surface (ε s = 1) Key assumptions: 1) System is determined only by longwave radiation exchanges 2) System is completely closed (which violates the second law of thermodynamics)

A more complete view (albeit still oversimplified) Net longwave loss to space Atmosphere (ε a < 1) ε s σt 4 s > ε a σt 4 a ε s > ε a and T a > T s ε s σt 4 s + ε a σt 4 a + F A = 0 ε s σt s 4 ε a σt a 4 F A Surface (ε s = 1) Surface turbulent fluxes and the shortwave radiation flux are small. Leakage of longwave radiation to space is balanced by horizontal heat flux convergence.

Monthly median inversion top (top of bars), base (bottom of bars) and temperature difference (solid lines) from a) drifting station data from the central Arctic Ocean; b) station Zhigansk over the Siberian tundra [from Serreze et al., 1992b, by permission of AMS]. Inversions are still common in summer but tend be elevated above the surface. Shallow surface-based melting inversions are also common in summer over sea ice..

Climate feedbacks involving the surface energy budget

Schematic of the ice- albedo feedback mechanism using the framework of Kellogg [1973]. The direction of the arrow indicates the direction of the interaction. A + indicates a positive interaction (an increase in the first quantity leads to an increase in the second). A - indicates a negative interaction (an increase in the first quantity leads to a decrease in the second quantity). A +/- indicates that the sign of the interaction is uncertain or that the sign changes over the annual cycle [from Curry et al., 1996, by permission of AMS].

The cloud-radiation feedback mechanism [from Curry et al., 1996, by permission of AMS].