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A Simple Model for the Seasonal Cycle of Energy Fluxes in the high latitudes

A Simple Model for the Seasonal Cycle of Energy Fluxes in the high latitudes. Aaron Donohoe and David S. Battisti Thanks to Dargan Frierson and Arnaud Czaja. Photo: Ed WB IV. 5.7 PW. 5.9 PW. How do the absorbed solar (ASR), outgoing longwave (OLR), and meridional

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A Simple Model for the Seasonal Cycle of Energy Fluxes in the high latitudes

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  1. A Simple Model for the Seasonal Cycle of Energy Fluxes in the high latitudes Aaron Donohoe and David S. Battisti Thanks to Dargan Frierson and Arnaud Czaja Photo: Ed WB IV

  2. 5.7 PW 5.9 PW How do the absorbed solar (ASR), outgoing longwave (OLR), and meridional heat transport (MHT) each contribute to the high latitude balance? How does this picture change seasonally?

  3. OUTLINE I) Annual, zonal averaged energy flux (obs) 2) Zonal mean seasonal energy balance Observed, 3-box EBM, aquaplanet GCM 3) Land-ocean contrasts and seasonal energy balances Observed, 6-box EBM 4) Conclusions

  4. 1) Zonal and Annual Averaged Energy Flux (global mean removed) ASR = Absorbed solar SHF = Surface heat flux (-)OLR = Outgoing longwave MHT = Meridional Heat Transp. CTEN = (-) Atmos Column tendency Observed NH • All signs defined wrt the atmosphere (e.g., positive OLR is an energy flux to the atmosphere) • Surface heat flux = the total energy flux (radiative plus turbulent) through the surface/atmosphere interface • In the annual mean, positive SHF is equal to oceanic heat flux convergence

  5. Annual mean of energy budget poleward of 300N(Departures from global annual mean) Absorbed Solar (ASR) 2.2 PW Surface Heat Flux (SHF) 7.9 PW Negative OLR 4.3 PW North Polar Region Tropics Meridional Heat Transport (MHT) 1.4 PW

  6. ASR SHF MHT 2) Zonal and Seasonal Averaged Energy Flux (zonal, annual average removed) Observed NH (-) OLR CTEN (-) Atmospheric Column tendency

  7. North Polar Region Seasonal Energy Balance (Seasonal Anomalies from local annual mean) JULY JANUARY 15.8 PW 13.9 PW 3.0 PW 3.4 PW 1.8 PW 0.2 PW 2.3 PW 0.8 PW 8.4 PW 9.8 PW ocean ocean (-) OLR ASR SHF MHT (-) CTEN

  8. How do we understand the seasonal partitioning of energy flux on an equator-to-pole scale? • What parameters & physics dictate the amount of energy (insolation) that goes into ocean storage vs. that that enters the atmosphere to drive temperature, OLR, and MHT changes? • What controls the ratio OLR:MHT:CTEN? • STRATEGY: build a ‘toy’ model; a linear 3-box model Energy Balance Model (EBM) with only the essential processes

  9. An atmospheric layer in radiative* equilibrium Space Absorbed atmosphere LH = BLH(TS-CLH) Atmosphere SENS = BSENS(TS-TA-CSENS) Surface Solar Radiation Terrestrial Radiation Our EBM has three atmospheric layers - this is a schematic

  10. The EBM basic state • Emissivity is a function of basic state temperature, assumed fixed relative humidity (75%) and CO2 according to Emmanuel (2002) TA3= 225 K TA2= 248 K TA1= 262 K TS= 287 K Surface (black body)

  11. 4σ TS3TS’ The linearized basic state • We fix the layer emissivities but take the water vapor feedback into effect ASR’ (prescribed) 3 TA’ CWV 4 CWV 3 4 TA’ LH’ = BLHT’S SENS’ = BSENS(TS’-TA’) 4 TS3TS’ 4 TS3TS’ Sensible heat affects lowest atmosphere layer; latent distributed

  12. Vertical energy exchanges in the perturbed system Change in OLR if the Column heats up uniformly BOLR = BOLR,S +[BOLR,A] = 2.6 Wm-2K-1 If only the surface heats up 0.8 Wm-2 K-1 1.8 Wm-2 K-1 BOLR,S [BOLR,A] BLW↑,S = 5.3 Wm-2 K-1 BLH = 4.0 Wm-2 K-1 BSENS = 3.0 Wm-2 K-1

  13. TROPICS POLAR REGION BMHT(TA3,T-TA3,P)/3 BMHT(TA2,T-TA2,P)/3 BMHT(TA1,T-TA1,P)/3 Linearized Meridional Heat Transport • Diffusive in each atmospheric layer: MHT = BMHT ( [ T’A,Tropics] - [ T’A, Polar] ) (brackets = column mean) • BMHT = 3.4Wm-2K-1 (found by fitting obs)

  14. Motivation For Diffusive Heat Transport Monthly atmospheric heat transport into polar region vs. polar – tropics atmospheric temperature difference Similar results hold for pre-industrial climate, 4xPI CO2 and the LGM

  15. Annual mean polar region energy balance • Assume no vertical temperature structure • Global mean energy balance requires: OLR’ = 0 or TT = - TP = -ΔT ASR’ ΔT OLR’ -ΔT MHT’ TROPICS POLAR So, MHT = BMHT2ΔT andOLR’ = BOLRΔT Hence, MHT / OLR = 2BMHT/BOLR = 2.3 [Observed ratio is 2.6 (including ocean heat transport)]

  16. Seasonal energetics with 24 meter slab ocean

  17. What to compare the EBM to? • Real world is complicated by land-ocean contrast (later) • We compare our simple model runs to an aquaplanet slab ocean GCM • GFDL version 2.1 • Ensemble with different slab ocean depths of 2.4, 6.0, 12.0, 24.0 and 50 meters • Average the output equatorward and poleward of 300

  18. Seasonal energetics with 24 meter slab ocean EBM Aquaplanet GCM

  19. Seasonal amplitudes vs. slab ocean depth Asterisk = Aquaplanet GCM results Solid Line = EBM Seasonal Amplitude of Temperature Seasonal Amplitude of Energy Flux These sum, in quadrature, to ASR Slab Ocean Depth (m)

  20. Seasonal amplitudes vs. slab ocean depth Why is the seasonal amplitude of atmospheric temperature nearly equal to that of surface temperature? What controls the quantity of energy that gets stored in the ocean vs. what gets fluxed to the atmosphere? What controls the partitioning of the seasonal amplitude of MHT, OLR and CTEN? Seasonal Amplitude of Temperature Seasonal Amplitude of Energy Flux Slab Ocean Depth (m)

  21. i) Why is the seasonal amplitude of atmospheric temperature nearly equal to that of surface temperature? Asterisk = Aquaplanet GCM results Solid Line = EBM Step I : If we put energy into the atmosphere, negative feedbacks go to work: As a result, the atmosphere come to equilibrium on a time scale much shorter than the seasonal cycle

  22. i) Why is the seasonal amplitude of atmospheric temperature nearly equal to that of surface temperature? Step II : We can account for the (small) quantity of energy stored by the atmosphere by: Assume the temperature variations are annual, then the tendency of energy associated with annual cycle of atmospheric temperature is:

  23. LH LW↑ SENS CTEN MHT LW SENS i) Why is the seasonal amplitude of atmospheric temperature nearly equal to that of surface temperature? Step III: The atmosphere is nearly in equilibrium at all times Equating the input and output • The near equivalence in the seasonal amplitude of atmosphere and surface temperatures is a consequence of model parameters – our choices capture the GCM behavior

  24. Implications The component of the climate system that is the least efficient in exporting energy undergoes the largest seasonal temperature change Example: What the atmosphere gets more efficient at exporting energy (ie, double BMHT)? Our equation predicts:

  25. Repeat, but reduce BMHT by half =0.85 The atmosphere must undergo a larger seasonal cycle to export a similar quantity of heat

  26. Revisiting BOLR The general linearized expression for OLR: OLR’ = BOLR,S T’S+ [BOLR,A] [TA]’ OLR’ = BOLR [TA]’ , where BOLR == K BOLR,S + [BOLR,A] and [BOLR,A] 1.8 Wm-2 K-1 Note: 1/BOLR is the climate sensitivity when K =1. [TA]’ BOLR,S 0.8 Wm-2 K-1 TS’

  27. ii) What controls the quantity of energy that gets stored in the ocean vs. what gets fluxed to the atmosphere? Concept: • The seasonal variations in absorbed solar radiation go directly into the ocean layer • Energy only gets fluxed to the atmosphere after the ocean surface heats up • The energy fluxed to the atmosphere is used to drive seasonal changes in MHT, OLR and CTEN

  28. ii) What controls the quantity of energy that gets stored in the ocean vs. what gets fluxed to the atmosphere? Step I: The seasonal amplitude of ocean energy fluctuations = 33 W/(m2 K ) for a 40 meter deep ocean So the seasonal amplitude of energy stored in ocean = BOClTSl Step II : The energy fluxed to the atmosphere is the sum of the seasonal variations in MHT, OLR, and CTEN (BMHT+BOLR+BCTEN) lTAl These add in quadrature to equal the seasonal amplitude of ASR (BMHT+BOLR+BCTEN)2 lTAl2 + BOC2lTAl2κ2 = lASR’l2

  29. What controls the quantity of energy that gets stored in the ocean vs. what gets fluxed to the atmosphere? • Given κ and B coefficients, we can figure out lTAl and lTSl • Therefore, we can determine the amount of seasonal solar • energy that is stored in the ocean vs. the seasonal energy • that is fluxed into the atmosphere Dashed lines are the result of these equations Solid lines = EBM * = AGCM + slab

  30. iii) What controls the petitioning of the seasonal amplitude of MHT, OLR and CTEN? Assuming tropical temperature doesn’t vary much seasonally, the seasonal cycle of atmospheric heat transport, OLR and atmospheric energy tendency will scale as BMHT : BOLR : BCTEN = 3.4 : 2.6 : 2.0

  31. At shallow slab ocean depths, the seasonal amplitude exceeds the annual mean The annual mean MHT from the EBM is 5.5 PW For ocean depths shallower than about 12 meters, our model predicts that the equator to pole temperature gradient and heat transport changes sign seasonally!

  32. The pole to equator solar insolation gradient does change signs seasonally Could the temperature gradient and MHT also changes signs? Or is it simply a property of the simple EBM?

  33. The surface temperature gradient does change signs in summer The ‘mid-latitude jet is Easterly Baroclinic eddies transport heat out of the northern polar region Aquaplanet GCM simulation6m slab ocean; JULY SURFACE TEMPERATURE K 300 hPa Zonal Velocity m/s

  34. 3) Land Ocean Contrast and Seasonal Energy Fluxes - OBSERVATIONS Zonal Anomaly over Land ASR = Absorbed solar SHF = Surface heat flux (-)OLR = Outgoing longwave MHT = Meridional heat transp. CTEN = (-) Atmos column tendency ZHT = Zonal heat transport Zonal Anomaly over Ocean

  35. NH January energy flux schematic- OBSERVATIONS Zonal averaged energy flux balance (annual mean removed) LAND & OCEAN sub-domains (zonal average removed) LAND OCEAN 13.9 PW 3.0 PW 0.4 PW 0.4 PW 0.3 PW 0.3 PW 0.1 PW 4.3 PW 0.1 PW 2.3 PW 0.2 PW 4.3 PW 4.3 PW 8.4 PW ocean WE ASSUME MHT IS ZONALLY INVARIANT ASR (-) OLR CTEN MHT SHF Zonal Heat Transport (ZHT)

  36. Model the observed climate system • Specify land fractions of 0.5,0.25, and 0.10 in the NH polar region, tropics, and SH polar region • Ocean mixed layer depth fixed at 60 meters • Ocean and land both influence each other in the NH, Land can barely influence the ocean in the SH N FO,L= Land, Ocean Fraction BZHT /FO,L= 20Wm-2 K-1 in NH BMHT = 3.4 Wm-2 K-1 ZHT is “FAST”

  37. How does the land/ocean contrast influence the energy transport in the polar domains? Solid = Observations (ERBE/NCEP) Dashed = 6-box “control” EBM All terms are anomalies from the global annual mean

  38. The energy Balance in the land and ocean subdomains Solid = observations Dashed = EBM All terms are local seasonal anomalies in W/m2

  39. How do the energy fluxes and climatology respond to changes in land fraction in the polar region? • Take an ensemble of EBM runs with different polar land fractions (equal in both hemispheres) More seasonal variations Of temp/OLR/MHT/CTEN More Seasonal Energy fluxed to atmos More Land

  40. Seasonal amplitude of surface and atmospheric temperature • Over Land: the seasonal amplitude of surface temperature exceeds that of atmospheric temperature • vice versa over the ocean Polar Land Fraction

  41. If we had isolated ocean and land domains 1.3 TA’ = 20K TA’ = 5K TS’ = 5K TS’ = 26K Ocean Land

  42. If we remove the barrier between the ocean and land Κ goes up Κ goes down TA’ = 20K 15K TA’ = 5K 10K TS’ = 5K 6K TS’ = 26K 24K Ocean Land

  43. 4. Conclusions • In the annual mean, the polar region deficit in solar radiation is balanced by MHT and OLR in approximate ratio of 2.5 : 1 • This ratio can be understood in terms of the relative BMHT and BOLR coefficients • The seasonal cycle of ASR in the polar region is primarily balanced by ocean heat storage; MHT, OLR, and CTEN play a decreasingly important role in the seasonal energy balance • The relative importance of each of these process can be understood in terms of the relative magnitudes of BOC, BMHT, BOLR, and BCTEN

  44. 4. Conclusions (cont) • In the zonal mean, as the polar region land fraction increases, more seasonal energy is supplied to the atmosphere and the seasonal amplitude of temperature, MHT, and OLR increase • The small land surface heat capacity causes ASR to be balanced by ZHT to the ocean domain where the energy is transferred into the surface ocean

  45. Mid-summer (both hemispheres) ASR’ +SHF= Seasonal Energy supplied to the atmosphere W/m2 • If we stopped the atmospheric circulation – the atmosphere over • the high latitude ocean would cool in the middle of the summer • Energy that is transported by the atmosphere (meridionally and • zonally) goes (primarily) into seasonal storage in the polar ocean • This buffers the climate system’s seasonal cycle of temperature

  46. Seasonal amplitude of surface and atmospheric temperature • Over Land: the seasonal amplitude of surface temperature exceeds that of atmospheric temperature • vice versa over the ocean • WHY? • More seasonal energy enters the atmosphere over land leading to a larger of seasonal amplitude of temperature there (compared to the ocean) • Aloft, energy is fluxed zonally away from the land and to the ocean in the warm season • Vice versa in the cold season • Thus, zonal transport reduces the seasonal cycle of air temperature over land and enhances it over ocean Polar Land Fraction

  47. Add land and ocean subdomains to the 3 box EBM BZHT= 10 W/(m2 K) • The heat transport between the ocean and land domain is diffusive in each atmospheric layer: Fo,L= Land or Ocean Fraction Effective BZHT for NH is 20 W/(m2 K) POLAR REGION OCEAN LAND BZHT(TA3,O-TA3,L)/3 BZHT(TA2,O-TA2,L)/3 LH is turned off over land BZHT(TA1,O-TA1,L)/3

  48. How to incorporate zonal heat transport into the EBM • In the observed monthly data, the heat transport divergence associated with land/ocean advection (at each latitude) scales linearly with atmospheric temperature contrast between the land and ocean • The slope in the NH mid-latitude is 20 W/(m2 K) • We speculate that the offset between the fits at different latitudes is due to water vapor transport (Fasullo and Trenberth, 2008)

  49. LH LW↑ SENS CTEN MHT LW SENS Seasonal amplitude of surface and atmospheric temperature • Review: In aquaplanet mode, lTS’l/ l[TA’]l is dictated by: energy in = energy out ENERGY INTO ATMOS If we enhance the efficiency of atmospheric heat export – the surface temp. undergoes larger seasonal Variations than the atmos/ ENERGY EXPORTED BY ATMOS DOUBLE BMHT Experiment

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