1. Seasonal Cycle of Global Energy Balance Aprilish, 2009

2. The seasonal cycle of energy imbalance is of order the total heat transport in the climate system- it largely reflects changes in ASR, re-inforced by OLR (Identical to Trenberth Results)

3. Break down the Solar Absorbed solar anomalies driven by precession- Changes in reflected solar primarily reflect the incoming solar (fixed albedo) though slightly more complicated

4. Alternative Break Down Albedo is area and insolation weighted The solar insolation dominates the signal and the albedo changes have a complicated seasonal pattern that generally counters the insolation

5. Understanding Solar Area weighted Albedo Break SW into annual mean and anomaly at each location Same for albedo Break the [albedo] into four terms Mean (SW) and mean(ALB) Mean(SW) and anomaly ALB [fixed sw] = part due to seasonally changing albedo Mean(ALB) and anomaly SW [ fixed albedo] = part due where the insolation weights the albedo Anomaly ALB and anomaly SW [Covariance] because local albedo changes and weighting are anti-correlate – projects onto the mean (this part isn’t plotted) Also- in all calculations the seasonal cycle of global mean insolation is removed by normalizing the spatial pattern of insolation to the annual mean value

7. JANAPRIL JULY OCTOBER ALBEDO MAPS

8. FIXED SW Peaks in Jan. when Siberia is snowy Also peaks in July when SH sea ice extent is large Minnimum in April when Siberia has melted and neither hemisphere has much sea ice Also minnimum in September when Arctic sea ice is low There is a hemispheric asymmetry because the NH albedo changes are larger in magnitude and aerial extent

9. FIXED ALBEDO Spatial pattern of annual mean albedo is high in the high latitudes and low in the tropics The solstices weight the high latitudes and thus the solar area weighted is high at solstice The equinoxes weight the tropics and the global albedo is low at equinix Many of these effects are compensated by the co-variance, since the areas of low albedo realize there seasonal maxima when the sun shines on them, and thus these effects aren’t realized

10. Combine the terms where the SW changes seasonally (fixed albedo +covar)

11. What balances the global mean radiation seasonal cycle?

12. Seasonality of Zonal Mean Radiation

13. Defining Contribution to Heat Transport Define 3 domains that are seasonally invariant: 1.Arctic Cap- poleward of 36N 2.Antaractic Cap- poleward of 36S 3.Tropics- 36S to 36S In the annual mean, the tropics receive more solar radiation than the caps, if no other processes were at play, the heat transport would have to the cap’s deficit of ASR relative to the global mean ASR: this defines the Solar contribution to heat transport Similarly, the caps have a deficit of OLR relative to the global mean OLR- this diminishes the heat transport because the caps are losing less energy than the tropics Globally, annually OLR =ASR. This isn’t true seasonally. All domain deficits are defined relative to the seasonal mean of OLR and ASR. Some of these decisions are arbitrary- I’m not sure these are the best practices!!!

14. NH Heat Trans by Radiation Only

15. SH Heat Trans by Radiation Only

16. Add the tendency and surface fluxes to the heat transport If we define Δ as the integral over the tropics – the integral over the caps In equiblibruim 2*HT max = ΔASR – ΔOLR For a developing system with surface heat fluxes 2*HT max = ΔASR – ΔOLR + ΔFS – ΔTENDENCY We can calculate the latter two terms over the polar caps in the same manner as the radiation We use a seasonally invariant domain cutoff of 36N/S All integrations are for anomalies relative to the globally averaged mean at that time

17. Seasonality of Zonal mean Tendency and Surface Fluxes

18. NH HEAT trans ALL TERMS

19. SH HEAT trans ALL TERMS

20. Dynamics Partitioning

21. NH Partitioning at latitude of max

22. Transient HT mean map W/m

23. Stationary HT mean map W/m

24. Pattern of Seasonal TE Annomaly- NH W/m std

25. Pattern of Seasonal SE Annomaly- NH W/m std

26. SH Partitioning at latitude of max

27. Pattern of Seasonal TE Annomaly- SH W/m std

28. Dynamics + Radiation

29. Seasonal EBM Expand the temperature and heat transport in a set of legendre fourier modes. Each Legendre polynomial has unit spatially weighted variance

30. Fourier Legendre modes WN 2 annual mean and WN 1 annual cycle are the whole story

31. Fit annual mean heat transport divergence to temperature diffussion If perfect A T,N * D *(n*(n+1))/a^2=A HTD, N Where A are the annual mean legendre coefficients

32. Reconstruct the annual mean heat transport using these Ds Using D from the second mode only ain’t bad D/a^2 =.97

33. Do the same deal with the seasonal cycle

34. Seasonal Cycle max heat trans

35. Repeat using the w#1(annual cycle) and w#2 (annual mean)

37. CC’s seasonal EBM Calculated as D grad T over ocean and land separately (is this right?)

38. Surface heat flux Calculate emissivity from Czaja’s script. Function of h20 and co2. H20 from 750 mb temp and RH If ocean: FS= solar – sig Ts^4 + emis * sig Ta^4 FA= emiss ( sig Ts^4 - 2 sig Ta^4) If land FA= solar – sig Ts^4 (1-emiss) – 2 emis sig Ta^4 TOA OLR = sig Ts^4(1-emis) + sig emis (Ta^4)

39. Emissivity, from Czaja script

40. Jan OLR – observed and simulated

41. Erbe is from residual- radiative is Czaja

42. Atmospheric Heat Flux (Radiative)

43. Heat trans from atmospheric radiation (last slide)- neglect tendency Polar area is required heat transport

44. Need to add atmospheric column tendency