Seasonal Cycle of Global Energy Balance Aprilish, 2009

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)

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

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

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

JANAPRIL JULY OCTOBER ALBEDO MAPS

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

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

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

What balances the global mean radiation seasonal cycle?

Seasonality of Zonal Mean Radiation

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!!!

NH Heat Trans by Radiation Only

SH Heat Trans by Radiation Only

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

Seasonality of Zonal mean Tendency and Surface Fluxes

NH HEAT trans ALL TERMS

SH HEAT trans ALL TERMS

Dynamics Partitioning

NH Partitioning at latitude of max

Transient HT mean map W/m

Stationary HT mean map W/m

Pattern of Seasonal TE Annomaly- NH W/m std

Pattern of Seasonal SE Annomaly- NH W/m std

SH Partitioning at latitude of max

Pattern of Seasonal TE Annomaly- SH W/m std

Dynamics + Radiation

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

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

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

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

Do the same deal with the seasonal cycle

Seasonal Cycle max heat trans

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

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

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)

Emissivity, from Czaja script

Jan OLR – observed and simulated

Erbe is from residual- radiative is Czaja

Atmospheric Heat Flux (Radiative)

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

Need to add atmospheric column tendency