Seeking a consistent view of energy and water flows through the climate system

Seeking a consistent view of energy and water flows through the climate system Robert Pincus University of Colorado and NOAA/Earth System Research Lab

Atmospheric Energy Balance [Wm -2 ] 340.1±0.1 97-101 237-241 ~22 (atmospheric window) 23-30 71-82 (absorbed solar) 161-168 17-21 78-88 337-348 395-399

Incoming solar 340..1 Atmospheric absorption 7 Reflected solar Shortwave t 47 100. Sensible heating All-sk y atmospheric window TO A imbalance 0 Latent heating Clear-sk y emission 266. 3 26.7 Longwave 239.7.3 t Outgoing longwave radiation All-s ky longwave absorption -187. 2 Clear-sky refection 27. 6 Surface shortwave absorption Surface reflection Surface emission 9 Clear-sky emission to surface All-s ky emission to surface Surface imbalance 0

Syntheses satisfy large-scale constraints TOA energy balance to within ocean heat storage Surface energy balance ditto Surface water balance Satisfying these constraints requires creativity because individual best estimates don t satisfy balance constraints

Global Surface Energy Budget R n (SW) + R d (LW) R u (LW) S LE = N Wm -2 R n (SW) R u (LW) R d (LW) R n S LE S + LE KT97 168 390 324 102 24 78 102 TFK09 161 396 333 98 17 80 97 ISCCP FD 165 396 345 114 SRB 166 397 343 112 CERES EBAF-SFC 163 398 345 110 Stephens et al (2012) 165 398 346 113 24 88 112 ERA-I 164 398 342 108 18 84 102 MERRA 169 394 330 105 18 76 94 Radiation datasets suggests net surface radiation (R n ) is 12-16 Wm -2 larger than TFK09, which determines R n as residual of S + LE + N, where S is determined from reanalysis, LE is inferred from global precipitation (LP=LE), and N is energy imbalance (~0.9 Wm -2 in KTF09). Can we explain the difference? Is S+LE too low? R n too high? What are the uncertainties? Do the difference impact our ability to track year-to-year and longerterm changes in surface energy budget?

An unconstrained view of the energy budget isn t balanced Work in progress by Tristan L Ecuyer (U. Wisconsin)

Syntheses satisfy large-scale constraints TOA energy balance to within ocean heat storage Surface energy balance ditto Surface water balance Satisfying these constraints requires creativity because individual best estimates don t satisfy balance constraints In practice, large-scale fluxes are determined by using satellite observations to infer flux validating against sparse point measurements

CERES is our most direct estimate of TOA flux, but still requires models for spectral corrections directional corrections temporal corrections Original CERES estimates were out of balance by 6.5 3 W/m 2

How CERES achieves top-of-atmosphere energy balance Identify error sources and uncertainty! Assume Gaussian, unbiased errors P (F F obs,r obs )=e (F F obs) T S 1 obs (F F obs) e R R obs 2 R Adjust each error source as little as possible relative to its uncertainty to achieve balance within its uncertainty, i.e. minimize J =(F F obs ) T S 1 obs (F F obs)+ R R obs 2 R

1FEBRUARY 2009 L O E B E T A L. 755 TABLE 3. Net flux sensitivity (a i ), standard deviation of error (s i ), maximum likelihood error (x i ), and error effect on net TOA flux. Parameter Net TOA flux sensitivity, a i (W m 22 % 21 ) 2s uncertainty, d i (%) Maximum likelihood solution, x i (%) TOA flux adjustment (W m 22 ) SW gain 20.977 2.0 1.6 1.57 LW gain 22.37 1.0 0.972 2.3 Unfiltered SW 20.977 0.5 0.105 0.1 Unfiltered LW (N) 21.19 0.2 0.022 0.03 Unfiltered LW (D) 21.19 0.38 0.07 0.08 SW radiance to flux 20.977 0.20 0.017 0.02 LW radiance to flux 22.37 0.13 0.016 0.04 Time-averaging SW 20.977 0.30 0.038 0.04 Time-averaging LW 22.37 0.13 0.016 0.04 Reference level, SW 20.977 0.10 0.004 0.00 Reference level, LW 22.37 0.08 0.007 0.02 Incoming solar 3.40 0.06 20.005 20.02 Total SW 1.7 Total LW 2.5 Total net 24.2 a. Constrainment algorithm The global average net TOA flux is expressed as follows: Let a i 5 R N p i denote the partial derivatives of global mean net flux with respect to each parameter p i, and represent x i and a i as vectors x and a, so that Eq. (4) may be written as R N 5 E o ðf SW 1 F LW Þ; ð1þ a t x 5 e RN : ð5þ where E o is the annual mean solar insolation at the TOA averaged over the globe and F SW and F LW are the global average SW and LW TOA fluxes. If the earth were in radiative balance for the annual mean, R N would be zero. However, given a warming trend, there is a net imbalance because of heat storage within the We have one equation with N unknowns, where N is the number of parameters to adjust. The criterion for selecting these parameters is to choose the most likely set of parameters x i that satisfy Eq. (5) using a maximum likelihood estimate for the x i. The following assumptions are made: (i) x i has mean 0 for all i; (ii) all x i s

Surface radiation from CERES (and others) Surface radiation budget relies on radiative transfer models applied to profiles of clouds, aerosols, atmospheric state Properties are retrieved independently of CERES top-ofatmosphere fluxes; modeled fluxes using these properties may not reproduce top-of-atmosphere fluxes Adjust atmospheric properties as little as possible relative to uncertainty to match observed fluxes to within uncertainty

013 K A T O E T A L. 2731 TABLE 4. Global annual mean irradiances in W m 22 computed using data from March 2000 through February 2010. Irradiance component Ed 2 SYN1deg- Month Surface EBAF Ed2.6r EBAF Ed2.6r TOA Incoming solar 340 340 340 LW (all-sky) 237 240 240 SW (all-sky) 99 100 100 Net (all-sly) 4.1 0.6 0.6 LW (clear-sky) 264 266 266 SW (clear-sky) 53 53 53 Net (clear-sly) 24 22 22 Surface LW down (all-sky) 342 344 LW up (all-sky) 398 398 SW down (all-sky) 187 187 SW up (all-sky) 23 24 Net (all-sky) 108 108 LW down (clear-sky) 314 314 LW up (clear-sky) 397 398 SW down (clear-sky) 242 243 SW up (clear-sky) 29 30 Net (clear-sky) 131 130. Histogram of monthly mean downward (top) longwave tom) shortwave irradiance difference; 24 buoy observam 2001 through 2007 are used. The red line is for EBAFnd black line is for SRB surface irradiance (Stackhouse 1). Numbers shown in the figure are in W m 22 except for is the number of monthly observations. Note that biases Clear-sky irradiances are derived by weighted clear-sky fraction. irradiances; Approximately 5%, 12%, and 2% of 18318 grid surface downward shortwave, upward shortwave, and upward longwave adjustments, respectively, exceed

An unconstrained view of the energy budget isn t balanced Work in progress by Tristan L Ecuyer (U. Wisconsin)

Would consistency help? (i - a priori) The GEWEX integrated product does indeed start out by assuming that we can all use the same ancillary data. This includes issues like the same land/ocean mask, the same sea ice and the same vegetation class. Trickier is the same aerosols, and then the same temperature and humidity profiles. Temperature and humidity matter quite a bit for all the radiation as well as the turbulent fluxes. What we ran into is that while we agreed to use the new HIRS product for temperature and humidity, the near surface quantities seemed to introduce artifacts into SeaFLux and LandFlux The decision was let each product continue to diverge from the integrated assumption if they felt that the integrated assumptions were making the product worse. Email from Chris Kummerow (GEWEX data panel), Mar 2014

Would consistency help (ii - a posteriori) (More from work in progress by Tristan L Ecuyer) Assess mean and uncertainty in components of surface energy and water budgets on continental/basin scale Assume Gaussian, unbiased errors in flux components Adjust each component as little as possible relative to its uncertainty to achieve balance within its uncertainty

Work in progress by Tristan L Ecuyer (U. Wisconsin)

So I think this grand challenge will be with us for quite a while. The silver lining is that the precip and radiation datasets appear to be fairly stable (bias is fairly constant with time), which means they might provide some useful information for monitoring changes in the various components of the energy budget. All bets are off if there are huge swings in the heavy precipitation range Email from Norman Loeb, Mar 2014

Errors are strongly conditioned, not random This restricts our ability to stratify (even assuming understand our observations well) How can we best build a self-consistent view of energy and water flows through the climate system? Can reanalyses be revisited? How can we diagnose the limits of such a view?