Energy conservation in NorESM on Olivia

[adagj]

This is the net budget for area, heat and water after one year on Olivia for run #362

(med_diag_print_summary) NET AREA BUDGET (m2/m2): period =   annual: date =   8120101     0
                           atm            lnd            ocn         ice nh         ice sh        *SUM*
    area            -1.00000000     0.29352499     0.65881147     0.02220025     0.02546299    -0.00000031

(med_diag_print_summary) NET HEAT BUDGET (W/m2): period =   annual: date =   8120101     0
                           atm            lnd            rof            ocn         ice nh         ice sh            glc        *SUM*
    hfreeze          0.00000000     0.00000000     0.00000000     0.03710923    -0.00909098    -0.02801825     0.00000000     0.00000000
    hmelt            0.00000000     0.00000000     0.00000000    -0.94746453     0.32079840     0.62666613     0.00000000    -0.00000000
    hnetsw        -165.57586866    42.13590079     0.00000000   122.30108191     0.57687527     0.57030548     0.00000000     0.00829479
    hlwdn         -338.17610603    87.41737186     0.00000000   240.68916503     4.53962995     5.52696488     0.00000000    -0.00297432
    hlwup          396.26616042  -108.17274103     0.00000000  -276.30537555    -5.33578866    -6.45105025     0.00000000     0.00120493
    hlatvap         86.90536939   -12.25634777     0.00000000   -74.47445471    -0.04848356    -0.12630849     0.00000000    -0.00022513
    hlatfus          0.83825626    -0.28496725     0.00000000    -0.36863560    -0.04607539    -0.13848155     0.00000000     0.00009648
    hiroff           0.00000000     0.04382105     0.00000000    -0.04381896     0.00000000     0.00000000     0.00000000     0.00000210
    hsen            20.02401310    -8.92259470     0.00000000   -11.11877474    -0.02199366     0.03870308     0.00000000    -0.00064691
           *SUM*     0.28182449    -0.03955704     0.00000000    -0.23116792    -0.02412862     0.01878103     0.00000000     0.00575194

(med_diag_print_summary) NET WATER BUDGET (kg/m2s*1e6): period =   annual: date =   8120101     0
                           atm            lnd            rof            ocn         ice nh         ice sh            glc        *SUM*
    wfreeze          0.00000000     0.00000000     0.00000000    -0.09838630     0.02410256     0.07428373     0.00000000    -0.00000000
    wmelt            0.00000000     0.00000000     0.00000000     0.61102773    -0.10739568    -0.50363205     0.00000000     0.00000000
    wrain          -32.24678467     7.16118721     0.00000000    25.01751225     0.03795841     0.02828667     0.00000000    -0.00184013
    wsnow           -2.51200558     0.85396239     0.00000000     1.10469163     0.13807429     0.41498816     0.00000000    -0.00028911
    wevap           34.73316541    -4.89375879     0.00000000   -29.77787074    -0.01715616    -0.04447059     0.00000000    -0.00009087
    weqsaltf         0.00000000     0.00000000     0.00000000    -0.00474144    -0.00578953     0.01053097     0.00000000     0.00000000
    wrunoff          0.00000000    -2.94560431     0.00687450     2.93781925     0.00000000     0.00000000     0.00000000    -0.00091055
    wfrzrof          0.00000000    -0.13131871    -0.00000000     0.13131242     0.00000000     0.00000000     0.00000000    -0.00000629
           *SUM*    -0.02562484     0.04446779     0.00687450    -0.07863518     0.06979388    -0.02001310     0.00000000    -0.00313695

And this is for the last 5 years (861 - 866):

(med_diag_print_summary) NET AREA BUDGET (m2/m2): period = all_time: date =   8660101     0
                           atm            lnd            ocn         ice nh         ice sh        *SUM*
    area            -1.00000000     0.29352499     0.65725740     0.02144297     0.02777433    -0.00000031

(med_diag_print_summary) NET HEAT BUDGET (W/m2): period = all_time: date =   8660101     0
                           atm            lnd            rof            ocn         ice nh         ice sh            glc        *SUM*
    hfreeze          0.00000000     0.00000000     0.00000000     0.03835028    -0.00924303    -0.02910725     0.00000000     0.00000000
    hmelt            0.00000000     0.00000000     0.00000000    -0.94317788     0.31058791     0.63258996     0.00000000     0.00000000
    hnetsw        -165.68601318    42.16206684     0.00000000   122.30100769     0.57760319     0.64847346     0.00000000     0.00313799
    hlwdn         -337.15800651    87.10799688     0.00000000   239.63924853     4.41270226     5.99765962     0.00000000    -0.00039922
    hlwup          395.43476496  -107.88598339     0.00000000  -275.35134895    -5.17722678    -7.02019296     0.00000000     0.00001287
    hlatvap         86.50293663   -12.19480171     0.00000000   -74.11102728    -0.04815579    -0.14921297     0.00000000    -0.00026113
    hlatfus          0.86054179    -0.28570464     0.00000000    -0.37417404    -0.04422838    -0.15641585     0.00000000     0.00001888
    hiroff           0.00000000     0.04191983    -0.00000000    -0.05131600     0.00000000     0.00000000     0.00939505    -0.00000112
    hsen            20.10790756    -8.95400973     0.00000000   -11.18922689    -0.02613896     0.06078312     0.00000000    -0.00068490
           *SUM*     0.06213124    -0.00851592    -0.00000000    -0.04166453    -0.00409959    -0.01542287     0.00939505     0.00182338

(med_diag_print_summary) NET WATER BUDGET (kg/m2s*1e6): period = all_time: date =   8660101     0
                           atm            lnd            rof            ocn         ice nh         ice sh            glc        *SUM*
    wfreeze          0.00000000     0.00000000     0.00000000    -0.10167664     0.02450570     0.07717094     0.00000000    -0.00000000
    wmelt            0.00000000     0.00000000     0.00000000     0.61391295    -0.15841537    -0.45549758     0.00000000    -0.00000000
    wrain          -31.99027503     7.00135210     0.00000000    24.92207729     0.03969311     0.02707622     0.00000000    -0.00007632
    wsnow           -2.57878871     0.85617214     0.00000000     1.12128869     0.13253933     0.46873196     0.00000000    -0.00005659
    wevap           34.57104551    -4.86896119     0.00000000   -29.63255789    -0.01706207    -0.05256868     0.00000000    -0.00010432
    weqsaltf         0.00000000     0.00000000     0.00000000    -0.00185111     0.00035764     0.00149346     0.00000000     0.00000000
    wrunoff          0.00000000    -2.82542981     0.00016423     2.82526177     0.00000000     0.00000000     0.00000000    -0.00000380
    wfrzrof          0.00000000    -0.12562132     0.00000000     0.15377884     0.00000000     0.00000000    -0.02815418     0.00000335
           *SUM*     0.00198176     0.03751192     0.00016423    -0.09976609     0.02161835     0.06640632    -0.02815418    -0.00023768

If we compare the budgets to #338 which is the same experiment, but run on Betsy, the numers are very similar

For year 811

(med_diag_print_summary) NET AREA BUDGET (m2/m2): period =   annual: date =   8110101     0
                           atm            lnd            ocn         ice nh         ice sh        *SUM*
    area            -1.00000000     0.29352499     0.65968789     0.02220664     0.02458017    -0.00000031

(med_diag_print_summary) NET HEAT BUDGET (W/m2): period =   annual: date =   8110101     0
                           atm            lnd            rof            ocn         ice nh         ice sh            glc        *SUM*
    hfreeze          0.00000000     0.00000000     0.00000000     0.03758384    -0.00951291    -0.02807093     0.00000000     0.00000000
    hmelt            0.00000000     0.00000000     0.00000000    -0.89488902     0.30403961     0.59084941     0.00000000    -0.00000000
    hnetsw        -166.21670180    42.14945687     0.00000000   122.93309549     0.58009889     0.55685977     0.00000000     0.00280921
    hlwdn         -338.67992660    87.55191544     0.00000000   241.19771419     4.59707348     5.33276630     0.00000000    -0.00045719
    hlwup          396.77465436  -108.14924816     0.00000000  -277.01086834    -5.36564798    -6.24887133     0.00000000     0.00001855
    hlatvap         87.20110253   -12.41919279     0.00000000   -74.60404617    -0.04530084    -0.13281127     0.00000000    -0.00024854
    hlatfus          0.83045474    -0.28531403     0.00000000    -0.35621319    -0.04742309    -0.14150581     0.00000000    -0.00000137
    hiroff           0.00000000     0.04391239    -0.00000000    -0.05214201     0.00000000     0.00000000     0.00823152     0.00000190
    hsen            19.97813238    -8.89839810     0.00000000   -11.11741575    -0.02026117     0.05728716     0.00000000    -0.00065549
           *SUM*    -0.11228440    -0.00686838    -0.00000000     0.13281903    -0.00693400    -0.01349670     0.00823152     0.00146707

(med_diag_print_summary) NET WATER BUDGET (kg/m2s*1e6): period =   annual: date =   8110101     0
                           atm            lnd            rof            ocn         ice nh         ice sh            glc        *SUM*
    wfreeze          0.00000000     0.00000000     0.00000000    -0.09964462     0.02522123     0.07442339     0.00000000    -0.00000000
    wmelt            0.00000000     0.00000000     0.00000000     0.54829102    -0.13684993    -0.41144109     0.00000000    -0.00000000
    wrain          -32.34157894     7.06096468     0.00000000    25.22014986     0.03818797     0.02226989     0.00000000    -0.00000654
    wsnow           -2.48862672     0.85500157     0.00000000     1.06746535     0.14211294     0.42405097     0.00000000     0.00000412
    wevap           34.85072135    -4.95820603     0.00000000   -29.82968660    -0.01615764    -0.04677058     0.00000000    -0.00009950
    weqsaltf         0.00000000     0.00000000     0.00000000     0.00014479    -0.00195877     0.00181398     0.00000000     0.00000000
    wrunoff          0.00000000    -2.77731827    -0.00206339     2.77940274     0.00000000     0.00000000     0.00000000     0.00002108
    wfrzrof          0.00000000    -0.13159243     0.00000000     0.15625416     0.00000000     0.00000000    -0.02466741    -0.00000568
           *SUM*     0.02051569     0.04884952    -0.00206339    -0.15762329     0.05055581     0.06434655    -0.02466741    -0.00008652

For the last 5 years

(med_diag_print_summary) NET AREA BUDGET (m2/m2): period = all_time: date =   8110101     0
                           atm            lnd            ocn         ice nh         ice sh        *SUM*
    area            -1.00000000     0.29352499     0.65925019     0.02166487     0.02555965    -0.00000031

(med_diag_print_summary) NET HEAT BUDGET (W/m2): period = all_time: date =   8110101     0
                           atm            lnd            rof            ocn         ice nh         ice sh            glc        *SUM*
    hfreeze          0.00000000     0.00000000     0.00000000     0.03839486    -0.00937486    -0.02902000     0.00000000     0.00000000
    hmelt            0.00000000     0.00000000     0.00000000    -0.91210009     0.31511042     0.59698967     0.00000000    -0.00000000
    hnetsw        -166.07132568    42.07865210     0.00000000   122.85201586     0.56197660     0.58144747     0.00000000     0.00276635
    hlwdn         -337.75610176    87.26797081     0.00000000   240.51020047     4.44084035     5.53671446     0.00000000    -0.00037567
    hlwup          395.99089894  -107.90355677     0.00000000  -276.39029496    -5.21689671    -6.48014455     0.00000000     0.00000595
    hlatvap         86.92230850   -12.40983711     0.00000000   -74.32920362    -0.04961470    -0.13391297     0.00000000    -0.00025989
    hlatfus          0.85079598    -0.29167193     0.00000000    -0.36884306    -0.04475765    -0.14550804     0.00000000     0.00001529
    hiroff           0.00000000     0.04416849    -0.00000000    -0.05244644     0.00000000     0.00000000     0.00827782    -0.00000014
    hsen            19.91495979    -8.78840182     0.00000000   -11.15986575    -0.02486206     0.05748020     0.00000000    -0.00068964
           *SUM*    -0.14846424    -0.00267623    -0.00000000     0.18785727    -0.02757861    -0.01595376     0.00827782     0.00146226

(med_diag_print_summary) NET WATER BUDGET (kg/m2s*1e6): period = all_time: date =   8110101     0
                           atm            lnd            rof            ocn         ice nh         ice sh            glc        *SUM*
    wfreeze          0.00000000     0.00000000     0.00000000    -0.10179486     0.02485522     0.07693964     0.00000000    -0.00000000
    wmelt            0.00000000     0.00000000     0.00000000     0.50728971    -0.09188475    -0.41540496     0.00000000     0.00000000
    wrain          -32.18576696     7.17479484     0.00000000    24.94794921     0.03841307     0.02453874     0.00000000    -0.00007110
    wsnow           -2.54958339     0.87405434     0.00000000     1.10531334     0.13412542     0.43604446     0.00000000    -0.00004583
    wevap           34.73932880    -4.95484860     0.00000000   -29.71979353    -0.01762833    -0.04716219     0.00000000    -0.00010385
    weqsaltf         0.00000000     0.00000000     0.00000000     0.00677656    -0.00710455     0.00032799     0.00000000    -0.00000000
    wrunoff          0.00000000    -2.89504181     0.00003239     2.89501247     0.00000000     0.00000000     0.00000000     0.00000306
    wfrzrof          0.00000000    -0.13235987    -0.00000000     0.15716645     0.00000000     0.00000000    -0.02480617     0.00000042
           *SUM*     0.00397846     0.06659891     0.00003239    -0.20208064     0.08077607     0.07528368    -0.02480617    -0.00021730

[adagj]

@matsbn @oyvindseland @DirkOlivie

[oyvindseland]

Is the energy mismatch a lat-lon interpolated vs native SE issue?

[adagj]

At least these budgets are calculated online, on the native grid.

[oyvindseland]

calculated RESTOM for n1850.ne16pg3_tn14.noresm3_0_beta11.Run8.Olivia.2026-03-08 year 861-865 is -0.116 W m-2
I presume this can be compared to 0.06 W/m2 for the net heat budget sum? So a mismatch of close to 0.2 Wm-2 ?
--> We really need to be able to do diagnostics on the native grid

[adagj]

I don't think that is the correct way of doing it, because you are comparing net top of the atmosphere energy balance with the surface atmosphere energy balance. I think, if the concern is that the ocean is not responding as expected to the RESTOM, you should compare RESTOM with the net ocean surface balance which is -0.04166453 W/m2 (which shows that the ocean is loosing energy with a negative RESTOM) - so at least they have the same sign and behave as we expect. @matsbn @oyvindseland

[matsbn]

@oyvindseland, I think the positive atmospheric surface heat budget of 0.06 W m-2 you mention is heat flux into the atmosphere. Assuming no heat accumulation in the atmosphere it should be matched by a RESTOM of -0.06 W m-2 with the sign convention we use. So the sign at least seems correct, but the mismatch is still a bit worrying for 5 year averages.

The ocean surface heat budget of -0.04166453 W m-2 indicates heat lost by the ocean and by a quick calculation (possibly too quick :) this should give a cooling of about -0.013 K per hundred years.

[adagj]

I plotted the ocean volume temperature from Run8 on Betzy (#338) and on Olivia (#362), and I really don't find any suprising mismatch in #362. Maybe @oyvindseland and @matsbn can add some more clarifying numbers/figures? It seems like the ocean volume temperature in NorESM3 warms even with a slight negative radiative imbalance @ TOA - so that is potentially a mismatch - however the energy budgets from the logs which I have plotted in the figures below seem closed. Apparently the radiative imbalance @ TOA is larger when running Run8 on Olivia and hence the cooling... but please double check these numbers. I must say, given my calculations that £338 seems more "strange" than #362.

Here are figures of the heat budgets from the coupler and also including RESTOM, and a comparison between Run8 on Betzy #338 and Run8 on Olivia #362

For Run8 on Betzy the ocean component is loosing energy and RESTOM is negative, so although the magnitude is somewhat different, I think this is consistent with what we expect

For Run8 on Olivia, #362, RESTOM is negative, -0.1074 W/m2 averaged over the length of the simulation. And the ocean is loosing heat on average, but an order of magnitude less. The land is also loosing heat, although that is balanced by glacier.

If we look at the individual terms in BLOM, they seem pretty balanced to me, with a net negative mean of -0.015 W/m2

I also made some Hovmoller figures with anomalies from the start of the simulation

For Run8 on Betzy , RESTOM is also slightly negative, I find it to be -0.055 W/m2 averaged over the entire simulation (225 years). The Ocean mean is slightly positive, indicating that the ocean is gaining some heat.

Here we see the individual terms in BLOM, with a net positive mean of 0.032 W/m2

And the ocean warming

[DirkOlivie]

I have looked at simulation #362 (period 811-855) and #338 (period 586-810). I compared the warming in the ocean (end year minus begin year), and average TOA flux (over whole period). A negative TOA flux is a flux directed to space.

Issue	SImulation	Periond	mean TOA flux	Ocean temperature change between end and begin
#362	beta11.Run8.Olivia.2026-03-08	811-855	-0.086 W/m2	-0.005 K
#338	beta11.Run8.2026-02-07	586-810	-0.026 W/m2	0.018 K

The result for #338 is worrying : loosing heat at the TOA, but at the same time heating the ocean.

Based on these data points, one can derive that if the ocean temperature would be constant, we would still have an imbalance of -0.039 W/m2. I think we had a similar inconsistency in NorESM2 (on the order of 0.05 W/m2, but I don't remember the sign).

[adagj]

Thank you @DirkOlivie . Your results are in accordance with my results (so that is reassuring :) Would be good to fully understand this @matsbn

[TomasTorsvik]

I'm running a comparison of NorESM3 simulations based on the pre-beta12a branch pr-noresm3_0_beta12a with ne30pg3_tn14 grid and exact same input data

• n1850.ne30pg3_tn14.noresm3_0_beta12a-run1_yr001.20260313 #367
• n1850.ne30pg3_tn14.noresm3_0_beta12a-run1_yr001_olivia.20260313 #368

So far I have only 10 years from Betzy, 20 years from Olivia (Olivia throughput is significantly higher!). The runs are not BFB, as one would expect, and it is probably a bit too soon to conclude if the runs are climatologically equivalent based on the first 10 years. Plan to run 30 years and make new comparison plots.