Conservation of temperature and salinity in HADCM3

This page gives two sets of results for conservation of temperature and salinity in HADCM3.

AAXZD (a variant of HADCM3 having unmodified Indonesian throughflow) 2051-2052: Analysis of rates of change of T and S using the complete set of rate diagnostics.

AAXZC (HADCM3 control run) 2261-2271: Analysis of the ``scientific'' subset of rate diagnostics (i.e. omitting the small terms), and comparison with the global-average fluxes.

`AAXZD` (HADCM3 with unmodified Indonesian throughflow) 2051-2052

Job AATZH is parallel to AAXZD, and was run for a year from 1/12/2051 with the complete set of recommended diagnostics for rates of change of temperature and salinity (i.e. including the Mediterranean outflow and the filters). The output from the PV-WAVE routine check_hadcm3_rates is shown below. In summary,

The change in temperature over the year differs from the sum of the increments by 1e-3 K on average at the surface, and no more than 3e-2 K locally. At the bottom, the average error is 1e-6 K and the maximum local error 3e-4 K.
Overall, the ocean model conserves to 1e-5 W m-2 on the global average. This is the extent to which the input and output of heat balance the change in heat content. The inputs include the deliberate and diagnosed non-conservation of heat in the ocean-floor "heatsink", which is -0.028 W m-2 in this run, and is included in the ice processes term. The main input and output of heat is through the penetrative solar and non-penetrative surface flux terms, of course, which are seven orders of magnitude larger than the non-conservation, making it plausible that the latter is just the result of the inaccuracy of single-precision arithmetic. All the other terms simply move heat around and appear to conserve satisfactorily. The Robert filter is responsible for the largest error, of 1e-4 W m-2.
The change in salinity is matched by the increments within 2e-8 on average at the surface (2e-5 PSU) and 2e-4 locally (0.2 PSU). At the bottom the errors are 1e-10 on average and 1e-7 locally, so again rather small.
The overall non-conservation is equivalent to 0.2 mm of water per year at the surface falling on a 50 m thick layer of water. This is only four orders of magnitude smaller than the surface fluxes, revealing a significant inaccuracy. Probably this comes from the inland-seas fix, which definitely does not conserve. We do not currently have a diagnostic for this specifically, but the size is plausible. Of the diagnosed terms, the most serious non-conservation is again from the Robert filter.

The full listing is appended.

If you check the budgets with just the diagnostics recommended above for scientific purposes (i.e. excluding Mediterranean outflow, the Fourier and Robert filters) the global conservation should still be very accurate. Locally, however, there will be substantial discrepancies between the rates and the change in state in the regions affected by the Fourier filter (I found this to be O(1) K over three months) and the points involved in the Mediterranean mixing (0.2 K over three months).

Experiment AATZH from 2051/12/01 00:00 to 2052/12/01 00:00

Change in potential temperature/K
            Change over period                Discrepancy: rates-state       
lev     mean         max         min         mean         max         min    
  1 -1.27644e-02  7.7973e+00 -7.5985e+00 -9.45419e-04  2.9912e-02 -1.6457e-02
  2 -1.62700e-02  7.7941e+00 -7.5985e+00  3.85104e-04  1.9273e-02 -1.3623e-02
  3 -3.88619e-02  7.5059e+00 -7.5985e+00  1.82585e-04  5.2029e-02 -1.5874e-02
  4 -6.32856e-02  7.5059e+00 -6.4327e+00  7.29980e-05  4.8853e-02 -1.4132e-02
  5 -6.67340e-02  7.5059e+00 -6.9272e+00  4.45814e-05  1.7694e-02 -1.4361e-02
  6 -6.19640e-02  7.5059e+00 -6.4498e+00  1.91414e-05  5.0754e-02 -1.0500e-02
  7 -8.57262e-02  7.5156e+00 -7.5959e+00 -2.81523e-05  6.5793e-03 -5.1029e-03
  8  1.59812e-02  8.1950e+00 -6.1257e+00  8.03550e-07  6.6321e-03 -7.3999e-03
  9  3.21340e-02  6.5465e+00 -5.5445e+00  1.36999e-05  9.3166e-03 -2.8041e-02
 10  1.54258e-02  5.5075e+00 -5.2734e+00  6.72732e-06  1.8760e-02 -6.8139e-03
 11  1.00434e-02  6.6930e+00 -4.1371e+00  4.50608e-06  9.5616e-03 -4.5582e-03
 12  3.74565e-03  2.8079e+00 -5.2209e+00  1.94953e-06  3.4249e-03 -6.0704e-03
 13  1.72176e-03  1.9492e+00 -1.9357e+00  8.31966e-07  7.1310e-03 -2.7289e-03
 14 -4.23044e-04  1.4925e+00 -1.7270e+00 -1.21942e-06  5.0615e-03 -7.7321e-03
 15 -6.64625e-04  9.0857e-01 -2.0803e+00  1.73494e-07  6.8386e-03 -5.7959e-03
 16 -3.97842e-04  9.5941e-01 -1.0226e+00  4.90556e-07  6.1494e-03 -2.2884e-03
 17  6.51551e-04  1.2313e+00 -1.0762e+00  1.57072e-07  9.5770e-04 -2.7902e-03
 18 -2.32845e-04  8.2806e-01 -1.5755e+00 -5.98826e-08  3.4552e-04 -6.5686e-04
 19 -8.91079e-04  4.2054e-01 -6.2411e-01 -3.10004e-07  2.4195e-04 -2.5949e-04
 20 -2.14151e-03  2.9491e-01 -3.6155e-01 -9.79213e-07  1.2319e-04 -2.6400e-04

Temperature tendencies converted to W m-2
                                                   max         min
Discrepancy: rates-state    -1.00323e-05 H  5.0660e-04 -1.2437e-03
dtheta/dt from x-advection   5.95048e-07 H  4.5798e-07 -3.5214e-07
dtheta/dt from y-advection   1.63607e-06 H  9.7398e-07 -6.0956e-07
dtheta/dt from z-advection  -1.57924e-06 V  4.3334e-03 -7.0646e-03
dtheta/dt from x-diffusion   1.59092e-08 H  6.7872e-09 -4.9403e-09
dtheta/dt from y-diffusion  -3.96881e-07 H  3.9864e-10 -2.6504e-08
dtheta/dt from z-diffusion   7.88105e-07 V  1.5196e-04 -1.2012e-04
dtheta/dt from sfc. fluxes  -8.51811e+01                          
dtheta/dt from pen. solar    8.68171e+01                          
dtheta/dt from ice physics  -1.60496e+00                          
dtheta/dt from ml physics    2.06915e-06 V  1.3985e-04 -9.6586e-05
dtheta/dt from convection    7.42637e-08 V  5.1766e-04 -6.6745e-04
dtheta/dt from fourier fil   6.55435e-10                          
dtheta/dt from robert filt  -8.02384e-05                          
dtheta/dt from med. outflo   7.56840e-09 H  1.4608e-10 -1.2965e-10
dtheta/dt from g&mcw schem   7.39606e-07

Change in salinity/1e3 PSU
            Change over period                Discrepancy: rates-state
lev     mean         max         min         mean         max         min    
  1 -3.19002e-05  6.9160e-02 -1.2620e-02 -1.96142e-08  2.3213e-04 -1.2776e-04
  2 -3.09258e-05  6.9071e-02 -1.2620e-02 -8.77192e-08  2.3009e-04 -5.1048e-06
  3 -2.35388e-05  6.5866e-02 -1.2620e-02  9.81068e-09  1.8013e-04 -4.8026e-06
  4 -1.45772e-05  6.2685e-02 -1.2620e-02  1.76482e-08  1.4422e-04 -6.0439e-06
  5 -1.42387e-06  5.8672e-02 -9.2662e-03  1.24690e-08  1.0232e-04 -3.9424e-06
  6  5.68697e-06  5.1195e-02 -2.7020e-03  6.74530e-10  2.7579e-05 -2.1098e-06
  7  5.82138e-07  4.3538e-02 -2.0197e-03 -4.58633e-10  1.5877e-05 -1.4058e-06
  8  7.05388e-06  3.6637e-02 -1.3742e-03  3.94393e-09  2.4999e-05 -1.5576e-06
  9  5.04537e-06  1.3988e-03 -1.8710e-03  2.29155e-09  2.1662e-06 -2.0658e-06
 10  4.00457e-07  6.6040e-04 -7.3566e-04  5.30502e-11  1.7765e-06 -2.4684e-06
 11 -2.22278e-07  5.7203e-04 -4.5742e-04 -5.42438e-11  1.6125e-06 -1.8651e-06
 12  2.35731e-07  3.2052e-04 -5.3260e-04  1.19573e-10  6.9703e-07 -9.9036e-07
 13  3.33333e-07  2.3812e-04 -2.1138e-04  1.41137e-10  1.4928e-06 -4.6816e-07
 14  2.07845e-07  1.9163e-04 -1.4475e-04 -1.17278e-10  1.1580e-06 -1.7202e-06
 15  1.28044e-07  7.3724e-05 -2.2066e-04  1.42339e-10  1.5621e-06 -1.2717e-06
 16  2.63565e-07  5.8655e-05 -5.3290e-05  2.11245e-10  1.1562e-06 -6.6655e-07
 17  3.14323e-07  6.4051e-05 -3.1092e-05  9.83965e-11  1.7640e-07 -7.8065e-07
 18  3.47899e-07  8.1691e-05 -3.1237e-05  1.55148e-10  6.1262e-08 -4.3846e-08
 19  3.69221e-07  4.1262e-05 -3.4015e-05  1.72903e-10  7.5466e-08 -1.4908e-08
 20  3.61542e-07  4.3726e-05 -1.0635e-04  1.23373e-10  1.9524e-08 -8.3608e-08

Salinity tendencies converted to mm a-1 over a 50 m layer of water at 35 PSU
                                                   max         min
Discrepancy: rates-state     1.86469e-01 H  2.9185e-01 -1.2531e+00
ds/dt from x-advection (oc  -2.39258e-04 H  3.4106e-04 -3.2043e-04
ds/dt from y-advection (oc   7.27205e-03 H  3.4693e-04 -5.5365e-04
ds/dt from z-advection (oc  -5.94700e-04 V  6.5259e+00 -5.5195e+00
ds/dt from x-diffusion (oc   4.21070e-06 H  6.5362e-06 -9.5247e-06
ds/dt from y-diffusion (oc   2.19686e-04 H  2.4656e-07 -5.0249e-05
ds/dt from z-diffusion (oc   2.38684e-03 V  3.6131e-01 -5.2266e-01
ds/dt from sfc. fluxes (oc   2.02245e+03                          
ds/dt from ice physics (oc  -9.29908e+02                          
ds/dt from ml physics (ocn  -8.08106e-04 V  2.4578e+00 -3.3053e+00
ds/dt from convection (ocn   3.24348e-04 V  1.9577e+00 -8.8460e-01
ds/dt from fourier filt (o  -2.01569e-05                          
ds/dt from robert filt (oc   2.02454e+01                          
ds/dt from med. outflow (o  -3.95520e-05 H  3.9241e-08 -1.5512e-06
ds/dt from g&mcw scheme gs  -7.65877e-03

`AAXZC` (HADCM3 control run) 2261-2271

Means are analysed here from the decade of the HADCM3 control run beginning 1/12/2261. (Note that not all of the rate diagnostics are present and correct before 2201 of this experiment.) The output from the PV-WAVE routine check_hadcm3_rates is shown below. The terms for the Mediterranean outflow, Fourier and Robert filters in temperature and salinity are not available, and nor is the contribution of the Gent-McWilliams scheme to salinity. In summary,

Because of the missing terms, there are locally large errors. Hence the analysis of the changes in T and S shows large discrepancies (maximum errors of 1e2 K over the decade).
The diagnosed terms which move heat and salinity around conserve accurately in the global average.
There is a discrepancy between rates and state of 1e-4 W m-2. In the analysis of one year of AAXZD, the discrepancy was only 1e-5. In that year, the Robert filter which is not diagnosed here, gave a non-conservation of only 1e-4 W m-2, which could be the explanation. However, an analysis of a decade of data from the 4*CO2 run ABBDC, which has this diagnostic, still had an inequality of about the same size. This is unexplained, but might result from numerical inaccuracy in calculating the area-averages.

The net heat flux into the ocean over this period is -0.162592 W m-2 diagnosed from the fluxes (by the PV-WAVE routine pats_oc_netheatflux). These fluxes are categorised as: penetrative solar radiation, non-penetrative surface heat fluxes, and fluxes associated with ice processes, including the so-called ``heatsink'' term, which is a deliberate non-conservation at the bottom of the ocean, amounting to -0.0433971 W m-2 in this experiment. Diagnosed from the heat contents (by pats_oc_heatcontent), the net heat flux into the ocean should be -0.160540 W m-2. The difference implies an unexplained gain of 0.002052 W m-2 by the ocean. This is an order of magnitude larger than the imbalance between the rate diagnostics and the change of state, so it must come from a mismatch between the fluxes applied to the ocean, and the heating which results from them as shown by the rate diagnostics.

The solar heat flux is 87.0304 W m-2, as measured both by the flux diagnostic and by the resulting rate of change shown below. The rate diagnostic for non-penetrative heat fluxes should equal ocean diagnostic 30206 (gbm htn into ocean budget w/m**2). In fact they are not quite equal, being -85.5697 W m-2 and -85.5680 W m-2 respectively, a difference of 0.0017 W m-2, in the wrong sense to explain the flux mismatch (the ocean is cooling more than the surface heat flux requires). There must therefore be errors in both the application of the surface heat fluxes and the ice processes. These are unexplained. (It is possible, again, that check_hadcm3_rates is inaccurately calculating the area- and volume-averages.)

Experiment AAXZC from 2261/12/01 00:00 to 2271/12/01 00:00

Change in potential temperature/K
            Change over period                Discrepancy: rates-state       
lev     mean         max         min         mean         max         min    
  1 -5.19713e-02  1.0016e+01 -1.3900e+01  4.02989e-03  2.0940e+01 -2.2378e+01
  2 -4.71843e-02  9.6124e+00 -1.3900e+01 -1.16267e-02  2.3822e+01 -2.6850e+01
  3 -4.84129e-02  8.8364e+00 -1.3900e+01 -1.59807e-04  2.8713e+01 -3.6140e+01
  4 -2.20915e-02  6.8639e+00 -1.2121e+01  5.24184e-04  3.6454e+01 -3.9154e+01
  5  3.95770e-03  7.4745e+00 -1.0545e+01  9.62028e-04  7.0425e+01 -7.2369e+01
  6  1.83023e-02  7.9713e+00 -1.1485e+01  9.52771e-04  1.0740e+02 -1.3027e+02
  7 -1.61382e-02  8.0800e+00 -1.0545e+01  4.45820e-04  1.3589e+02 -1.6968e+02
  8 -7.05823e-02  1.1274e+01 -8.6558e+00  2.20347e-04  1.2892e+02 -1.6853e+02
  9 -3.87223e-02  4.8492e+00 -5.7985e+00  1.54403e-04  1.2622e+02 -1.2433e+02
 10 -1.01361e-02  5.7422e+00 -4.7038e+00  6.18454e-05  9.3141e+01 -7.8024e+01
 11  9.81679e-03  5.7850e+00 -6.4368e+00 -3.33096e-05  1.0899e+02 -9.5214e+01
 12  4.77853e-03  4.5815e+00 -3.7512e+00  2.23794e-06  8.6399e+01 -8.1634e+01
 13  5.81553e-04  2.5830e+00 -2.8720e+00  6.95499e-06  1.3607e+01 -1.4090e+01
 14  1.96425e-03  1.2413e+00 -1.5625e+00 -1.06393e-06  2.2436e+01 -2.4531e+01
 15  4.40224e-03  1.6317e+00 -1.2208e+00 -2.22072e-06  2.5108e+01 -3.1323e+01
 16 -2.82129e-03  9.8753e-01 -1.2059e+00  5.16156e-06  3.4182e+01 -4.1113e+01
 17 -6.73635e-03  1.0383e+00 -1.0120e+00  3.00874e-06  2.0107e+01 -2.2325e+01
 18 -6.06667e-03  1.0945e+00 -1.4193e+00  1.60518e-06  5.5509e+00 -8.1922e+00
 19 -2.91931e-03  9.5529e-01 -8.5729e-01  5.10136e-08  3.1986e-01 -6.1155e-01
 20 -5.91690e-03  4.1895e-01 -5.7232e-01  3.40080e-06  3.6670e-03 -5.3335e-04

Temperature tendencies converted to W m-2
                                                   max         min
Discrepancy: rates-state     1.37149e-04 H  5.3013e-04 -1.5295e-03
No fields for dtheta/dt from x-advection k/gs
No fields for dtheta/dt from y-advection k/gs
No fields for dtheta/dt from z-advection k/gs
dtheta/dt from x-diffusion   2.58879e-09 H  5.5249e-09 -4.3244e-09
dtheta/dt from y-diffusion   7.74066e-08 H  1.4996e-10 -2.0161e-08
dtheta/dt from z-diffusion   6.18359e-07 V  9.6617e-05 -9.6648e-05
dtheta/dt from sfc. fluxes  -8.55697e+01                          
dtheta/dt from pen. solar    8.70304e+01                          
dtheta/dt from ice physics  -1.61231e+00                          
dtheta/dt from ml physics    3.52345e-06 V  2.7302e-04 -1.4235e-04
dtheta/dt from convection    2.72805e-08 V  3.1989e-04 -1.3381e-03
No fields for dtheta/dt from fourier filt k/gs
No fields for dtheta/dt from robert filt k/gs
No fields for dtheta/dt from med. outflow k/gs
dtheta/dt from g&mcw schem   3.87990e-07                          
dtheta/dt from z-adv+z-dif  -1.51559e-07                          

Change in salinity/1e3 PSU
            Change over period                Discrepancy: rates-state       
lev     mean         max         min         mean         max         min    
  1 -1.57901e-05  4.9217e-03 -6.5572e-03  9.51010e-08  1.9850e-02 -1.7362e-02
  2 -1.51727e-05  4.9217e-03 -6.5572e-03  2.86453e-06  2.5541e-02 -3.1573e-02
  3 -5.64827e-06  5.6678e-03 -6.5572e-03 -1.42690e-06  6.2861e-02 -6.4525e-02
  4 -1.00302e-05  4.9217e-03 -6.6255e-03 -1.35559e-06  6.7349e-02 -6.8777e-02
  5 -1.20888e-05  4.1243e-03 -4.4835e-03 -8.76528e-07  5.9843e-02 -7.8601e-02
  6 -1.28108e-05  3.1895e-03 -3.1464e-03 -3.68905e-07  8.2233e-02 -9.2972e-02
  7 -1.47398e-05  1.7569e-03 -2.8671e-03 -1.03745e-07  1.0745e-01 -1.0389e-01
  8 -1.80021e-05  2.5678e-03 -2.2366e-03 -1.55204e-08  1.1216e-01 -1.0784e-01
  9 -1.34617e-05  4.3614e-03 -1.3374e-03  1.84802e-08  8.2208e-02 -7.8210e-02
 10 -9.61784e-06  1.1268e-03 -8.9120e-04  9.31258e-09  4.6378e-02 -4.6549e-02
 11 -8.47166e-06  6.3292e-04 -6.0908e-04 -1.36331e-09  2.1106e-02 -2.3910e-02
 12 -4.79047e-06  4.7405e-04 -3.5789e-04  1.94927e-09  1.8936e-02 -1.9053e-02
 13 -1.33173e-06  2.9201e-04 -1.9486e-04  2.82617e-09  7.2027e-03 -6.9321e-03
 14  2.28293e-06  2.8092e-04 -1.3852e-04 -1.88652e-09  1.1206e-03 -1.1459e-03
 15  3.44254e-06  1.6081e-04 -7.7181e-05 -1.40509e-09  9.5291e-04 -1.0237e-03
 16  3.05966e-06  1.9215e-04 -8.9912e-05 -7.05306e-11  1.2021e-03 -1.4476e-03
 17  2.72211e-06  1.3354e-04 -9.9162e-05 -7.75335e-10  1.0453e-03 -8.9869e-04
 18  2.86239e-06  1.1602e-04 -1.3847e-04 -1.12488e-09  2.0740e-04 -3.3642e-04
 19  3.19182e-06  1.0517e-04 -7.3868e-05 -1.36244e-09  1.5032e-05 -2.7502e-05
 20  3.05126e-06  4.9829e-05 -5.0908e-05 -6.52052e-10  9.8709e-07 -1.5701e-07

Salinity tendencies converted to mm a-1 over a 50 m layer of water at 35 PSU
                                                   max         min
Discrepancy: rates-state    -3.45136e+00 H  4.0922e+00 -2.0384e+00
No fields for ds/dt from x-advection (ocn) gs**-1
No fields for ds/dt from y-advection (ocn) gs**-1
No fields for ds/dt from z-advection (ocn) gs**-1
ds/dt from x-diffusion (oc  -2.07468e-05 H  2.8783e-06 -1.1372e-05
ds/dt from y-diffusion (oc   1.23104e-03 H  3.9563e-06 -4.7090e-05
ds/dt from z-diffusion (oc   1.41442e-03 V  4.3075e-01 -4.5024e-01
ds/dt from sfc. fluxes (oc   1.04058e+03                          
ds/dt from ice physics (oc  -9.38572e+02                          
ds/dt from ml physics (ocn  -3.76855e-04 V  7.9455e-02 -1.8605e-01
ds/dt from convection (ocn   1.71278e-04 V  5.6545e-01 -5.0895e-01
No fields for ds/dt from fourier filt (ocn) gs**-1
No fields for ds/dt from robert filt (ocn) gs**-1
No fields for ds/dt from med. outflow (ocn) gs**-1
ds/dt from g&mcw scheme gs  -5.83248e-03                          
ds/dt from z-adv+z-diff (o   1.07287e-03

Jonathan Gregory / hadsa@hc0400 / jmgregory@meto.gov.uk

Conservation of temperature and salinity in HADCM3

AAXZD (HADCM3 with unmodified Indonesian throughflow) 2051-2052

AAXZC (HADCM3 control run) 2261-2271

`AAXZD` (HADCM3 with unmodified Indonesian throughflow) 2051-2052

`AAXZC` (HADCM3 control run) 2261-2271