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paper notes: drift
When reviews come back...
- Add these models: MRI-ESM2-0 (already processed; it does apply a heat flux correction)
What is drift? Unforced long term trends arising from incomplete model spin up and/or non-closure of the energy or mass budget (referred to as leakage).
We look at energy and mass drift and conservation for physical insights and for budget analyses. Mass conservation is more difficult than energy conservation Drift magnitude has not improved from CMIP5 to CMIP6, but energy, mass and salt conservation has improved after accounting for long-term leakage.
While drift doesn't matter in atmospheric variables (at a global scale), quantities like OHC and thermosteric sea level are vitally important.
Closure is important for studies that use surface fluxes (e.g. Levang2015, refs in He2019) or surface fluxes and changes in ocean storage to get the true advective transport (e.g. Irving2019, He2019). If the surface fluxes and ocean state aren't actually physically linked, those inferred transports aren't real.
Drift:
- Covey2000?
- Covey2007: CMIP2+
- SenGupta2012: CMIP3
- SenGupta2013: CMIP5 (and CMIP3)
- Hobbs2015: CMIP5
Leakage:
- Liepert2012: CMIP3 (atmosphere)
- Liepert2013: CMIP5 (atmosphere)
- Hobbs2015: CMIP5 (ocean)
Table: Improvements CMIP2-3-5 mainly due to longer spinup times?
- TODO: Check to see if CMIP6 spinup times are the same as CMIP5 (document in my model table)
- Covey2006 have "ocean only spinup", "coupled ocean-atmosphere spinup"" and "archived control years" columns:
- Ocean-only spin-up is the length of time after initialization (and after relaxation of deep ocean to observations, if this was done) but before two-way coupling between ocean and atmosphere.
- Coupled spin-up is the length of time after two-way coupling between ocean and atmosphere started, including any ‘‘control run’’ time prior to taking data for trends.
- SenGupta2012 has "coupled spinup (prior to PICNTRL) (yr)" and "Additional PICNTRL prior to 20C3M (yr) columns"
- SenGupta2013 gives a sentence or two description of the spin up procedure for each model
The details of initialization procedures (‘‘spin-up’’) vary among the CMIP2+ models. Most groups first ran the atmosphere and ocean components in stand-alone mode (often using information derived from the atmospheric simulation as boundary forcing for the ocean) before initiating the coupled system. The CCSM2.0, HadCM2 and HadCM3 were the exceptions to such a sequential procedure. In these models, simulation of the coupled system proceeded directly after initialization of the atmosphere and ocean components from relevant climatology.
In the early days of climate modeling, coupled ocean-atmosphere GCM simulations drifted relatively quickly and steadily away from the observed climate unless constrained by ad hoc flux adjustments (and in some cases did so even with flux adjustments). Although improved flux adjustment techniques were proposed, it seemed that some minimal form of flux adjustment would be necessary for any acceptable century scale climate simulation. This situation persisted through assembly of the first phase of the CMIP database, as shown in Figure 1 of Covey et al. [2000]. Excessive climate drift appears in all nonflux-adjusted models in that figure except the newly developed Climate System Model (CSM, see above). In recent years, however, the situation has improved dramatically. This improvement was documented in the most recent IPCC assessment report and is confirmed by the results given above. Although most of the CMIP2+ models employ flux adjustments, both the flux-adjusted and the non-fluxadjusted models exhibit acceptably small climate drift on century-long time scales and beyond. What reasons can we infer for this improved model behavior? Since we are considering a large number of models, no single factor can be expected to be responsible, but one prominent feature emerging from Table 1 is very long spin-up times. Another enhancement of control run stability arises from more careful initialization of the coupled ocean-atmosphere system... Two other factors, model resolution and ‘‘physics,’’ seem less important. The question of whether improved subgridscale physical parameterizations could remedy climate drift is more difficult to answer, but we have found no indication that this is so.
Results:
- Surface temperature trends in control run simulations are small compared with observed trends.
- Sea ice changes in the models are dominated by interannual variations.
- Deep ocean temperature and salinity trends are small enough for model control runs to extend over 1000 simulated years or more, but trends in some regions, most notably the Arctic, differ substantially among the models and may be problematic.
- Methods used to initialize coupled GCMs can mitigate climate drift but cannot eliminate it.
- Lengthy ‘‘spin-ups’’ of models, made possible by increasing computer power, are one reason for the improvements this paper documents.
While drift in globally averaged surface properties is generally considerably smaller than observed and simulated twentieth-century trends, it can still introduce nontrivial errors in some models. Furthermore, errors become increasingly important at smaller scales.
In some instances drift is of primary importance and cannot be ignored. For example, in the deep ocean or for depth-integrated properties drift may dominate over any externally forced signal. In some applications, however, climate drift has a relatively minor effect and can be safely ignored. This is often the case when dealing with multimodel means of the surface climate. Drift appears not to be systematic with regards to its sign and tends to cancel out where a large number of models are considered... As surface drift is spatially heterogeneous, the regional importance of drift for individual models can be much larger than the global figures suggest.
Spurious trends in temperature and salinity suggests that density would also show substantial drift, although some degree of density compensation tends to occur in the models (Fig. 9). This would in turn drive dynamical changes to the ocean via changes in stratification, the overturning circulation, and geostrophic flow where there are spatial differences in density drift.
Significant efforts by the climate modeling community have gone into reducing climate drift, which has meant that most climate models can now be successfully run without the need for unphysical flux adjustments.
Climate drift tends to operate on two distinct time scales (previously referred to as ‘‘major drift’’ for large magnitude rapid drift and ‘‘minor drift’’ for slow long time scale drift, Cai and Gordon 1999). Large discontinuities in surface fluxes during the coupling of the various component models can cause rapid drift. The initial adjustment of the atmosphere, surface ocean, and sea ice to this perturbation is relatively fast, with a new equilibrium generally being achieved after a few years. A variety of techniques have been used to reduce this ‘‘coupling shock.’’ For example, individual model components can be equilibrated using different boundary forcing combinations in sometimes quite elaborate multistage spinup procedures (e.g., Moore and Gordon 1994; Power 1995; Cai and Chu 1996; Large et al. 1997). However, some initial, albeit reduced adjustment to the coupling, generally persists. A more pervasive problem relates to the millennial adjustment time scale of the deep ocean. This may be associated with various factors including 1) deficiencies in the model physics, 2) inaccuracies in the model formulation (which might for example lead to heat or salt/ freshwater not being conserved), 3) the propagation of discontinuities associated with coupling shock through the ocean interior, and 4) a sparsity in the observational data used to initialize the model. Climate model simulations are often initialized from some observational dataset (Table 1). Given a perfect model and a perfect set of observations, the simulated climate system should be initialized in a dynamical balance. However, deficiencies in model physics mean that a model’s dynamical balance will be different to that of the real world. The model will therefore drift. A lack of observational data, particularly in the deep ocean, and the need to interpolate this data will also mean that a dynamically consistent observationally based initial state is unlikely to exist. As such even with a perfect model some drift would still occur.
In the Coupled Model Intercomparison Project phase 2 (CMIP2), 10 of the 17 models employed ad hoc and nonphysical flux adjustments to reduce climate drift to maintain a relatively stable simulated climate state (Houghton et al. 2001; Ra¨isa¨nen 2001). Even with flux adjustment, however, drift was still evident (Covey et al. 2006). In CMIP3, only 6 of the 24 contributing models used flux adjustments.
They have a long discussion in the introduction about the various approaches to drift removal:
- Linear trend for corresponding control time period
- Difference between two time periods:
- Another approach is to find the difference in a given climate variable between two time slices in both the forced and the control simulation. Subtraction of these differences provides an estimate of the forced signal. This method has the advantage of requiring less model output to calculate the forced change, but conversely is subject to more extreme aliasing as a result of natural variability.
- Fitting polynomial to full control run
In comparison to CMIP21 models (Covey et al. 2006, their Table 2) there has been a general reduction in spinup times (the time between coupling and the start of 20C3Msimulations) in the CMIP3 generation of models. The median spinup time has gone from ;250 yr (Covey et al. 2006, their Table 2) to 200 yr (CMIP3, Table 1). This is in part a consequence of improvements in model stability. However, it may also be symptomatic of the fact that the increase in model complexity and resolution and the need for multiple scenario experiments has overshadowed increases in computational power. In addition, timelines for inclusion in the CMIP–IPCC process often mean that modeling groups have insufficient time in which to perform long simulations. Table 1 contains various gaps and conflicting pieces of information, which are indicative of the lack of information provided by some of the modeling groups regarding the spinup procedures either to PCMDI or in the relevant model documentation.
APPROACH FOR REGIONAL ANALYSIS: While forced trends in surface temperature are positive almost everywhere around the globe, this is not the case for the drift, nor is it the case for forced trends in other properties including salinity and precipitation. As such, a more appropriate metric for expressing the relative importance of the drift can be achieved by first taking the magnitude of the trend (for both 20C3M and PICNTRL) at each grid box before averaging globally (Fig. 3). This provides an average measure of the typical local error in the 20C3M trend if drift is unaccounted for—a very different measure to that shown in Fig. 2.
Drift shows little systematic directional bias either from region to region or from model to model. As a result, drift generally becomes less important (compared to any forced trend) for larger regions or when considering averages across multiple models.
Even though the adjustment time scale of the atmosphere is fast, as the ocean is coupled to the atmosphere, if surface ocean properties drift then atmospheric properties will also drift.
Drift can be caused by a number of factors. For example, a simulation’s initial state may not be in dynamical balance with the representation of physics in the model; ‘‘coupling shock’’ may occur during the coupling of model components resulting in discontinuities in surface fluxes (e.g., Rahmstorf 1995) or numerical errors may exist in the model that mean that heat or moisture is not fully conserved (e.g., Lucarini and Ragone 2011; Liepert and Previdi 2012). In these cases, a model may drift from its initial state toward a quasi-steady state over some period of time (although in the case of nonconserved heat or water a steady solution may not be attainable). The time scale over which the climate system adjusts will be determined by the time it takes for anomalies to be advected or mixed through the ocean, which may be many thousands of years [e.g., Peacock and Maltrud (2006); the adjustment of the atmosphere and land surface is many orders of magnitude faster]. Given the complexity and resolution of modern climate models, spinup periods of thousands of years are prohibitive given the available computational resources and the requirement for numerous transient simulations [e.g., as part of phase 5 of the Coupled Model Intercomparison Project (CMIP5); Taylor et al. (2012); see the appendix for a complete list of model names and expansions]. Instead, models are generally spun up for a few hundred years (although multimillennium spinups and complex multistage spinups are sometimes performed; Table 1). As a result, externally forced climate model experiments (e.g., where changes are made to greenhouse gases, aerosols, ozone, or insolation) are undertaken in models that are often not fully equilibrated and may exhibit changes that are associated with the adjustment process, in addition to any changes that are directly related to external forcing or internal variability
Based on SST, precipitation, and steric sea level, there is a clear overall reduction in the magnitude of drift in the newer generation of models. In particular, for globally averaged steric sea level, which integrates the drift throughout the ocean, the average size of drift in CMIP5 is about half of that in CMIP3, although there are still a few outlier models with high drift magnitudes. For some models this improvement may in part relate to longer spinup periods... [gives examples]... The reduced drift may also result from improved representation of physical parameterizations (e.g., cloud microphysics) and numerical schemes (e.g., advection or diffusion) and/or higher horizontal and vertical resolution.
Note that Hobbs et al (2016) show in their supplementary materials that (a) there is drift in the masso variable, and (b) that has a negligible impact on ocean heat content calculations (i.e. you can use a constant mass and you'll be fine).
Atmospheric water cycle: In 13 of the 18 CMIP3 models examined, global annual mean precipitation exceeds global evaporation, indicating that there should be a 'leaking' of moisture from the atmosphere whereas for the remaining five models a 'flooding' is implied. Nonetheless, in all models, the actual atmospheric moisture content and its variability correctly increases during the course of the 20th and 21st centuries. These discrepancies therefore imply an unphysical and hence 'ghost' sink/source of atmospheric moisture in the models whose atmospheres flood/leak. They refer to this non-closure as a "bias". They note that the biases are not constant over time and can drift significantly, but in most cases don't. To put them in perspective, the trends in the model biases (i.e. drift) were typically less than a few percent of simulated precipitation changes in the historical and future experiments.
(They note that atmospheric moisture content is by far the smallest storage term in the global water cycle.)
The CMIP5 update shows only a small number of models with big drift or closure issues. They look at control simulations this time, and dW/dt is therefore approximatley zero in all models (the small number where P-E isn't approximately zero have presumably introduced a ghost source/sink to achieve constant atmospheric moisture in the control climate.
It would be interesting in the CMIP5 ocean runs whether there is a key variable (e.g. ocean mass) that is tuned to a 'correct' value (i.e. like atmospheric moisture content). I suspect not.
From Lembo2019 (TheDiaTo paper; although they are mostly talking about the time-mean atmospheric energy budget, as opposed to trends/drifts): Inconsistencies in the overall energy budget of long-term stationary simulations have been carefully pointed out (Lucarini and Ragone, 2011; Mauritsen et al., 2012), and various aspects of the radiative and heat transfers within the atmosphere and between the atmosphere and the oceans have been evaluated in order to constrain models to a realistic climate (Wild et al., 2013; Loeb et al., 2015). A substantial bias in the energy budget of the atmosphere, in particular, has been identified in many global climate models (GCMs), resulting from either the imperfect closure of the kinetic energy budget (Lucarini and Ragone, 2011) or of the mass balance in the hydrological cycle (Liepert and Previdi, 2012). This picture is made even more complicated by the difficult task of having an accurate observational benchmark of the Earth's energy budget (e.g. Loeb et al., 2009; von Schuckmann et al., 2016). Many authors have recently suggested that the improvement of climate models requires improving the energetic consistency of the modelled system (Hansen et al., 2011; Lucarini et al., 2011, 2014).
Water mass budget has been assessed in observations (L'Ecuyer et al., 2015; Rodell et al., 2015), as well as in climate models, focusing on the hydrological cycle alone (Terai et al., 2018) or evaluating it in conjunction with the energy budgets (Demory et al., 2014; Vannière et al., 2019).
The discussion until this point is valid for a highly realistic ocean model. That is, a free surface (as opposed to rigid lid) model that applies freshwater fluxes (as opposed to virtual salt fluxes) and no Boussinesq approximation. In reality, almost all CMIP5 and CMIP6 ocean models apply a Boussinesq approximation (Table 1), which means they conserve volume as opposed to mass. More specifically, steric processes (i.e. contraction/expansion of sea water due to a temperature and/or salinity change) are represented as a change in ocean mass as opposed to volume (e.g. a warming drift will lead to a decrease in density and thus mass). To avoid confusion, modeling groups in CMIP6 were asked to archive a global ocean mass variable equal to the reference density times the ocean volume, as opposed to the actual Boussinesq ocean mass. All CMIP5 models (with the exception of those using MOM) did not do this, so we make the calculation ourselves.
\textit{TODO: Can't check the steric category because of how the masso variable is now reported...}
The other (relatively rare) model type in the CMIP ensemble is non-Boussinesq ocean models that apply a virtual salt flux. In this case, mass conservation cannot be assessed using the model's global ocean mass variable (because the model doesn’t include freshwater fluxes) or the global ocean volume variable (because it can vary in response to barystatic virtual salt fluxes as well as steric influences). The only possible comparison is between the global average salinity and cumulative net water flux at the ocean surface, but any mismatch could be due to mass or salt leakage (or a combination of both).
My thoughts...
Why don’t the energy and mass budgets close? The potential causes are many and varied, but to my mind they fall into two categories.
- Deficiencies in model coupling, numerical schemes and physical processes
The heat flux associated with water transport across the ocean boundary generally represents a global net heat loss for the ocean, because evaporation transfers water away at a temperature typically higher than precipitation adds water. The documented size of this global heat loss ranges from 0.15 Wm−20.15;Wm^{-2}0.15Wm−2 (Delworth et al., 2006) to 0.30 Wm−20.30;Wm^{-2}0.30Wm−2 (Griffies et al., 2014). In a steady state, this heat loss due to advective mass transfer is compensated by ocean mass and heat transport, which is in turn balanced by atmospheric transport. However, most atmospheric models do not account for the heat content of their moisture field, meaning they represent the moisture mass transport but not the heat content transport (Griffies et al., 2016). Leakage in the coupled global heat budget therefore arises due to a basic limitation of the modeled atmospheric thermodynamics.
When precipitation forms in the cool upper troposphere in the ACCESS-CM2 model (and presumably other models) and falls onto the relatively warm ocean surface, it is immediately warmed to that surface temperature without the necessary energy actually coming from anywhere.
Luciarni2011: The inconsistency in the net energy balance of the atmosphere is mainly related to the fact that kinetic energy dissipated by various processes, including viscosity and diffusion, cloud parameterization, and interaction with the boundary layer, is not exactly reinjected in the system as thermal energy. (Becker 2003)
Eden2014: It is common for the dissipation of the (available) potential energy of the turbulent balanced flow in ocean models by an additional mesoscale eddy-driven advection velocity (Gent et al. 1995), the dissipation of resolved kinetic energy by harmonic or biharmonic lateral friction, and the dissipation of energy in bottom boundary layers. For all those processes, the kinetic and potential energy that is dissipated is simply lost instead of being transferred to the relevant connecting dynamical regime or to a different form of energy. On the other hand, at other places and for other parameterizations, this missing energy needs to be artificially created again. The most prominent example is the unaccounted supply of energy that is needed to mix the density in ocean models, but the same holds for almost any other parameterization and dynamical regime. In other words, current ocean models have no complete account on the energy cycle and are thus inconsistent in this way. [Not sure if that means the ocean doesn't conserve heat on the whole and the fake energy is created to exactly balance the missing?]
I’d refer to that as “real” leakage, as opposed “apparent” leakage related to data issues that have nothing to do with deficiencies in the actual model. For instance…
- Data issues
Missing diagnostics: e.g. If a model hasn’t saved/archived the upward geothermal heat flux at sea floor (hfgeou), does that mean there is no geothermal heat flux, or they just haven’t uploaded it to the ESGF?
Vague definitions: the document defining the CMIP5 standard output says the water flux into the ocean diagnostic (wfo) should ‘probably’ be the sum of the precipitation flux (pr), snowfall flux (prsn), evaporation flux (evs), river flux (friver) and iceberg flux (ficeberg) diagnostics
Data errors: These are especially important for cumulative totals (e.g. netTOA, surface heat and freshwater fluxes). Bogus values at just a couple of time steps can throw off the cumulative sum (but these are relatively easy to catch – we excluded some models on that basis).
Other random notes:
Run on their own, we would expect the latest state-of-the-art climate models to conserve mass and salt. (Noting that the state-of-the-art models have a free surface instead of rigid lid, which means the are able to incorporate changes in mass through freshwater input.) The ocean model leakage in a coupled setup is therefore likely best interpreted as an "apparent" as opposed to real leakage, due to a mismatch between the reported boundary forcing (i.e. wfo or no variable for salt flux) and the actual boundary forcing.
Interpretation of energy leakage is a little more complex, as it likely arises from a combination of real \citep{Eden2014} and apparent leakage.
(Or in a minority of cases it's due to non-physical manipulation of a variable - e.g. constant volume or wfo... not quite sure how to cover these cases.)
The unreported component of the boundary forcing tends to be time constant, which means that interannual variability in the dedrifted data is highly correlated (i.e. there's a physically consistent link between the variables).
From \cite{Gregory2013}: Before going further, we would like to clarify our terminology. By “thermal expansion,” we mean the contribution to GMSLR from change in seawater density due to change in temperature. We propose a new word “barystatic” for the contribution to GMSLR from the change in the mass of the ocean. A new term would be helpful because the word “eustatic” is now used with various different meanings and has consequently become confusing. The barystatic effect on sea level change is the mass of freshwater added or removed, converted to a volume using a reference density of 1000 kg m−3, and divided by the ocean surface area. It does not include the effects on regional sea level associated with changes in the gravity field and the solid earth (discussed in section 7d) or in salinity. Although salinity change is important to regional sea level change, in the global mean the halosteric effect of adding freshwater to the ocean is practically zero (Munk 2003; Lowe and Gregory 2006, appendix A).
From Hochet and Tailleux 2019 use the term "Boussinesq mass" https://journals.ametsoc.org/doi/full/10.1175/JPO-D-19-0055.1 "... volume considered by Holmes et al. (2019) is best interpreted as a proxy for the Boussinesq mass M0 = ρ0V, where ρ0 is the reference Boussinesq density. If V were truly meant to represent volume rather than a proxy for the Boussinesq mass, the Boussinesq expression for dV/dt would have to be regarded as inaccurate because of its neglect of the volume changes resulting from mean density changes."
BO = Boussinesq; NB = non-Boussinesq. FS = free surface; RL = rigid lid. FWF = freshwater flux; VSF = virtual salt flux.
All models are BO, FS, FWF except...
\citep{Fox-Kemper2019}: Traditional Boussinesq ocean models with a rigid lid struggled to incorporate changes in mass through freshwater input, because they were models with a fixed volume of fluid so any changes in mass had to come through virtual salt fluxes or temperature-related density changes. However, modern models using an explicit free surface with a natural water boundary condition overcome the limitations of the rigid lid (e.g., Griffies et al., 2001; Campin et al., 2004), thus accepting changes in ocean volume even while preserving Boussinesq dynamics. This numerical improvement, or post-simulation analysis with similar intent (Griffies and Greatbatch, 2012), has greatly improved the directness of sea level change estimation within the model framework.
In CMIP5, most boussinesq models archive a masso variable that varies due to both barystatic and steric factors (i.e. volo is conserved in the absence of freshwater fluxes and thus density changes are reflected in masso). The difference between rhovolo and masso therefore gives the steric contribution. It doesn't always match zossga, which might be (I'm honestly not sure) due to the fact that the rhovolo and masso difference only captures the global steric effect and not the full non-Boussinesq steric effect described by Griffies and Greatbatch (2012).
\cite{Heuze2015} have a good list of models that have similar atmospheric or ocean model components.
"Physical processes that impact the evolution of global mean sea level in ocean climate models"
*They talk about a non-Boussinesq steric effect (i.e. reorganisation of ocean mass can change the sea level) which I haven't considered.
It looks like there are two types of Boussinesq models. Those where the density (and thus mass) changes in response to steric processes, and those where volume and mass vary together (i.e. constant density). Papers such as Griffies & Greatbatch (2012) only really talk the case where density changes. They document "D.3.3. Adjusting for the spurious mass source", so I'm wondering whether some models (like ACCESS) did this when they submitted their masso variable?
The Boussinesq approximation is commonly made for ocean climate models (see Table 1), whereby the kinematics is approximated by those of a volume conserving fluid. The volume of a Boussinesq ocean changes in the presence of precipitation, evaporation, or runoff, and remains constant if the net volume of water added to the global ocean vanishes. In contrast, the mass of a Boussinesq ocean generally changes even without a boundary mass flux, since density changes translate into mass changes in a volume conserving fluid.
Rather than conserving mass, the Boussinesq fluid conserves volume, which is realized by introducing a nonzero mass source/sink to the Boussinesq fluid. That is, for a volume conserving Boussinesq ocean, in the absence of surface boundary fluxes, so that seawater mass picks up a spurious source associated with changes in global mean density. Consequently, if the density changes, the Boussinesq mass changes, even when there are zero fluxes of mass across the ocean boundaries. For example, when the ocean warms with a positive thermal expansion coefficient, then density decreases. In order to maintain a constant volume for the Boussinesq fluid, there must in turn be a decrease in ocean mass when density decreases. We consider this change in mass to be physically spurious, since it is not a process that appears in the real ocean. Nonetheless, it is a process that occurs in Boussinesq ocean models, and must be considered when examining their mass budget. In particular, if interested in the mass distribution of seawater, such as needed for angular momentum (Bryan, 1997), bottom pressure (Ponte, 1999), or geoid perturbations (Kopp et al., 2010), one must account for this spurious mass change that arises due to the oceanic Boussinesq approximation.
Nearly all IPCC-class ocean models constructed during the past decade have eliminated the rigid lid method, which contrasts to the dominance of rigid lid methods until the mid-1990s.
Boussinesq models conserve volume but not mass.
An increasing number of ocean models have removed the Boussinesq approximation, and so are now mass conserving non-Boussinesq models. One benefit of non-Boussinesq models is that the sea level height is more accurate, since these models include steric effects within the prognostic equations.
If there are no net boundary fluxes of volume, then a conservative Boussinesq model will retain a constant total volume to within numerical roundoff. In contrast, a non-Boussinesq model will generally alter its volume in cases where the ocean density changes (i.e., via steric effects).
If there is no net boundary flux of mass, then a non-Boussinesq model ideally should retain a constant total mass to within numerical roundoff. In contrast, a Boussinesq model will generally alter its mass even without boundary fluxes, since Boussinesq fluids conserve volume rather than mass.
It is thus important that the “comments” attribute for this variable (zos) contain information regarding whether the field was obtained from a Boussinesq or non-Boussinesq ocean model simulation.
Non-Boussinesq models contain all ocean effects (including steric) within the ocean acting on the sea level. Hence, the field global average sea level change in a non-Boussinesq model is determined from its global averaged sea level increment. In contrast, for a Boussinesq model, the steric effect must be diagnosed and then added to the model’s global mean sea level. Please note in the “comment” attribute any assumptions or methodological details related to calculation of this time-series.
The field global average thermosteric sea level change represents that part of the global mean sea level change due to changes in ocean density arising just from changes in temperature. In the following endnote, we offer definition of this field.14 For many purposes the sea level rise under a warming planet is dominated by thermal effects, in which case the steric and thermosteric contributions are nearly the same. However, saline effects become nontrivial as increasing fresh water melt enters the ocean, thus making it important to distinguish all three contributions
Models that employ a virtual salt flux, and so do not allow for the transfer of water mass across the liquid ocean boundary, will report zero for each of these fields (i.e. the water flux fields like wfo)
The first term in equation (4.40) alters sea level by adding or subtracting mass from the ocean, with the name eustatic associated with these processes. The second term arises from temporal changes in the global mean density; i.e., from steric effects. The steric effect is missing in Boussinesq models, so that the global mean sea level in a Boussinesq model is altered only by net volume fluxes across the ocean surface. (They do however derive the steric influence and add it to their change in global sea level variable.)
OGCMs in early times are usually formulated under the rigid lid approximation with a virtual salt flux at the ocean surface. However, there have only two models (CanESM2 and CSIROMk3-6-0) using this approximation, and six models (CanESM2, CSIRO-Mk3-6-0, CCSM4, CESM1-BGC, NorESM1-M and NorESM1-ME) using a virtual salt flux. Other models employ a free surface scheme with explicit freshwater fluxes on the ocean surface.
Marsland2013:
As described in Bi et al. (2013b),the ACCESS-OM uses the Boussinesq approximation so the ocean interior is volume conserving. However, the surface freshwater fluxes are real mass fluxes, which allows the ocean volume to change according to the balance of precipitation, evaporation, ocean to sea-ice freezing, sea-ice to ocean melting, and river runoff from land. The surface freshwater flux imbalance for the piControl and historical simulations is shown in Bi et al. (2013a). They conclude that the hydrological cycle is not balanced in both ACCESS1.0 and ACCESS1.3, which remains a challenge for future development of the ACCESS-CM. Compared to the respective piControl simulations, there is little difference in the evolution of total ocean salinity in the historical experiments, while all the scenario runs show some freshening relative to their respective piControl simulations, with the exception of the ACCESS1.3 abrupt4xCO2 experiment.
Finally, the opposite responses between ACCESS1.0 and ACCESS1.3 global salinity (Figs 2(c) and 2(d)) and the sea-level evolution related to surface mass fluxes (Figs 14(e) and 14(f)) suggest problems in the closure of the hydrological cycle in both model versions. It remains a challenge for ACCESS-CM to produce a fully closed hydrological cycle across all model components.
Bi et al 2013a: (which is consistent with my analysis)
For the piControl run global ocean volume-averaged salinity, ACCESS1.0 shows a weak decrease whilst ACCESS1.3 undergoes a considerable increase. Examination of the ocean surface fresh water budget (Fig. 15(b)) reveals that both models are losing water.
With a loss rate of 0.121 mm/year, ACCESS1.3 has a sea level decrease of 60.5cm by the end of the 500-year piControl, which largely, but not completely, explains the salinity increase of about 0.007 psu seen in Fig. 17(b). In fact, with the model’s volume conserving configuration (excluding change associated with the surface mass fluxes of freshwater), an increase of 0.00756 psu (from 34.7265 psu to 34.7341 psu) in the global ocean salinity indicates a water volume decrease of 2.896×10^14 m^3, equivalent to a sea level drop of 80.1cm.
In the ACCESS1.0 case, however, the global ocean is freshening throughout the piControl run, despite the ocean surface budget showing a net loss of water (39.2 cm/500 years) from the ocean. These mismatches indicate some unknown leak of water in ACCESS1.3 but a spurious source of water in ACCESS1.0, requiring further investigation. The differences in the non-conservation of hydrology between ACCESS1.0 and ACCESS1.3 impede the diagnosis of the models sea level as discussed in Marsland et al. (2013) and require further investigation.
Bi et al 2013b:
ACCESS-OM is configured as a hydrostatic and Boussinesq (volume conserving) ocean with mass exchange of surface freshwater fluxes.
Griffies2011
Although the ocean model components of CM2.1 and CM3 are formulated using the Boussinesq approximation for which volume rather than mass is conserved in the absence of net boundary fluxes, the simulated dynamic sea level can realistically represent the horizontal gradient of sea level with a globally constant adjustment approximating the more accurate non-Boussinesq sea level (Greatbatch 1994).
Salt within the ocean is constant, except for the small amounts exchanged with the sea ice model
Dufresne2013
"The surface salinity has almost no drift, nor has the sea surface height (about 2 cm/century, not shown), confirming that the water cycle is closed." [I'D SAY THEY NEED TO DIG DEEPER!]
Voldoire2013
The estimation of future sea level rise within climate change frameworks is a challenging task and the conservation of water has been particularly checked when developing the model. In PiCTL, the drift is equal to 21 cm per century and is still therefore far from being negligible compared to the sea level rise estimate of 17 cm over the 20th century from Church and White (2006). The reasons for such a drift are still under investigation. Preliminary results show that the accumulation of snow over glaciers (except over Greenland and Antarctica) is responsible for 40% of this drift. In the next version of the model, the parameterisation already active over Antarctica and Greenland, which avoids such an accumulation, will be activated over all glaciers. Another part of this drift may be related to the erroneous coupling between sea-ice and ocean but, as for salt, it has not been quantified yet.
Bentsen2012
"The long-term mean of E-P is 2.3×10−5mm d−1, confirming a very well balanced fresh water budget of the atmosphere. This is consistent with the virtually negligible drift of global mean salinity discussed above, (they document a slight positive trend) indicating that NorESM conserves the fresh water substance to a large extent."
[THEY CLEARLY HAVEN'T LOOKED AT THEIR WFO OUTPUT]
"With no mass exchange through the ocean surface and assuming balanced freshwater surface fluxes and fairly constant sea ice volume, the global mean salinity should remain close to constant."
Couldn't find anything about water conservation or drift in the papers about the CMCC models (searched for Fogli papers), GFDL-ESM models (Dunne2012), MIROC-ESM (Watanable et al., 2011), MPI-ESM (Jungclaus et al., 2013), CCSM4 (https://journals.ametsoc.org/doi/full/10.1175/JCLI-D-11-00091.1),
Calculate the reference observed trend in atmospheric water content by multiplying the 1990-2019 surface air temperature trend 0.2C/decade, estimated mass of water in the atmosphere (1.2 X 10^16 kg; from raw CMIP6 data) and the Clausius–Clapeyron scaling (7% C−1).
From SenGupta2013: The quantification of drift requires the examination of control simulations in which forcing terms (e.g., solar irradiance, greenhouse gases) are maintained at fixed levels. Any long-term trend in these control simulations will be due to climate drift (and possibly low-frequency variability). Forced simulations that are initialized from these control simulations will therefore also contain a trend component that is spurious and associated with drift.
PRINCIPLE: Most of the models are Boussinesq, which means they conserve volume (rather than mass). That makes it difficult to sensibly analyse the volo (or perhaps even masso) variables. (e.g. The sea level can go up despite the fact that volume doesn't change.) Having said that, perturbations to the global ocean mass should still be internally consistent. In other words, changes to wfo should be reflected in corresponding changes in soga and eustatic sea level (zosga - zossga) (after the removal of drifts and water leaks/non-conservation)
In addition to the piControl simulations, the sensitivity of model imbalances to the presence of external forcings was tested using the historical and rcp85 experiments.
TODO: I need to pull apart why the difference between two decadal climatologies method (e.g. \cite{Levang2015}) is no good for quantities where accumulation is important (e.g. hfds, wfo). That method completely bypasses the need for fitting a polynomial, which is the correct method (I'm not sure that Hobbs or Sen Gupta say that).
- If the change isn't linear (as is common in historical experiments), then the difference between the start and end isn't representative of change over the experiment for variables where cumulative anomalies matter.
Contrary to temperature variations, which mainly result from heat transfer through the sea surface, changes in salinity are not induced by salt fluxes but by ocean volume variations.
Need to consider both drift (incomplete spinup) and conservation (water leaks, missing terms in water budget).
Plot: Timeseries of the comparable quantities on the same plot.
- Comment on the shape of the drift (i.e. is it linear, implying a constant imbalance over time)
- Compare the magnitude of the sea level drift to observed trends
- Comment on moisture conservation (i.e. is the drift at least the same for the various quantities?)
(Need to check if conservation is the same for different external forcing. By definition drift is the same, but it's not obvious that conservation would be.)
Plot: time evolution of the non-conservation term (for wfo vs masso vs soga and volo vs zosga)
- Is it linear, or does the conservation improve/worsen over time?
- PROBLEM: Is the non-conservation term valid if we don't know how the global quantities used to calculate it were constructed?
- PROBLEM: Some models may use virtual salt fluxes, which makes using soga difficult perhaps?
Typically, the effect of moisture non-conservation is accounted for in forced simulations by calculating the non-conservation in piControl (i.e. when you "de-drift" by fitting a polynomial you actually capture the drift and non-conservation in the control run) and removing that value from the forced simulation. This assumes that non-conservation is not sensitive to external forcings. Here we test that assumption...
Plot: Scatter plots of the time mean non-conservation term for piControl and a forced experiment (one dot for each model).
- Use of the time mean relied on the non-conservation being linear?
- If the piControl run represents the imbalance under all forcing scenarios, then the values in the plot should fall along the one-to-one line.
- They go on to analyse the models who don't fall along the line in RCP 8.5.
Another question is whether the magnitude of the energy (moisture) imbalance in the models can impact the magnitude of the forced response for variables that are indirectly related to the energy (moisture) budget. They look at the transient climate response (TCR) which is calculated from the global mean surface temperature, but I guess we could look at water cycle amplification or sea level rise.
Plot: Scatter plot of the time mean of a key control run variable (e.g. masso_anomaly, non-closure term) vs change in sea level at end of 1pctCO2 experiment (for instance)
- The time mean of the key control variable basically represents the drift in that model
- Looking for an obvious relationship between sea level and drift/non-closure
Plot: Scatter plot with dots representing drift removal using different methods. Does it matter which method?
- They calculate the mean dOHC/dt and netTOA for every decade of the dedrifted control run.
- Repeat for different de-drifting methods (linear, quadratic, cubic, highpass filter)
- The dots for each decade/method (dOHC/dt vs netTOA) should fall on a line
I could add something at the end looking at forced run closure after dedrifting? (Like I did in the appendix of the energy budget paper.)
Conclusion: All models need to be dedrifted (except perhaps when considering very strongly forced simulations), some can't even be used after that because there isn't a physically consistent link between variables.
Incorporate the metrics into ESMValTool... https://www.esmvaltool.org/ https://cmip-esmvaltool.dkrz.de/ https://github.com/ESMValGroup/ESMValTool https://esmvaltool.readthedocs.io/en/latest/recipes/index.html (documentation for all the metrics) https://www.geosci-model-dev.net/9/1747/2016/
and/or Coordinated Model Evaluation Capabilities (CMEC) https://cmec.llnl.gov/ https://github.com/PCMDI/CMEC
Eyring2019 gives an overview of all the great model evaluation going on (including ESMValTool and CMEC).
They find that most models have a spurious netTOA imbalance. If the model energy budgets were balanced, then you would expect to see a corresponding change in ocean heat content. However, the change in OHC is typically not consistent with the change in netTOA, which implies significant non-conservation in the models. Most of this occurs in the atmosphere, which means ocean model drift is largely (but not entirely) a physically valid response to the surface heat flux.
In my study I would say that most models display a trend in wfo. If the ocean moisture budget was balanced, you'd expect to see a corresponding change in the mass of the global ocean and also the mean ocean salinity. If that's not typically the case, you could say that ocean model drift (i.e. in mass and salinity) does not, in general, arise as a response to the surface freshwater flux. It's difficult to say why the trend in wfo arises in the first place, because all the relevant source terms (i.e. atmosphere, cryosphere, land) are not archived. It's also not clear exactly how the modelling groups construct global variables such as volo and masso.
Conservation truth in Hobbs paper: netTOA (i.e. netTOA is kind of the truth you're aiming for with dOHC/dt) Conservation truth in this paper: ??? (which representation of ocean mass/volume is "correct")
- The best cases are where masso and volo match. Non-closure with zosga and wfo would then mean missing sea level / water input terms. Non-closure with soga could mean ? Drift truth: it should be zero.