IGOR POLYAKOV
Harper L. Simmons and Igor V. Polyakov
Details of this research may be found in our paper [download pdf - Simmons and Polyakov, 2004].
Cumulative effects of model errors may result in drift of a numerical solution and may dominate simulations of climate trends and variability. Artificial terms added to the equation for scalar quantities (like water temperature and salinity) are often employed to drag the numerical solution toward observations. Restoring constrains temperature and/or salinity towards climatological values over some timescale, whereas flux adjustment balances surface fluxes at the ocean-atmosphere interface to maintain integral quantities of scalar variables. These two methods are commonly used in climate simulations. For example, four out of six models used in Arctic Ocean model inter-comparison use restoring [Steele et al., 2001]. There are suggestions that flux adjustment may suppress variability in climate models [Pierce et al., 1995]. However, Duffy et al. [2000], comparing variability of surface air temperature derived from 17 simulations with and without flux adjustment, argued that there is no evidence that flux adjustment suppresses variability. In this study we use an ocean model to show impacts of restoring and flux adjustment on the simulated variability of an idealized Atlantic Ocean.
The model consists of the free surface MOM4.0 z-coordinate ocean model. The domain configuration (Figure 1) aims to imitate the Atlantic Ocean. Potential temperature is our active tracer, initially set to be horizontally uniform with exponential stratification. 1000 years with no restoring or flux adjustment are used for the model spin-up. During this period the model is forced with an annually repeating NCEP-based climatology of daily winds and net atmospheric heat flux. Three 500-year experiments follow the spin-up. In these three experiments, forcing used to spin-up the model is modulated by decadal and multi-decadal modes (Figure 1). The first experiment (denoted as ``NO'') uses no restoring or flux adjustment. In the second experiment (denoted as ``RES3'') surface temperature is restored to values from the end of the spin-up with a 3-month restoring constant. The last experiment (denoted as ``FLAD'') uses flux adjustment for the atmospheric heat based on time-averaged daily heat flux diagnosed from the ``restoring'' part of the RES3 surface net heat flux.
Our modeling experiments show that restoring suppresses variability, causes lagging of phase, and misrepresents nonlinear relations in the model, suppressing overtones. Flux adjustment is less damaging for simulated variability. However, for some important climatic parameters flux adjustment distorts variability in a way similar to restoring. For example, it suppresses low-frequency variability of the meridional overturning circulation and causes a phase shift of multi-decadal mode of the meridional heat transport. Flux adjustment is also selective with regards to nonlinear effects, suppressing some overtones and amplifying others. An important negative effect of flux adjustment found in our simulations is that it may mis-represent physical mechanisms substituting, for example, dynamically-driven meridional heat transport by equivalent amount of heat supplied thermodynamically (i.e. through local surface heat fluxes). Our simple model suggests that restoring provides a poor framework for simulation of climate variability. Flux adjustment may be useful for simulation of some parameters, however there is a danger of suppressing or amplifying modes of variability, creating phase distortions and/or misrepresenting physical mechanisms hidden behind natural variability.
Acknowledgments:
We would like to thank U. Bhatt for help in data preparation and J. Moss for help with illustrations. Comments of J. Walsh and A. Weaver were most useful. This project was supported by the International Arctic Research Center, University of Alaska Fairbanks (IARC-NSF grant #0327664) and Geophysical Fluid Dynamics Laboratory, NOAA.
References:
Duffy, P. B., J. Bell, C. Covey, L. Sloan and CMIP investigators, Effect of flux adjustment on temperature variability in climate models, Geophys. Res. Lett., 27(6), 763-766, 2000.
Pierce, D. W., T. P. Barnett, and U. Mikolajewicz, Competing roles of heat and freshwater fluxes in forcing thermohaline oscillations, J. Phys. Oceanogr., 25, 2046-2064, 1995.
Steele, M., W. Ermold, S. Hakkinen, D. Holland, G. Holloway, M. Karcher, F. Kauker, W. Maslowski, N. Steiner, and J. Zhang, Adrift in the Beaufort Gyre: A model intercomparison, Geophys. Res. Lett., 28(15), 2935-2938, 2001.
Schematic showing the model domain and forcing. Amplitudes of decadal and multi-decadal modes are shown by A_phi and B_phi}, respectively. Arrows for ``RES3'' experiment show restoring of the simulated temperature to the initial condition whereas arrows for ``FLAD'' experiment show correction of the solution by spatially varying but constant in time heat flux.
Time series of detrended basin-averaged water temperature (WTA, top, degC), meridional overturning circulation (MOC, middle, Sv=10^6 m^3/s), and meridional heat transport (MHT, bottom, PW) anomalies relative to the last 400 years of the model integration. WTA from experiments ``NO'' and ``FLAD'' are practically identical whereas WTA variability at periods>10 years is strongly suppressed by restoring (green line in top). There is also a 5-6 year delay of the WTA response to atmospheric forcing in ``RES3'' experiment compared with WTA from ``NO'' and ``FLAD'' experiments. MOC variability is much more complex than the WTA variability, with stronger decadal mode in all time series and pronounced differences between MOC from ``NO'', ``FLAD'', and ``RES3'' experiments. The MOC phase shift from the ''FLAD'' experiment is modest relative to ''NO'' , with the multi-decadal mode from ``RES3'' experiment lagging those from ``NO'' and ``FLAD'' experiments (middle). Surprisingly, the MHT from ``FLAD'' and ``RES3'' (not ``NO'') experiments show coordinated set of changes with concerted envelopes of multi-decadal mode. These envelopes delay those from ``NO'' experiment by approximately 5 years.
Power spectra of the water temperature (top), meridional overturning circulation (middle), and meridional heat transport (bottom). Vertical bars show 95% confidence intervals. Spectral analysis shows that the effect of restoring is similar to that of high-pass filter (top, green line (``RES3'') is lower than blue (``NO'') and red (``FLAD'') lines at periods >20 years. Restoring damps MOC variability at almost all frequencies (green line, middle which is lower relative to other curves). Flux adjustment is more selective, suppressing low frequencies only (>50yrs). At basin-wide scale, restoring and flux adjustment do not suppress intensity of decadal and multi-decadal modes of variability (bottom) however, restoring damps variability at periods >50 years. Flux adjustment amplifies almost every frequency peak.
(Top) Meridional heat transport (MHT (TW), color) and vertically-averaged circulation anomalies (``NO'' experiment) for the negative phase of the MHT multi-decadal variability. (Middle and bottom) The MHT and circulation anomaly differences between ``RES3'' and ``NO'' experiments and ``FLAD'' and ``NO'' experiments, respectively. Anomalies of MHT and vertically-averaged circulation are averaged for a negative phase of the MHT multi-decadal mode (years 435-460, see Figure 2, bottom). The anomalies are calculated relative to a mean over a complete 50-year cycle (435-485). Because of shift of phase between MHT in "RES3" and "FLAD" experiments compared with ``NO'' experiment, MHC and circulation anomalies and means for ``RES3''and ``FLAD'' experiments are calculated instead over model years 418-443 and 418-468.
This figure (top) shows that the multi-decadal MHT and circulation variability is strong in the Northern Hemisphere with intensive variability of hemisphere-wide cyclonic gyre supplying the north-east part of the basin with heat (red color in the upper right corner of the upper panel). Both restoring (middle panel) and flux adjustment (bottom panel) partially suppress this variability. For example, multi-decadal variability of the idealized ``Gulf Stream'' (lower part of the cyclonic gyre) is weakened by restoring and flux adjustment with reduced MHT variations. Since the advective northeastward heat transport is suppressed in ``FLAD'' experiment, there should be other means by which the system maintains an appropriate level of low-frequency WTA in the idealized North Atlantic. Surface heat flux diagnozed from experiments with restoring and used for flux adjustment provides these means: this flux does not exceed 1-2 W/m^2, however, local values over the ``Gulf Stream'' area are as high as 10-15 W/m^2. This suggests that flux adjustment mis-represents physical mechanisms substituting, for example, dynamically-driven meridional heat transport by equivalent amount of heat supplied thermodynamically (i.e. locally, through surface heat fluxes).
Last modified: July 23, 2004. 13:45:10 pm