A practical step-by-step guide to wavelet analysis is given, with examples taken from time series of the El Nino–Southern Oscillation (ENSO). The guide includes a comparison to the windowed Fourier transform, the choice of an appropriate wavelet basis function, edge effects due to finite-length time series, and the relationship between wavelet scale and Fourier frequency. New statistical significance tests for wavelet power spectra are developed by deriving theoretical wavelet spectra for white and red noise processes and using these to establish significance levels and confidence intervals. It is shown that smoothing in time or scale can be used to increase the confidence of the wavelet spectrum. Empirical formulas are given for the effect of smoothing on significance levels and confidence intervals. Extensions to wavelet analysis such as filtering, the power Hovmoller, cross-wavelet spectra, and coherence are described. The statistical significance tests are used to give a quantitative measure of change...

https://atoc.colorado.edu/research/wavelets/bams_79_01_0061.pdf

A Practical Guide to Wavelet Analysis.

If model parameterizations of unresolved physics, such as the variety of upper ocean mixing processes, are to hold over the large range of time and space scales of importance to climate, they must be strongly physically based. Observations, theories, and models of oceanic vertical mixing are surveyed. Two distinct regimes are identified: ocean mixing in the boundary layer near the surface under a variety of surface forcing conditions (stabilizing, destabilizing, and wind driven), and mixing in the ocean interior due to internal waves, shear instability, and double diffusion (arising from the different molecular diffusion rates of heat and salt). Mixing schemes commonly applied to the upper ocean are shown not to contain some potentially important boundary layer physics. Therefore a new parameterization of oceanic boundary layer mixing is developed to accommodate some of this physics. It includes a scheme for determining the boundary layer depth h, where the turbulent contribution to the vertical shear of a bulk Richardson number is parameterized. Expressions for diffusivity and nonlocal transport throughout the boundary layer are given. The diffusivity is formulated to agree with similarity theory of turbulence in the surface layer and is subject to the conditions that both it and its vertical gradient match the interior values at h. This nonlocal “K profile parameterization” (KPP) is then verified and compared to alternatives, including its atmospheric counterparts. Its most important feature is shown to be the capability of the boundary layer to penetrate well into a stable thermocline in both convective and wind-driven situations. The diffusivities of the aforementioned three interior mixing processes are modeled as constants, functions of a gradient Richardson number (a measure of the relative importance of stratification to destabilizing shear), and functions of the double-diffusion density ratio, Rρ. Oceanic simulations of convective penetration, wind deepening, and diurnal cycling are used to determine appropriate values for various model parameters as weak functions of vertical resolution. Annual cycle simulations at ocean weather station Papa for 1961 and 1969–1974 are used to test the complete suite of parameterizations. Model and observed temperatures at all depths are shown to agree very well into September, after which systematic advective cooling in the ocean produces expected differences. It is argued that this cooling and a steady salt advection into the model are needed to balance the net annual surface heating and freshwater input. With these advections, good multiyear simulations of temperature and salinity can be achieved. These results and KPP simulations of the diurnal cycle at the Long-Term Upper Ocean Study (LOTUS) site are compared with the results of other models. It is demonstrated that the KPP model exchanges properties between the mixed layer and thermocline in a manner consistent with observations, and at least as well or better than alternatives.

Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization

A Description of a Three-Dimensional Coastal Ocean Circulation Model

Results are presented from a new version of the Hadley Centre coupled model (HadCM3) that does not require flux adjustments to prevent large climate drifts in the simulation The model has both an improved atmosphere and ocean component In particular, the ocean has a 125° × 125° degree horizontal resolution and leads to a considerably improved simulation of ocean heat transports compared to earlier versions with a coarser resolution ocean component The model does not have any spin up procedure prior to coupling and the simulation has been run for over 400 years starting from observed initial conditions The sea surface temperature (SST) and sea ice simulation are shown to be stable and realistic The trend in global mean SST is less than 0009 °C per century In part, the improved simulation is a consequence of a greater compatibility of the atmosphere and ocean model heat budgets The atmospheric model surface heat and momentum budget are evaluated by comparing with climatological ship-based estimates Similarly the ocean model simulation of poleward heat transports is compared with direct ship-based observations for a number of sections across the globe Despite the limitations of the observed datasets, it is shown that the coupled model is able to reproduce many aspects of the observed heat budget

The simulation of SST, sea ice extents and ocean heat transports in a version of the Hadley Centre coupled model without flux adjustments

Considerable evidence has emerged of a sub- stantial decade-long change in the north Pacific atmo- sphere and ocean lasting from about 1976 to 1988. Ob- served significant changes in the atmospheric circula- tion throughout the troposphere revealed a deeper and eastward shifted Aleutian low pressure system in the winter half year which advected warmer and moister air along the west coast of North America and into Alaska and colder air over the north Pacific. Conse- quently, there were increases in temperatures and sea surface temperatures (SSTs) along the west coast of North America and Alaska but decreases in SSTs over the central north Pacific, as well as changes in coastal rainfall and streamflow, and decreases in sea ice in the Bering Sea. Associated changes occurred in the surface wind stress, and, by inference, in the Sverdrup trans- port in the north Pacific Ocean. Changes in the month- ly mean flow were accompanied by a southward shift in the storm tracks and associated synoptic eddy activi- ty and in the surface ocean sensible and latent heat fluxes. In addition to the changes in the physical envi- ronment, the deeper Aleutian low increased the nu- trient supply as seen through increases in total chloro- phyll in the water column, phytoplankton and zoo- plankton. These changes, along with the altered ocean currents and temperatures, changed the migration pat- terns and increased the stock of many fish species. A north Pacific (NP) index is defined to measure the de- cadal variations, and the temporal variability of the in- dex is explored on daily, annual, interannual and de- cadal time scales. The dominant atmosphere-ocean re- lation in the north Pacific is one where atmospheric changes lead SSTs by one to two months. However, strong ties are revealed with events in the tropical Pa- cific, with changes in tropical Pacific SSTs leading SSTs in the north Pacific by three months. Changes in the storm tracks in the north Pacific help to reinforce and maintain the anomalous circulation in the upper tro-

/pdf/decadal-atmosphere-ocean-variations-in-the-pacific-4dbg5vvmr8.pdf

Decadal atmosphere-ocean variations in the Pacific

Measurements indicate that mixing processes are intense in the surface layers of the ocean but weak below the thermocline, except for the region below the core of the Equatorial Undercurrent where vertical temperature gradients are small and the shear is large. Parameterization of these mixing processes by means of coefficients of eddy mixing that are Richardson-number dependent, leads to realistic simulations of the response of the equatorial oceans to different windstress patterns. In the case of eastward winds results agree well with measurements in the Indian Ocean. In the case of westward winds it is of paramount importance that the nonzero heat flux into the ocean be taken into account. This beat flux stabilizes the upper layers and reduces the intensity of the mixing, especially in the cast. With an appropriate surface boundary condition, the results are relatively insensitive to values assigned to constants in the parameterization formula.

Parameterization of Vertical Mixing in Numerical Models of Tropical Oceans

The unexpected and prolonged persistence of warm conditions over the tropical Pacific during the early 1990s can be attributed to an interdecadal climate fluctuation that involves changes in the properties of the equatorial thermocline arising as a result of an influx of water with anomalous temperatures from higher latitudes The influx affects equatorial sea-surface temperatures and hence the tropical and extratropical winds that in turn affect the influx A simple model demonstrates that these processes can give rise to continual interdecadal oscillations

https://science.sciencemag.org/content/sci/275/5301/805.full.pdf

Interdecadal Climate Fluctuations That Depend on Exchanges Between the Tropics and Extratropics

At intervals that vary from 2 to 10 yr sea-surface temperatures and rainfall are unusually high and the tradewinds are unusually weak over the tropical Pacific Ocean. These Southern Oscillation El Nino events which devastate the ecology of the coastal zones of Ecuador and Peru, which affect the global atmospheric circulation and which can contribute to severe winters over northern America, often develop in a remarkably predictable manner. But the event which began in 1982 has not followed this pattern.

El Niño Southern Oscillation phenomena

Although the distribution of sunshine is symmetrical about the equator, the earth's climate is not. Climatic asymmetries are prominent in the eastern tropical Pacific and Atlantic Oceans where the regions of maximum sea surface temperature, convective cloud cover, and rainfall are north of the equator. This is the result of two sets of factors: interactions between the ocean and atmosphere that are capable of converting symmetry into asymmetry, and the geometries of the continents that determine in which longitudes the interactions are effective and in which hemisphere the warmest waters and the intertropical convergence zone are located. 'The Ocean-atmosphere interactions are most effective where the thermocline is shallow because the winds can readily affect sea surface temperatures in such regions. The thermocline happens to shoal in the eastern equatorial Pacific and Atlantic, but not in the eastern Indian Ocean, because easterly trade winds prevail over the tropical Atlantic and Pacific wher...

Why the ITCZ Is Mostly North of the Equator

During the early Pliocene, 5 to 3 million years ago, globally averaged temperatures were substantially higher than they are today, even though the external factors that determine climate were essentially the same. In the tropics, El Nino was continual (or "permanent") rather than intermittent. The appearance of northern continental glaciers, and of cold surface waters in oceanic upwelling zones in low latitudes (both coastal and equatorial), signaled the termination of those warm climate conditions and the end of permanent El Nino. This led to the amplification of obliquity (but not precession) cycles in equatorial sea surface temperatures and in global ice volume, with the former leading the latter by several thousand years. A possible explanation is that the gradual shoaling of the oceanic thermocline reached a threshold around 3 million years ago, when the winds started bringing cold waters to the surface in low latitudes. This introduced feedbacks involving ocean-atmosphere interactions that, along with ice-albedo feedbacks, amplified obliquity cycles. A future melting of glaciers, changes in the hydrological cycle, and a deepening of the thermocline could restore the warm conditions of the early Pliocene.

/pdf/the-pliocene-paradox-mechanisms-for-a-permanent-el-nino-2tj90kqj20.pdf

Samuel Philander

Papers

Parameterization of Vertical Mixing in Numerical Models of Tropical Oceans

Interdecadal Climate Fluctuations That Depend on Exchanges Between the Tropics and Extratropics

El Niño Southern Oscillation phenomena

Why the ITCZ Is Mostly North of the Equator

The Pliocene paradox (mechanisms for a permanent El Niño).