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One-Dimensional Modeling of the Ocean Upper Layer


           by Viktor Zholudev

In the figs.1A (Left Panel) and A2 (Right Panel) are shown the results of modeling of the the thermal structure of the upper oceanic layer with depth about 125 meters [4A, 5A].



Fig. A1. Hysteresis loops reflecting annual behavior of the potential energy (P) and the temperature (T) vs. heat content (H) of the upper oceanic 125 m one-unit-column of water. Smooth curves modeled: A calculated within the framework of the synoptic model described in [5A]; curves B  are mainly given by all the other known that time models (references are given in [5A]); C  intermediate model. Broken line is observed data [3A]. Numbers at curves mark months.

Fig. A2. Heat flux between the ocean and atmosphere. Smooth curves modeled: 1 corresponds to A of Fig. A1, 2 to C, and 3 to B.

4 and 5 are monthly mean values for two years 1972 and 1973 [3A]. Broken line 6 is the heat flux caused by currents (observed [1A]).

It should be noted that to get these results for annual behavior of the upper ocean the model was used with the same set of empirical constants as for modeling the synoptic variability of the ocean (see [5A] and another page of this website, i.e. Hurricane).


 Earlier Niiler [2A] noted that various models could give identical results that in particular fit the observed oceanic surface temperature (i.e. like variations of T0 (4 to 13 degrees) shown by all the curves, including observational data, on the lower panel of Fig.A1) for the annual trend, but that in such a case calculated heat exchange rate occurred to be 2 times less than observed (it is shown by the “bad” curve 3 on Fig.A2 comparing with data 4 and 5); and taking into account “lateral” heat transfer by currents  (like data 6) did not eliminate this discrepancy. It was found within the framework of the model [5A] (but it was not a feature of the model only), that this discrepancy was greatly smoothed out by including into the model turbulent heat transfer from the near-surface oceanic mixed layer downward (as in [4A] unlike the others models). An interesting conclusion can be seen from these  drawings: The more heat transfer from the atmosphere to the ocean the less maximum temperature of the upper ocean.

It seems that up to recent time, math models are suffering from the failure to include enough heat transfer downwards from the upper mixed layer (e.d. compare temperatures shown in the Fig.4 of GEORGE L. MELLOR, One-Dimensional, Ocean Surface Layer Modeling: A Problem and a Solution, March 2001, JOURNAL OF PHYSICAL OCEANOGRAPHY,  Vol.31, pp.790-809).


1A. Tabata S. An evaluation of the quality of the sea surface temperatures and salinities measured at Station P and Line P in the Northeast Pacific Ocean, J. Phys. Oceanography, 1978, v.8, No.6, p.970-986.

2A. Niiler P.P. One-dimensional models of the seasonal thermocline, In: The Sea, v.6 /Eds. Goldberg E.D. et al. N.Y.L.S.T., 1977, p.97-115.

3A. Oceanographic observations at ocean station P (50o N, 1450 W), vols 54 – 76, Environment Canada, B.C., Marine Sci. Branch, 1972 – 1976.

4A.  V. Zholudev, Modeling of the variability of the upper oceanic layer. Nalchik , 1982, 26 pp. (No.

4528-82, VINITI, 1982, Russia ). VINITI is:   All-Russian Institute of Scientific and Technical Information (

5A. V. Zholudev, A similarity theory for the upper boundary layer of the ocean. Oceanology, 1983, v.23, No.1, p.27-35