On the Physical Origin of the Semiannual 1 Component of Surface Air Temperature over 2 Mid-latitude and Subpolar Oceans


 With the understanding that seasonal cycle of the temperature are forced principally by the annually evolving solar irradiance, many previous studies have defined seasonal cycle of surface air temperature (SAT) as the sum of yearly-period sinusoidal component and its harmonics, especially semiannual component. In mid-latitude and subpolar regions, the ratio between the semiannual and annual components of solar irradiance is negligibly small but that of the SAT over oceans is not, which remains to be understood. In this study, a simple energy budget model including main energy sources and sinks of oceanic mixed layer is designed to understand this puzzle. It is revealed that, when the oceanic mixed layer is prescribed as a layer of constant depth, the phase and amplitude of the modeled SAT is not consistent with that of the observation. However, when the annually changing heat capacity of the oceanic mixed layer is included, both the amplitude and phase of the modeled SAT share these of the observed SAT, proving that the semiannual component of SAT over mid-latitude and subpolar oceans is a result of the heat capacity-varying oceanic mixed layer in response to annually evolving solar irradiance.

where a 0 is a non-negative constant, a k non-negative amplitude, φ k the phase 50 ranging from 0 to 2π, τ a the length of a year, and N corresponds to Nyquist 51 frequency. 52 Previously, many studies have made effort to obtain parameters of SAT in 53 Eq.
(1) through analyzing observations or modeled data and to explain the 54 causes or impacts of their changes [e.g. May et al (1992); Thomson (1995); warm seasons (Fig. 1a). In contrast, the phase relation is opposite (Fig. 1c)  In the following, we will answer this question through constructing a sim-127 ple energy budget-based model following first principles and comparing model results with observations. We will show that the model captures both ampli-  In this study, an energy budget-based conceptual model is constructed. This  The governing equation representing this model can be expressed as heat flux in mixed layer, which are essential in this study, are hard to be cal-186 culated directly. For convenience, F is assumed to be constant in our analysis. 187 We will discuss the nature of F at due locations and justify our assumption.  Fourier Transform but ignore components of higher order, i.e.

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S ≈ s 0 + s 1 sin( 2π where τ a is the length of one year, s 0 the yearly mean solar irradiance, and 202 s 1 and s 2 amplitudes of annual and semiannual components. And, to simplify 203 analysis, T 4 is linearized using Taylor expansion near a reference temperature With these simplifications and assuming F to be constant, Eq. (2) can be 207 rewritten as On the Physical Origin of the Semiannual Component of Surface Air Temperature ove After reorganization, we obtained When t is large enough, a stable solution to Eq. (4) is obtained: Compared to the phase in solar irradiation, the semiannual component of SAT S ≈ s 0 + s 1 sin( 2π τ a t + φ s1 ).

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The seasonally varying oceanic mixed layer depth D is now approximated as where d 0 and d 1 are non-negative and φ d ranges from 0 to 2π.

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With above approximations, the solution to Eq. (4) can be expressed as 299 (see Appendix A for more details) and, the amplitude ratio becomes It is noted here that the analytical expression of a ′ 1 is very complicated (see 306 Appendix A) and we use a 1 here instead to obtain a simplified expression. Our 307 numerical calculation later provides more precise results.

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The combination of seasonally varying heat capacity and solar irradiance where ∆D represents the additional part when oceanic mixed layer is deepen- The initial temperature is set to be 290 K in most cases and in each case the 362 model runs for 100 years to make sure that a stable seasonal cycle is achieved.

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The final year of each run is taken as the seasonal cycle to be further analyzed.

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When the seasonality of heat capacity is incorporated, D m is given as .

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Other parameters are assumed to be constant and will be specified in 371 Section 4.2.

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The result of this model run is displayed in Fig. 5d Note that the semiannual part in Eq. (A3) (the forth term on the right-hand-529 side) does not come directly from solar irradiance.

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The solution to this equation is hard to be explicitly expressed. To obtain 531 an approximate solution, we ignore the parameter, d1 d0 sin( 2π τa t + φ d ), in B 4 , 532 which results in the nonlinearity in thermal radiation term. Thus, in a stable 533 solution, T can be expressed in a similar way of Eq. (5):