RESPONSE TO THE REFEREE'S COMMENTS >abstract is somewhat misleading, since it is not clear that by modeling the background power asymmetry with respect to m at very low frequencies one can significantly improve the accuracy of frequency measurements, where the background is such a small fraction of the signal. Indeed, no improvement can be expected at frequencies higher than 3 mHz, where the backgrpund is small. We extemd the first sentence in the abstract to avoid this confusion. >Moreover, there is no clear indication that the background dependance on m seen at very low frequencies is independent of frequency and valid over the full frequency range. Validity of our model over the full frequency range was not properly explored indeed. We have now extended our data analysis to lowest frequencies, and add one more figure (Fig 4) to Section 4. It reveals clearly the signal coming from supergranulation rotation, wjich makes our analysis inapplicable at frequencies below 200 mkHz. At higher frequencies, it is solar data which shows that the m-dependence stays the same up to 1000 mkHz at least, where the noise measurement is still possible. >I would also recommend that the authors look if the same can be said from GONG and MDI observations, and if these data, using the same scheme returns a similar estimate of the surface differential rotation We have made this analysis with data available from MDI "dynamics" program. The results are discussed in two paragraphs added in Section 3. GONG data are not expected to provide measurements of comparable quality as power spectra are limited by degree l<=200. >Finally, I can't heip wondering if publishing every 8-10 years a paper on modelling solar oscillation power spectra warrants the I, II and III sequencing in the title. We are sorry that the progress is not as fast as it should. But we will appreciate if the title remains as it is. >Beyond fixing the spelling mistakes (like splittimgs ???> splittings, or rated ???> treated, etc.) and spelling inconsistencies (spatio-temporal or spatiotemporal, etc.) that suggests that the authors neglected to properly proofread the manuscript, the presentation needs a lot of work to make it clear for the reader including the referee. We've done our best now to improve presentation. >Specifically, although not extensive: ??? the verb 'address' is overused throughout the manuscript and should be in most instances replaced by a more specific wording. Same for the use of 'suggest'.??? the use of parenthesis and parenthetical remarks is confusing and/or distracting and often inadequate or simply erroneous (like in citations). Corrected. >??? a lot of variables are introduced without being properly defined (like $U$, $V$, $W$, or $P_{s}$, $PA{\ell}_{m}, or $R$, $H$, $T$, etc.) U, V and W are defined explicitly as expansion coefficients in Eq. 2 where they are intruduced, no further definition is actually needed. P_s(z) and P_\ell^m(z) are standard notations for Legendre polynomials and associated Legendre polynominals; however, we add definition of this notation for better clarity after Eqs 15, 16. Notation R, H, T for three leakage matrices is explained immediately after Eq. 22 where they are introduced. We have made a further thorough cheque to ensure that no notation is left unexplained. >??? l.126 & 1.136 explain or justify these assumptions l.126: Indeed, this assumption is formulated badly amd needs clarification. What is expected to be small is the influence of Coriolis forces on the detectable statistically-averaged properties of the velocity field, not on the local turbulent velocities themselves. l.136: Explanation: one can divide the sphere into thin latitudinal belts, assign individual corotating frame to each belt and add up the results. The text is improved with corresponding ammendmenrs and corrections. >??? Eq (14) justify/explain the '???' on the right???hand side, as I would have (naively?) expected a '+' since this is a variance. The equation is just a formal truncated-series expansion of its left-hand side. Derivative in the right-hand side is negative, hence the variance gets bigger at bigger \Omega. >??? I don't understand the last sentence on p.5 starting at l.l73. Please rewrite clearly, avoiding the use of a parenthetical statement. Done. >??? the typography is haphazard, like $\mu Hz$ vs $\mu$Hz, while $Var$ or $Cov$ are at best confusing notations for an operator (vs the operator $ES). Corrected. >??? Fig. 1 could use a better presentation: either 4 panels for the 4 cases (two $\ell$ and the two $\delta\nu$) or two panels (one for each $\ell$), or one panel but plot vs $m/\ell$, and use colors to differentiate the cases (and coul include more frequency ranges and/or values of $\ell$). The figure is redrawn as requested with two panels and with now three frequency ranges. >??? I would avoid using the same symbol, $\Omega$, for both solid angle and rotation rate (i.e., use a different symbol for the solid angle) Symbol for the solid angle is changed to \varpi. >- the "Solar B???angle" is the "heliospheric longitude at disk center", Definition of the B-angle is added (but latitude, not longitude---referee's misprint). >avoid "peak???bagging", use "mode fitting", etc. >??? "Doppler-velocity" ???> Dopplergrams >??? SDO HMI ???> "HMI instrument on SDO", spell out what HMI and SDO stands for and use HMI thereafter. >??? "observational power spectrum" -> "observed power spectrum" >??? "from 360d" ???> "using a 360 day???long time???series" Done. >??? Appendix equations: the appendix should be self-contained, I recommend that the authors include the equations 45, 47, 42, and 44 from their 2005 paper. Done. >??? add'l more specific suggestions: 1.23: error in solar p-modes frequencies -> error in estimating solar p-modes frequencies .24: analyzing the results of prolonged ???> analyzing long .25: a vast amount ???> a large amount .26: data???ana1ysis ???> data analysis .27: to employ ???> to exploit Done. . >71: vector spherical harmonics: vector? Yes, the standard terminology designating an extension of the scalar spherical harmonics >.79 and 1.84 these parenthetical remarks should be eliminated. >.119: let v is -> let v be Done. >.132: 'stationary' is irrelevant Dropped. >.141: expansion of rotation in polynomials pre???date R&L'91, they introduced CG coefs instead of Legendre polynomials Corrected. >1.149: in normalization suggested ???> following the normalization defined Done. >1.172: use a better presentation of a_1,a_3,a_5 and \Omega_l, \Omega_3, \Omega_5, like in a table, although the conversion is defined in eq (20) that really should be listed as 3 eqns. 1.180: again, maybe a table would improve the presentation and pick either synodic or sidereal (the conversion could go to a footnote if really needed). Unfortunately, we do not see a proper way to improve this piece of presentation. Even with conversion synodic-siderial referred to a footnote, a single table would request 3D structure (measurements from convective noise, from frequency splittings, and from correlation tracking). Our limited comparison hardly deserves arranging multiple tables. >1.185: poor presentation, avoid eq in the text >1.195, eq (21) define clearly $B_{\ell,m}$, $B_\ell$ and $\bar{B}$ Done. 1.198: channels? Replaced with "components". 1.244: went out to be the same ???> turned out to be the same? 1.262: a simplistic ???> a simple etc. Done. I can't help pointing out that since two of the authors are native English speakers, and while they could quibble on UK vs US English, they ought to help the first author to carefully review the manuscript and improve it. We have now tried our best. We are most greatful to the referee for the big effort invested to this work.