Level 4: Fitted Photospheric Flow Profiles for modelers

coeff_mf.txt and error_coeff_mf.txt have the Legendre fitting coefficients and the fitting uncertainties respectively for the corrected baseline meridional flow on the same latitude-time grid as Level 3 flow profiles. Similar coefficients for solar rotation rate are in coeff_dr.txt and error_coeff_dr.txt. The rotation rate is in Carrington frame of reference. Unit: m/s.

These are the coefficients of associated Legendre polynomials with order 1 and degrees 1 to 6 calculated as a function of time. The associated Legendre Polynomials are:

x = sind(info.lat(:,1));
x2 = cosd(info.lat(:,1));
p1 = x2;
p2 = 2*x.*x2;
p3 = .726*(5*x.^2-1).*x2 ;
p4 = 1*(7*x.^3-3*x).*x2 ;
p5 = .583*(21*x.^4-14*x.^2 +1).*x2 ;
p6 = .842*(33*x.^5 - 30*x.^3 + 5*x).*x2 ;

`coeff_mf.txt` 与 `error_coeff_mf.txt` 分别存储了经校正的基线子午流在与三级（Level 3）流廓线相同的纬圈-时间网格上的勒让德拟合系数（Legendre fitting coefficients）与拟合不确定度。针对太阳自转速率的同类系数存储于 `coeff_dr.txt` 与 `error_coeff_dr.txt` 中。自转速率采用卡林顿参考系（Carrington frame of reference），单位为米每秒（m/s）。

以下为阶数为1、次数为1至6的关联勒让德多项式（associated Legendre polynomials）的系数，其计算结果以时间为函数。所用关联勒让德多项式形式如下：
x = sind(info.lat(:,1));
x2 = cosd(info.lat(:,1));
p1 = x2;
p2 = 2*x.*x2;
p3 = .726*(5*x.^2-1).*x2 ;
p4 = 1*(7*x.^3-3*x).*x2 ;
p5 = .583*(21*x.^4-14*x.^2 +1).*x2 ;
p6 = .842*(33*x.^5 - 30*x.^3 + 5*x).*x2 ;