Daniel Zhengyu Huang (黄政宇)

What are these new changes?

Hi Bendong @TanBendong, Thank you for your interest！Yes, so far UKI only estimates mean and covariance of the posterior distribution. It performs good when the posterior is close to Gaussian....

For the cosine bells case (12 day / 1200 steps, ne = 16): element 23 has smallest averaged q, -5.4674658761003794e-5, all nodal values are negative [-5.064671434859331e-5 -5.501461995104535e-5 -5.501461995104534e-5 -5.4975440065034456e-5; -4.964183135120574e-5...

For the cosine bells case (120 day / 12000 steps, ne = 16): element 1118 has smallest averaged q,-0.004942804044896136, all nodal values are negative [-0.005017511375060559 -0.005011217573981225 -0.004867585800051765 -0.004691781410777255; -0.004890483207688044 -0.004898234251674527...

Suggestions from Mark Taylor: 1. check that whether it is due to that the roundoff accumulates over long times 2. Comparison with E3SM, "In E3SM, we still maintain the ability...

@valeriabarra @akshaysridhar @simonbyrne @charleskawczynski When you have time could you review this issue? Let me know whether the clipping method makes sense for you.

> Thanks Daniel. I think in the very first paragraph, you meant Q, tracer mass. Correct? Not tracer only Yes, thanks!

> The quadrature weights should also contain the Jacobian |dXdx| including the vertical distance. Yes, I agree! I think the algorithm preserves the total mass, and tracer mass, so it...

> @Zhengyu-Huang how does this integrate with the timestepper? i.e. at what point do they apply these? They apply it after Euler step, I think it corresponds to each RK...

> For implementation A, what is the sum over for `dqρw`? It it the sum of `dq*ρ*w`, so that the same of `q*ρ*w` will be addmass in the last step