text:   variational data assimilation problem",9,"[""We (@DrSarahDance, @amoslawless, @J_A_Waller and Nancy Nichols) have a new paper on arxiv this week!  <LINK>   As is my new tradition, here's an as-non-technical-as-possible overview (this time with GIFs!) 🧵: <LINK>"", 'In my PhD I studied how introducing correlated observation error covariance matrices (OECs) alters mathematical properties of variational data assimilation (DA) problems. DA appears everywhere, but is most well known for its use in weather forecasting. https://t.co/6giUJaexol', 'In this new paper we consider the preconditioned problem - this is where we solve a different but related problem that is computationally cheaper. The standard preconditioner for DA terms puts the OEC matrix in the same term as the background error covariance (BEC) matrix. https://t.co/t2ey0ZXSQW', 'Some maths: we study how cheap/expensive our problem is using a condition number. Large condition number = expensive! \nEigenvalues are properties of a matrix and relate to their condition number - if all the eigenvalues are close the condition no. is small, spread out = large https://t.co/D4jVsBLJh9', 'Previously we found for the UNpreconditioned system (BEC + OEC) that the smallest eigenvalue of the OEC matrix is important theoretically. If the eigenvalue is small, the DA problem is expensive! Numerics show that if we increase this eigenvalue, we can make the DA problem faster https://t.co/9MC6DImF2I', 'For the preconditioned problem (OECxBEC) we found that although the smallest eigenvalue is still important, numerically the DA problem is solved fastest when BEC and OEC have similar properties (e.g. related eigenvalues). https://t.co/pYm5kCJSZ5', ""So if all we care about is a fast solution, we should make BEC and OEC as similar as possible, right? Usually we don't get to choose BEC/OEC - they come from the underlying physics. However, in practice we often have to adapt OEC matrices before we use them. https://t.co/IwnKvrZPuq"", ""Our new theory and results could help us choose how to do this modification - and mean even faster convergence! This is great: OEC information is really important, but can be expensive to use. Better OEC matrices = better weather forecasts (NB I'm not promising better weather!) https://t.co/dPRXKR38G4"", ""Thanks for making it this far! Finishing this paper during COVID-19 times has been difficult. Collaborating virtually has taken some adjustment, and I've found focusing hard (not ideal for editing manuscripts!). But I'm going to celebrate this small win and keep plodding on! https://t.co/NJ4fAI6x05""]",20,10,2389