Presently we use individual TROPOMI observations in the observation vector y, and compare to the Kx from GEOS-Chem with TROPOMI operator applied. But there are typically manyTROPOMI observations per GEOS-Chem grid cell per day, and we could average them to reduce the size of y and resulting SO. We haven’t done it this way because the TROPOMI avker (and hence the TROPOMI operator) is different for each observation, but that’s not a good reason. Averaging would help reduce the dimensions of y and SO, and decrease the error correlation within SO that partly contributes to our need for the regularization coefficient gamma. Here’s how to do it:
Continue to apply the TROPOMI operator to the GEOS-Chem fields for each observation – no change here.
Average the observations for each grid cell and day to populate y and correspondingly average the simulated TROPOMI observations to populate Kx.
Keep track of the number of observations being averaged so that we can adjust SO – we don’t have a formula for that yet, but Zhen’s current work on error characterization will give us that.
From Daniel:
Presently we use individual TROPOMI observations in the observation vector y, and compare to the Kx from GEOS-Chem with TROPOMI operator applied. But there are typically manyTROPOMI observations per GEOS-Chem grid cell per day, and we could average them to reduce the size of y and resulting SO. We haven’t done it this way because the TROPOMI avker (and hence the TROPOMI operator) is different for each observation, but that’s not a good reason. Averaging would help reduce the dimensions of y and SO, and decrease the error correlation within SO that partly contributes to our need for the regularization coefficient gamma. Here’s how to do it:
Continue to apply the TROPOMI operator to the GEOS-Chem fields for each observation – no change here. Average the observations for each grid cell and day to populate y and correspondingly average the simulated TROPOMI observations to populate Kx. Keep track of the number of observations being averaged so that we can adjust SO – we don’t have a formula for that yet, but Zhen’s current work on error characterization will give us that.