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fix for misapplication of perturbation delta in jacobian sensitivity …
…calculation (#290) When we calculate our jacobian matrix we do the following calculation: sensitivity_xch4 = delta_xch4 / perturbation where the perturbation is the fractional change from the original emissions eg. 50% perturbation translates to a perturbation = 0.5. However, in HEMCO_Config.rc, when we apply the perturbation, a 50% perturbation is represented by a scale factor of 1.5. Since the introduction of #226, we did not account for this difference between the representations of the perturbation in HEMCO vs in the jacobian calculation. This introduces an error in the jacobian calculation. Luckily, since the emission perturbations are relatively high (targeting 1e-08 kg/m2/s) the impact on results should be relatively small. For example, if an emission element was perturbed by 52x, the jacobian calculations goes from sensitivity_xch4 = delta_xch4 / 52 to sensitivity_xch4 = delta_xch4 / 51. This expectation is confirmed by my CONUS work for 2019 which goes from 41.075 --> 40.810 Tg/a. Absolute differences shown in the image below. For OH, we are using a relatively small (10%) perturbation, so this bug matters a lot and would lead to very low sensitivity of OH to the observations in the jacobian. This bugfix addresses this issue for both the emission elements and the OH elements. Co-authored-by: eastjames <[email protected]>
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