. Author manuscript; available in PMC: 2019 Sep 1.

Published in final edited form as: Water Resour Res. 2018 Jul 17;54(9):6374–6392. doi: 10.1029/2017WR020991

Table 3:

Breakdown of the information-use efficiency metrics from an EnKF assimilation of LPRM retrievals into the Noah-MP land surface model as evaluated against SCAN data.

Measurement	Metric	Value
Info in model simulations^a	$\frac{I (Z; X)}{H (Z)}$	0.13
Info in retrievals^a	$\frac{I (Z; Y)}{H (Z)}$	0.08
Conditional info in retrievals^a	$\frac{I (Z; Y \| X)}{H (Z)}$	0.05
Total info from model and retrievals^a	$\frac{I (Z; X, Y)}{H (Z)}$	0.18
Fraction of retrieval info lost via CDF-matching	$1 - \frac{I (Z; Y^{C D F} \| X)}{I (Z; Y \| X)}$	0.11
Info from EnKF	$\frac{I (Z; X^{+})}{H (Z)}$	0.13
Efficiency of EnKF (𝜀_DA)	$\frac{I (Z; X^{+})}{I (Z; X, Y)}$	0.72
Efficiency of EnKF (𝜀_y)	$\frac{I (Z; X^{+}) - I (Z; X)}{I (Z; Y \| X)}$	0.03

Information metrics are normalized by the total entropy of the evaluation data Z so that their values range between zero and one. They are interpreted as, for example, “the fraction of total uncertainty about measurements Z that can be resolved given Y and X.”