Find function for standard suite in existing Python library or libraries

[alaws-USGS]

From Sydney:

Metric	Existing Python Lib	Reference
Nash-Sutcliffe efficiency (NSE)	hydroeval, nse	Nash, J. E., & Sutcliffe, J. V. (1970). River flow forecasting through conceptual models part I—A discussion of principles. Journal of hydrology, 10(3), 282-290.
Kling-Gupta efficiency (KGE)	hydroeval, kge	Gupta, H. V., Kling, H., Yilmaz, K. K., & Martinez, G. F. (2009). Decomposition of the mean squared error and NSE performance criteria: Implications for improving hydrological modelling. Journal of hydrology, 377(1-2), 80-91.
logNSE	hydroeval, nse , using transform=’log’	Oudin, L., Andréassian, V., Mathevet, T., Perrin, C., & Michel, C. (2006). Dynamic averaging of rainfall‐runoff model simulations from complementary model parameterizations. Water Resources Research, 42(7).
percent bias	hydroeval, pbias	a measure of the mean tendency of simulated values to be greater or less than associated observed values, units of percent
ratio of standard deviation	Statistics module in Python provides a function known as stdev(), this is just stdev(simulated values) divided by the stdev(observed values)	standard deviation of simulated values divided by the standard deviation of observed values
Pearson Correlation	pearsonr() SciPy function	K. Pearson (1896, 1900, 1920)
Spearman Correlation	spearmanr() SciPy function	Charles Spearman (1904, 1910)
percent bias in midsegment slope of the flow-duration curve (FDC) between Q20-Q70	exists in R package, hydroGOF, pbiasfdc	Yilmaz, K. K., Gupta, H. V., & Wagener, T. (2008). A process‐based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model. Water Resources Research, 44(9).
percent bias in FDC low-segment volume (Q0-Q30)	see below *	Yilmaz, K. K., Gupta, H. V., & Wagener, T. (2008). A process‐based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model. Water Resources Research, 44(9).
percent bias in FDC high-segment volume (Q98-Q100)	see below *	Yilmaz, K. K., Gupta, H. V., & Wagener, T. (2008). A process‐based diagnostic approach to model evaluation: Application to the NWS distributed hydrologic model. Water Resources Research, 44(9).

• The last two metrics from Yilmaz et al 2008 are difficult to find online anywhere (in R or any language). These were coded originally by Erin (on our team) in R. The current calculation of all the Yilmaz metrics in the analysis/stats evaluation notebook needs to be double checked against the R code because I was getting different values and I believe the python version may not be correct.

[alaws-USGS]

From Gene:

I've got all of these stats bundled together into the 'helper' library, so that code does not have to be reproduced in every benchmarking notebook -- and also so that large codeblocks are not needed to define the stat functions each time.

See https://github.com/USGS-python/hytest_notebook_tutorials/issues/7 for the 'helper' library, which includes those stats.