hydroGOF

hydroGOF is an R package that provides S3 functions implementing both statistical and graphical goodness-of-fit measures between observed and simulated values, mainly oriented to be used during the calibration, validation, and application of hydrological models.

Missing values in observed and/or simulated values can be automatically removed before the computations.

Bugs / comments / questions / collaboration of any kind are very welcomed.

Installation

Installing the latest stable version from CRAN:

install.packages("hydroGOF")

Alternatively, you can also try the under-development version from Github:

if (!require(devtools)) install.packages("devtools")
library(devtools)
install_github("hzambran/hydroGOF")

Reporting bugs, requesting new features

If you find an error in some function, or want to report a typo in the documentation, or to request a new feature (and wish it be implemented :) you can do it here

Citation

citation("hydroGOF")

To cite hydroGOF in publications use:

Zambrano-Bigiarini, Mauricio (2024). hydroGOF: Goodness-of-fit functions for comparison of simulated and observed hydrological time series. R package version 0.6-0. URL:https://cran.r-project.org/package=hydroGOF. doi:10.5281/zenodo.839854.

A BibTeX entry for LaTeX users is

@Manual{hydroGOF,
title = {hydroGOF: Goodness-of-fit functions for comparison of simulated and observed hydrological time series},
author = {Zambrano-Bigiarini, Mauricio},
note = {R package version 0.6-0},
year = {2024}, url = {https://cran.r-project.org/package=hydroGOF},
doi = {10.5281/zenodo.839854},
}

Goodness-of-fit measures

Quantitative statistics included in this package are:

me: Mean Error (Hill et al., 2006)
mae: Mean Absolute Error (Hodson, 2022)
mse: Mean Squared Error (Yapo et al., 1996)
rmse: Root Mean Square Error (Willmott and Matsuura, 2005)
ubRMSE: Unbiased Root Mean Square Error (Entekhabi et al., 2010)
nrmse: Normalized Root Mean Square Error
pbias: Percent Bias (Yapo et al., 1996)
rsr: Ratio of RMSE to the Standard Deviation of the Observations (Moriasi et al., 2007)
rSD: Ratio of Standard Deviations
NSE: Nash-Sutcliffe Efficiency (Nash and Sutcliffe, 1970)
mNSE: Modified Nash-Sutcliffe Efficiency (Krause et al., 2005)
rNSE: Relative Nash-Sutcliffe Efficiency (Legates and McCabe, 1999)
wNSE: Weighted Nash-Sutcliffe Efficiency (Hundecha and Bardossy, 2004)
wsNSE: Weighted Seasonal Nash-Sutcliffe Efficiency (Zambrano-Bigiarini and Bellin, A., 2012)
d: Index of Agreement (Willmott, C.J., 1981)
dr: Refined Index of Agreement (Willmott et al., 2012)
md: Modified Index of Agreement (Krause et al., 2005)
rd: Relative Index of Agreement (Krause et al., 2005)
cp: Persistence Index (Kitanidis and Bras, 1980)
rPearson: Pearson correlation coefficient (Pearson, 1920)
R2: Coefficient of determination (Box, 1966)
br2: R2 multiplied by the coefficient of the regression line between \code{sim} and \code{obs} (Krause et al., 2005)
VE: Volumetric efficiency (Criss and Winston, 2008)
KGE: Kling-Gupta efficiency (Gupta et al., 2009)
KGElf: Kling-Gupta Efficiency for low values (Garcia et al., 2017)
KGEnp: Non-parametric version of the Kling-Gupta Efficiency (Pool et al., 2018)
KGEkm: Knowable Moments Kling-Gupta Efficiency (Pizarro and Jorquera, 2024)
sKGE: Split Kling-Gupta Efficiency (Fowler et al., 2018)
APFB: Annual Peak Flow Bias (Mizukami et al., 2019)
HFB: High Flow Bias
rSpearman: Spearman’s rank correlation coefficient (Spearman, 1961)
ssq: Sum of the Squared Residuals (Willmott et al., 2009)
pbiasfdc: PBIAS in the slope of the midsegment of the flow duration curve (Yilmaz et al., 2008)
pfactor: P-factor (Abbaspour et al., 2009)
rfactor: R-factor (Abbaspour et al., 2009)

References

Abbaspour, K.C.; Faramarzi, M.; Ghasemi, S.S.; Yang, H. (2009), Assessing the impact of climate change on water resources in Iran, Water Resources Research, 45(10), W10,434, doi:10.1029/2008WR007615.
Abbaspour, K.C., Yang, J. ; Maximov, I.; Siber, R.; Bogner, K.; Mieleitner, J. ; Zobrist, J.; Srinivasan, R. (2007), Modelling hydrology and water quality in the pre-alpine/alpine Thur watershed using SWAT, Journal of Hydrology, 333(2-4), 413-430, doi:10.1016/j.jhydrol.2006.09.014.
Box, G.E. (1966). Use and abuse of regression. Technometrics, 8(4), 625-629. doi:10.1080/00401706.1966.10490407.
Barrett, J.P. (1974). The coefficient of determination-some limitations. The American Statistician, 28(1), 19-20. doi:10.1080/00031305.1974.10479056.
Chai, T.; Draxler, R.R. (2014). Root mean square error (RMSE) or mean absolute error (MAE)? - Arguments against avoiding RMSE in the literature, Geoscientific Model Development, 7, 1247-1250. doi:10.5194/gmd-7-1247-2014.
Cinkus, G.; Mazzilli, N.; Jourde, H.; Wunsch, A.; Liesch, T.; Ravbar, N.; Chen, Z.; and Goldscheider, N. (2023). When best is the enemy of good - critical evaluation of performance criteria in hydrological models. Hydrology and Earth System Sciences 27, 2397-2411, doi:10.5194/hess-27-2397-2023.
Criss, R. E.; Winston, W. E. (2008), Do Nash values have value? Discussion and alternate proposals. Hydrological Processes, 22: 2723-2725. doi:10.1002/hyp.7072.
Entekhabi, D.; Reichle, R.H.; Koster, R.D.; Crow, W.T. (2010). Performance metrics for soil moisture retrievals and application requirements. Journal of Hydrometeorology, 11(3), 832-840. doi:10.1175/2010JHM1223.1.
Fowler, K.; Coxon, G.; Freer, J.; Peel, M.; Wagener, T.; Western, A.; Woods, R.; Zhang, L. (2018). Simulating runoff under changing climatic conditions: A framework for model improvement. Water Resources Research, 54(12), 812-9832. doi:10.1029/2018WR023989.
Garcia, F.; Folton, N.; Oudin, L. (2017). Which objective function to calibrate rainfall-runoff models for low-flow index simulations?. Hydrological sciences journal, 62(7), 1149-1166. doi:10.1080/02626667.2017.1308511.
Garrick, M.; Cunnane, C.; Nash, J.E. (1978). A criterion of efficiency for rainfall-runoff models. Journal of Hydrology 36, 375-381. doi:10.1016/0022-1694(78)90155-5.
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. doi:10.1016/j.jhydrol.2009.08.003. ISSN 0022-1694.
Gupta, H.V.; Kling, H. (2011). On typical range, sensitivity, and normalization of Mean Squared Error and Nash-Sutcliffe Efficiency type metrics. Water Resources Research, 47(10). doi:10.1029/2011WR010962.
Hahn, G.J. (1973). The coefficient of determination exposed. Chemtech, 3(10), 609-612. Aailable online at: \url{https://www2.hawaii.edu/~cbaajwe/Ph.D.Seminar/Hahn1973.pdf}.
Hodson, T.O. (2022). Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not, Geoscientific Model Development, 15, 5481-5487, doi:10.5194/gmd-15-5481-2022.
Hundecha, Y., Bardossy, A. (2004). Modeling of the effect of land use changes on the runoff generation of a river basin through parameter regionalization of a watershed model. Journal of hydrology, 292(1-4), 281-295. doi:10.1016/j.jhydrol.2004.01.002.
Kitanidis, P.K.; Bras, R.L. (1980). Real-time forecasting with a conceptual hydrologic model. 2. Applications and results. Water Resources Research, Vol. 16, No. 6, pp. 1034:1044. doi:10.1029/WR016i006p01034.
Kling, H.; Fuchs, M.; Paulin, M. (2012). Runoff conditions in the upper Danube basin under an ensemble of climate change scenarios. Journal of Hydrology, 424, 264-277, doi:10.1016/j.jhydrol.2012.01.011.
Knoben, W.J.; Freer, J.E.; Woods, R.A. (2019). Inherent benchmark or not? Comparing Nash-Sutcliffe and Kling-Gupta efficiency scores. Hydrology and Earth System Sciences, 23(10), 4323-4331. doi:10.5194/hess-23-4323-2019.
Krause, P.; Boyle, D.P.; Base, F. (2005). Comparison of different efficiency criteria for hydrological model assessment, Advances in Geosciences, 5, 89-97. doi:10.5194/adgeo-5-89-2005.
Krstic, G.; Krstic, N.S.; Zambrano-Bigiarini, M. (2016). The br2-weighting Method for Estimating the Effects of Air Pollution on Population Health. Journal of Modern Applied Statistical Methods, 15(2), 42. doi:10.22237/jmasm/1478004000.
Legates, D.R.; McCabe, G. J. Jr. (1999), Evaluating the Use of “Goodness-of-Fit” Measures in Hydrologic and Hydroclimatic Model Validation, Water Resour. Res., 35(1), 233-241. doi:10.1029/1998WR900018.
Ling, X.; Huang, Y.; Guo, W.; Wang, Y.; Chen, C.; Qiu, B.; Ge, J.; Qin, K.; Xue, Y.; Peng, J. (2021). Comprehensive evaluation of satellite-based and reanalysis soil moisture products using in situ observations over China. Hydrology and Earth System Sciences, 25(7), 4209-4229. doi:10.5194/hess-25-4209-2021.
Mizukami, N.; Rakovec, O.; Newman, A.J.; Clark, M.P.; Wood, A.W.; Gupta, H.V.; Kumar, R.: (2019). On the choice of calibration metrics for “high-flow” estimation using hydrologic models, Hydrology Earth System Sciences 23, 2601-2614, doi:10.5194/hess-23-2601-2019.
Moriasi, D.N.; Arnold, J.G.; van Liew, M.W.; Bingner, R.L.; Harmel, R.D.; Veith, T.L. (2007). Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Transactions of the ASABE. 50(3):885-900.
Nash, J.E. and Sutcliffe, J.V. (1970). River flow forecasting through conceptual models. Part 1: a discussion of principles, Journal of Hydrology 10, pp. 282-290. doi:10.1016/0022-1694(70)90255-6.
Pearson, K. (1920). Notes on the history of correlation. Biometrika, 13(1), 25-45. doi:10.2307/2331722.
Pfannerstill, M.; Guse, B.; Fohrer, N. (2014). Smart low flow signature metrics for an improved overall performance evaluation of hydrological models. Journal of Hydrology, 510, 447-458. doi:10.1016/j.jhydrol.2013.12.044.
Pizarro, A.; Jorquera, J. (2024). Advancing objective functions in hydrological modelling: Integrating knowable moments for improved simulation accuracy. Journal of Hydrology, 634, 131071. doi:10.1016/j.jhydrol.2024.131071.
Pool, S.; Vis, M.; Seibert, J. (2018). Evaluating model performance: towards a non-parametric variant of the Kling-Gupta efficiency. Hydrological Sciences Journal, 63(13-14), pp.1941-1953. doi:10.1080/02626667.2018.1552002.
Pushpalatha, R.; Perrin, C.; Le Moine, N.; Andreassian, V. (2012). A review of efficiency criteria suitable for evaluating low-flow simulations. Journal of Hydrology, 420, 171-182. doi:10.1016/j.jhydrol.2011.11.055.
Santos, L.; Thirel, G.; Perrin, C. (2018). Pitfalls in using log-transformed flows within the KGE criterion. doi:10.5194/hess-22-4583-2018.
Schaefli, B., Gupta, H. (2007). Do Nash values have value?. Hydrological Processes 21, 2075-2080. doi:10.1002/hyp.6825.
Schober, P.; Boer, C.; Schwarte, L.A. (2018). Correlation coefficients: appropriate use and interpretation. Anesthesia and Analgesia, 126(5), 1763-1768. doi:10.1213/ANE.0000000000002864.
Schuol, J.; Abbaspour, K.C.; Srinivasan, R.; Yang, H. (2008b), Estimation of freshwater availability in the West African sub-continent using the SWAT hydrologic model, Journal of Hydrology, 352(1-2), 30, doi:10.1016/j.jhydrol.2007.12.025.
Sorooshian, S., Q. Duan, and V. K. Gupta. (1993). Calibration of rainfall-runoff models: Application of global optimization to the Sacramento Soil Moisture Accounting Model, Water Resources Research, 29 (4), 1185-1194, doi:10.1029/92WR02617.
Spearman, C. (1961). The Proof and Measurement of Association Between Two Things. In J. J. Jenkins and D. G. Paterson (Eds.), Studies in individual differences: The search for intelligence (pp. 45-58). Appleton-Century-Crofts. doi:10.1037/11491-005.
Tang, G.; Clark, M.P.; Papalexiou, S.M. (2021). SC-earth: a station-based serially complete earth dataset from 1950 to 2019. Journal of Climate, 34(16), 6493-6511. doi:10.1175/JCLI-D-21-0067.1.
Yapo P.O.; Gupta H.V.; Sorooshian S. (1996). Automatic calibration of conceptual rainfall-runoff models: sensitivity to calibration data. Journal of Hydrology. v181 i1-4. 23-48. doi:10.1016/0022-1694(95)02918-4.
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, W09417, doi:10.1029/2007WR006716.
Willmott, C.J. (1981). On the validation of models. Physical Geography, 2, 184–194. doi:10.1080/02723646.1981.10642213.
Willmott, C.J. (1984). On the evaluation of model performance in physical geography. Spatial Statistics and Models, G. L. Gaile and C. J. Willmott, eds., 443-460. doi:10.1007/978-94-017-3048-8_23.
Willmott, C.J.; Ackleson, S.G. Davis, R.E.; Feddema, J.J.; Klink, K.M.; Legates, D.R.; O’Donnell, J.; Rowe, C.M. (1985), Statistics for the Evaluation and Comparison of Models, J. Geophys. Res., 90(C5), 8995-9005. doi:10.1029/JC090iC05p08995.
Willmott, C.J.; Matsuura, K. (2005). Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance, Climate Research, 30, 79-82, doi:10.3354/cr030079.
Willmott, C.J.; Matsuura, K.; Robeson, S.M. (2009). Ambiguities inherent in sums-of-squares-based error statistics, Atmospheric Environment, 43, 749-752, doi:10.1016/j.atmosenv.2008.10.005.
Willmott, C.J.; Robeson, S.M.; Matsuura, K. (2012). A refined index of model performance. International Journal of climatology, 32(13), pp.2088-2094. doi:10.1002/joc.2419.
Willmott, C.J.; Robeson, S.M.; Matsuura, K.; Ficklin, D.L. (2015). Assessment of three dimensionless measures of model performance. Environmental Modelling & Software, 73, pp.167-174. doi:10.1016/j.envsoft.2015.08.012.
Zambrano-Bigiarini, M.; Bellin, A. (2012). Comparing goodness-of-fit measures for calibration of models focused on extreme events. EGU General Assembly 2012, Vienna, Austria, 22-27 Apr 2012, EGU2012-11549-1.

Vignette

Here you can find an introductory vignette illustrating the use of several hydroGOF functions.

R: a statistical environment for hydrological analysis (EGU-2010) abstract, poster.
Comparing Goodness-of-fit Measures for Calibration of Models Focused on Extreme Events (EGU-2012) abstract, poster.
Using R for analysing spatio-temporal datasets: a satellite-based precipitation case study (EGU-2017) abstract, poster.