hydroGOF-package: Goodness-of-fit (GoF) functions for numerical and graphical...
In hydroGOF: Goodness-of-Fit Functions for Comparison of Simulated and Observed Hydrological Time Series
hydroGOF-package R Documentation
Goodness-of-fit (GoF) functions for numerical and graphical comparison of simulated and observed time series, mainly focused on hydrological modelling.
Description
S3 functions implementing both statistical and graphical goodness-of-fit measures between observed and simulated values, to be used during the calibration, validation, and application of hydrological models.
Missing values in observed and/or simulated values can be removed before computations.
Details
Package: hydroGOF
Type: Package
Version: 0.6-0
Date: 2024-05-08
License: GPL >= 2
LazyLoad: yes
Packaged: Wed 08 May 2024 05:13:53 PM -04 ; MZB
BuiltUnder: R version 4.4.0 (2024-04-24) -- "Puppy Cup" ;x86_64-pc-linux-gnu (64-bit)
Quantitative statistics included in this package are:
me Mean Error
mae Mean Absolute Error
mse Mean Squared Error
rmse Root Mean Square Error
ubRMSE Unbiased Root Mean Square Error
nrmse Normalized Root Mean Square Error
pbias Percent Bias
rsr Ratio of RMSE to the Standard Deviation of the Observations
rSD Ratio of Standard Deviations
NSE Nash-Sutcliffe Efficiency
mNSE Modified Nash-Sutcliffe Efficiency
rNSE Relative Nash-Sutcliffe Efficiency
wNSE Weighted Nash-Sutcliffe Efficiency
wsNSE Weighted Seasonal Nash-Sutcliffe Efficiency
d Index of Agreement
dr Refined Index of Agreement
md Modified Index of Agreement
rd Relative Index of Agreement
cp Persistence Index
rPearson Pearson correlation coefficient
R2 Coefficient of determination
br2 R2 multiplied by the coefficient of the regression line between sim and obs
VE Volumetric efficiency
KGE Kling-Gupta efficiency
KGElf Kling-Gupta Efficiency for low values
KGEnp Non-parametric version of the Kling-Gupta Efficiency
KGEkm Knowable Moments Kling-Gupta Efficiency
sKGE Split Kling-Gupta Efficiency
APFB Annual Peak Flow Bias
HFB High Flow Bias
rSpearman Spearman's rank correlation coefficient
ssq Sum of the Squared Residuals
pbiasfdc PBIAS in the slope of the midsegment of the flow duration curve
pfactor P-factor
rfactor R-factor
----------------------------------------------------------------------------------------------------------
Author(s)
Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>
Maintainer: Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>
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: 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.
See Also
https://CRAN.R-project.org/package=hydroPSO
https://CRAN.R-project.org/package=hydroTSM
Examples
obs <- 1:100
sim <- obs
# Numerical goodness of fit
gof(sim,obs)
# Reverting the order of simulated values
sim <- 100:1
gof(sim,obs)
## Not run:
ggof(sim, obs)
## End(Not run)
##################
# Loading daily streamflows of the Ega River (Spain), from 1961 to 1970
require(zoo)
data(EgaEnEstellaQts)
obs <- EgaEnEstellaQts
# Generating a simulated daily time series, initially equal to observations
sim <- obs
# Getting the numeric goodness-of-fit measures for the "best" (unattainable) case
gof(sim=sim, obs=obs)
# Randomly changing the first 2000 elements of 'sim', by using a normal
# distribution with mean 10 and standard deviation equal to 1 (default of 'rnorm').
sim[1:2000] <- obs[1:2000] + rnorm(2000, mean=10)
# Getting the new numeric goodness of fit
gof(sim=sim, obs=obs)
# Graphical representation of 'obs' vs 'sim', along with the numeric
# goodness-of-fit measures
## Not run:
ggof(sim=sim, obs=obs)
## End(Not run)
hydroGOF documentation built on Nov. 4, 2024, 5:08 p.m.
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| hydroGOF-package | R Documentation |
Goodness-of-fit (GoF) functions for numerical and graphical comparison of simulated and observed time series, mainly focused on hydrological modelling.
Description
S3 functions implementing both statistical and graphical goodness-of-fit measures between observed and simulated values, to be used during the calibration, validation, and application of hydrological models.
Missing values in observed and/or simulated values can be removed before computations.
Details
| Package: | hydroGOF |
| Type: | Package |
| Version: | 0.6-0 |
| Date: | 2024-05-08 |
| License: | GPL >= 2 |
| LazyLoad: | yes |
| Packaged: | Wed 08 May 2024 05:13:53 PM -04 ; MZB |
| BuiltUnder: | R version 4.4.0 (2024-04-24) -- "Puppy Cup" ;x86_64-pc-linux-gnu (64-bit) |
Quantitative statistics included in this package are:
me Mean Error |
mae Mean Absolute Error |
mse Mean Squared Error |
rmse Root Mean Square Error |
ubRMSE Unbiased Root Mean Square Error |
nrmse Normalized Root Mean Square Error |
pbias Percent Bias |
rsr Ratio of RMSE to the Standard Deviation of the Observations |
rSD Ratio of Standard Deviations |
NSE Nash-Sutcliffe Efficiency |
mNSE Modified Nash-Sutcliffe Efficiency |
rNSE Relative Nash-Sutcliffe Efficiency |
wNSE Weighted Nash-Sutcliffe Efficiency |
wsNSE Weighted Seasonal Nash-Sutcliffe Efficiency |
d Index of Agreement |
dr Refined Index of Agreement |
md Modified Index of Agreement |
rd Relative Index of Agreement |
cp Persistence Index |
rPearson Pearson correlation coefficient |
R2 Coefficient of determination |
br2 R2 multiplied by the coefficient of the regression line between sim and obs |
VE Volumetric efficiency |
KGE Kling-Gupta efficiency |
KGElf Kling-Gupta Efficiency for low values |
KGEnp Non-parametric version of the Kling-Gupta Efficiency |
KGEkm Knowable Moments Kling-Gupta Efficiency |
sKGE Split Kling-Gupta Efficiency |
APFB Annual Peak Flow Bias |
HFB High Flow Bias |
rSpearman Spearman's rank correlation coefficient |
ssq Sum of the Squared Residuals |
pbiasfdc PBIAS in the slope of the midsegment of the flow duration curve |
pfactor P-factor |
rfactor R-factor |
| ---------------------------------------------------------------------------------------------------------- |
Author(s)
Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>
Maintainer: Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>
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: 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
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See Also
https://CRAN.R-project.org/package=hydroPSO
https://CRAN.R-project.org/package=hydroTSM
Examples
obs <- 1:100
sim <- obs
# Numerical goodness of fit
gof(sim,obs)
# Reverting the order of simulated values
sim <- 100:1
gof(sim,obs)
## Not run:
ggof(sim, obs)
## End(Not run)
##################
# Loading daily streamflows of the Ega River (Spain), from 1961 to 1970
require(zoo)
data(EgaEnEstellaQts)
obs <- EgaEnEstellaQts
# Generating a simulated daily time series, initially equal to observations
sim <- obs
# Getting the numeric goodness-of-fit measures for the "best" (unattainable) case
gof(sim=sim, obs=obs)
# Randomly changing the first 2000 elements of 'sim', by using a normal
# distribution with mean 10 and standard deviation equal to 1 (default of 'rnorm').
sim[1:2000] <- obs[1:2000] + rnorm(2000, mean=10)
# Getting the new numeric goodness of fit
gof(sim=sim, obs=obs)
# Graphical representation of 'obs' vs 'sim', along with the numeric
# goodness-of-fit measures
## Not run:
ggof(sim=sim, obs=obs)
## End(Not run)
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