# Nash-Sutcliffe model efficiency (NSE)

### Description

This function computes the Nash-Sutcliffe model efficiency (NSE) or "Nash and Sutcliffe’s coefficient of efficiency (E)".

### Usage

1 |

### Arguments

`predicted` |
numeric vector that contains the model predicted data points (1st parameter) |

`observed` |
numeric vector that contains the observed data points (2nd parameter) |

`na.rm` |
logical vector that determines whether the missing values should be removed or not. |

### Details

NSE or E is expressed as

*E = 1 - \frac{∑ \limits_{i=1}^n{≤ft(P_i - O_i\right)^2}}{∑ \limits_{i=1}^n{≤ft(O_i - \bar{O}\right)^2}}*

*E*"Nash and Sutcliffe’s coefficient of efficiency (E)"

*n*the number of observations

*P*the "model estimates or predictions"

*O*the "pairwise-matched observations that are judged to be reliable"

*\bar{O}*the "true" mean of the observations

Note: Both P and O should have the same units.

"Nash and Sutcliffe’s coefficient of efficiency (E)" and other "dimensionless measures of average error" are fully discussed in the Willmott reference.

### Value

Nash-Sutcliffe model efficiency (NSE) as a numeric vector. The
default choice is that any NA values will be kept (`na.rm = FALSE`

). This can
be changed by specifying `na.rm = TRUE`

, such as `vnse(pre, obs, na.rm = TRUE)`

.

### Source

r - Better error message for stopifnot? - Stack Overflow answered by Andrie on Dec 1 2011. See http://stackoverflow.com/questions/8343509/better-error-message-for-stopifnot.

### References

Cort J. Willmott, Scott M. Robeson, and Kenji Matsuura, "A refined index of model performance", *International Journal of Climatology*, Volume 32, Issue 13, pages 2088-2094, 15 November 2012, http://onlinelibrary.wiley.com/doi/10.1002/joc.2419/pdf.

### See Also

`mape`

for mean absolute percent error (MAPE), `mae`

for
mean-absolute error (MAE), `madstat`

for mean-absolute deviation (MAD), `dr`

for "index of agreement (dr)", and `rmse`

for root mean square error (RMSE).

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 | ```
library(ie2misc)
obs <- 1:10 # observed
pre <- 2:11 # predicted
vnse(pre, obs)
require(stats)
set.seed(100) # makes the example reproducible
obs1 <- rnorm(100) # observed
pre1 <- rnorm(100) # predicted
# using the vectors pre1 and obs1
vnse(pre1, obs1)
# using a matrix of the numeric vectors pre1 and obs1
mat1 <- matrix(data = c(obs1, pre1), nrow = length(pre1), ncol = 2,
byrow = FALSE, dimnames = list(c(rep("", length(pre1))),
c("Predicted", "Observed")))
vnse(mat1[, 2], mat1[, 1])
# mat1[, 1] # observed values from column 1 of mat1
# mat1[, 2] # predicted values from column 2 of mat1
# using a data.frame of the numeric vectors pre1 and obs1
df1 <- data.frame(obs1, pre1)
vnse(df1[, 2], df1[, 1])
# df1[, 1] # observed values from column 1 of df1
# df1[, 2] # predicted values from column 2 of df1
# using a data.table of the numeric vectors pre1 and obs1
df2 <- data.table(obs1, pre1)
vnse(df2[, 2, with = FALSE][[1]], df2[, 1, with = FALSE][[1]])
# df2[, 1, with = FALSE][[1]] # observed values from column 1 of df2
# df2[, 2, with = FALSE][[1]] # predicted values from column 2 of df2
``` |

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