Table 1 Description of the performance metrics considered in this systematic review

Marginal aspects (point estimates) of precipitation and temperature

1

Relative error or bias of the mean or a particular percentile (5th, 10th, 90th, 95th, other)

RME

or

AME

Relative or absolute difference between the observed mean or percentile determined from the observation source and the values obtained with the downscaled model (s)

Relative (−), bias in (mm) or (°C)

2

Relative error of the variance of precipitation and/or temperature

RVE

Relative difference between the observed variance and variance obtained with the downscaled model (s)

(-)

3

Relative error/ bias of a specific return level or period (i.e. 20-year, 30-year, 10-season)

RTE

or

ATE

Relative or absolute difference between the observed value for a specific return period and the value obtained for that same return period with the downscaled model (s)

Relative (−), bias in (mm) or (°C)

4

Bias in the number of threshold exceedances

AEE

Absolute difference between the number of times a threshold is exceeded in the observations and the value obtained with the downscaled model (s)

Threshold in (mm) or (°C) # of exceedances (−)

Temporal aspects or time series analysis

5

Mean squared error

MSE

The average squared difference between the observed values and the downscaled values

(mm²) or (°C²)

6

Coefficient of determination

R²

A number between − 1 and + 1 that measures the strength of the linear relationship between the observed and the downscaled time series

(−)

7

Percentage bias

PBIAS

The average amount that the downscaled numbers is greater or lower than the observed values, expressed as a percentage of the observed value

(%)

8

Bias in the mean (or any percentile) of spell length distribution

ME-SL

The duration of wet/dry spell lengths is analyzed with their distribution. Thus, the index quantifies the absolute difference between the observed mean (or any percentile) and the value obtained with the downscaled model (s)

(# of days)

9

Relative error/bias error of the minimum/maximum of the annual cycle

REMM

or

AEMM

Relative or absolute difference between the observed maximum/minimum value in the year and the correspondent value obtained with the downscaled model (s)

Relative (−), bias in (mm) or (°C)

Multivariable aspects (relation between precipitation/temperature with other variables)

10

Bias in the Pearson/rank correlation coefficient

ME-PRC

Absolute difference between the Pearson/Rank correlation coefficient in the observations and the downscaled model (s)

(−)

11

Bias in the probability of joint exceedance

ME-PJE

Absolute difference between the observed probability of joint exceedance and the probability from the downscaled model (s)

(−)