From 3cc174502a2eb701c2b5a59d6c37db6d8cc0edc8 Mon Sep 17 00:00:00 2001 From: Benjamin Thomas Schwertfeger Date: Thu, 1 Feb 2024 17:01:40 +0100 Subject: [PATCH] extend DQM formula --- doc/src/methods.rst | 22 +++++++++++++++++----- 1 file changed, 17 insertions(+), 5 deletions(-) diff --git a/doc/src/methods.rst b/doc/src/methods.rst index 5b3d575..f6151db 100644 --- a/doc/src/methods.rst +++ b/doc/src/methods.rst @@ -13,6 +13,8 @@ The Linear Scaling bias correction technique can be applied on stochastic and non-stochastic climate variables to minimize deviations in the mean values between predicted and observed time-series of past and future time periods. +This method requires that the time series can be grouped by ``time.month``. + Since the multiplicative scaling can result in very high scaling factors, a maximum scaling factor of 10 is set. This can be changed by passing the desired value to the hidden ``max_scaling_factor`` argument. @@ -76,6 +78,8 @@ The Variance Scaling bias correction technique can be applied only on non-stochastic climate variables to minimize deviations in the mean and variance between predicted and observed time-series of past and future time periods. +This method requires that the time series can be grouped by ``time.month``. + Since the the scaling by ratio can result in very high scaling factors, a maximum scaling factor of 10 is set. This can be changed by passing the desired value to the hidden ``max_scaling_factor`` argument. @@ -148,6 +152,8 @@ The Delta Method bias correction technique can be applied on stochastic and non-stochastic climate variables to minimize deviations in the mean values between predicted and observed time-series of past and future time periods. +This method requires that the time series can be grouped by ``time.month``. + Since the multiplicative scaling can result in very high scaling factors, a maximum scaling factor of 10 is set. This can be changed by passing the desired value to the hidden ``max_scaling_factor`` argument. @@ -298,7 +304,7 @@ distributional biases between modeled and observed time-series climate data like the regular Quantile Mapping. Detrending means, that the values of :math:`X_{sim,p}` are shifted to the value range of :math:`X_{sim,h}` before the regular Quantile Mapping is applied. After the Quantile Mapping was applied, the -mean is shifted back. Since it does not make sens to take the whole mean to +mean is shifted back. Since it does not make sense to take the whole mean to rescale the data, the month-dependent long-term mean is used. This method must be applied on a 1-dimensional data set i.e., there is only one @@ -315,21 +321,27 @@ equations of Alex J. Cannon and Stephen R. Sobie and Trevor Q. Murdock (2015) Preserve Changes in Quantiles and Extremes?"* (https://doi.org/10.1175/JCLI-D-14-00754.1). -In the following the equations of Alex J. Cannon (2015) are shown (without -detrending; see QM for explanations): +The following equations qre based on Alex J. Cannon (2015) but extended the +shift of :math:`X_{\text{sim},p}(i)`: + +**Shift of value range**: + +.. math:: + + X_{\text{sim},p}^{*DT}(i) = X_{\text{sim},p}(i) + \Delta\mu **Additive**: .. math:: - X^{*QM}_{sim,p}(i) = F^{-1}_{obs,h} \left\{F_{sim,h}\left[X_{sim,p}(i)\right]\right\} + X_{\text{sim},p}^{*DQM}(i) = F_{\text{obs},h}^{-1}\left\{F_{\text{sim},h}\left[X_{\text{sim},p}^{*DT}(i)\right]\right\} **Multiplicative**: .. math:: - X^{*QM}_{sim,p}(i) = F^{-1}_{obs,h}\Biggl\{F_{sim,h}\left[\frac{\mu{X_{sim,h}} \cdot \mu{X_{sim,p}(i)}}{\mu{X_{sim,p}(i)}}\right]\Biggr\}\frac{\mu{X_{sim,p}(i)}}{\mu{X_{sim,h}}} + X^{*DQM}_{sim,p}(i) = F^{-1}_{obs,h}\Biggl\{F_{sim,h}\left[\frac{\mu{X_{sim,h}} \cdot \mu{X_{\text{sim},p}^{*DT}(i)}}{\mu{X_{\text{sim},p}^{*DT}(i)}}\right]\Biggr\}\frac{\mu{X_{\text{sim},p}^{*DT}(i)}}{\mu{X_{sim,h}}} .. code-block:: python