the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 22 Feb 2022
Adaptive Smoothing of the Ensemble Mean of Climate Model Output for Improved Projections of Future Rainfall
Abstract. Ensemble simulations of future climate can be described as consisting of a forced climate change response and noise, where the noise arises from internal variability and errors in the different models. In the ensemble mean the noise is reduced, making it easier to identify the mean of the forced response. The noise in the ensemble mean can potentially be reduced further by spatial smoothing, and this potential has been explored by previous authors. Depending on the variable, the resolution and the size of the ensemble it has been reported that the benefit of spatial smoothing of the ensemble mean may be small, and that spatial smoothing may have the unwanted side-effect that it modifies genuine features in the forced response. However, the spatial smoothing methods that have been tested previously used the same degree of smoothing at all locations, which limits their effectiveness. We derive a novel adaptive smoothing methodology for the ensemble mean that utilizes ensemble information with respect to signal, uncertainty and spatial correlations in order to vary the degree of smoothing in space. The methodology corresponds to simple intuitive concepts, such as the idea that locations with higher signal to noise ratio should be smoothed less. We apply the method to EURO-CORDEX simulations of future annual mean rainfall, and by using cross-validation within the ensemble are able to demonstrate a three times greater increase in potential predictive accuracy than from the non-adaptive smoothing methods we compare with. The adaptive smoothing method also preserves sharp features in the ensemble mean to a greater extent than the non-adaptive methods. We conclude that adaptive smoothing may be a useful post-processing tool for improving the potential accuracy of climate projections.
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Preprint
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Interactive discussion
Status: closed
-
RC1: 'Comment on npg-2022-7', Anonymous Referee #1, 06 Mar 2022
GENERAL COMMENTS
Model projections of future climate change are expected to be the least reliable on the smallest resolved (grid box) scales, where the effects of both model errors and internal variability are maximized. Earlier studies have explored the possibility to improve the projections by smoothing the climate model output in space but have concluded that this potential is small for two reasons. First, the smoothing introduces a bias if the true climate change signal at the target locations differs from its environment. Second, multi-model ensemble means are more difficult to improve by smoothing than the output from individual models, because averaging over multiple models implicitly acts a spatial smoother.
In this manuscript, the authors show that the potential advantages of smoothing can be increased by an adaptive formulation, where the original multi-model mean climate change (m) at the target grid box is replaced by
my = m(1-α) + αp (5)
where p is a weighted average of the model projections in a surrounding region and α is an adaptive parameter. The value for α is derived theoretically and varies from grid box to grid box, whereas the size of the region over which p is calculated is the same everywhere. The novelty compared with earlier research is the introduction of α, which allows the magnitude of the smoothing to be varied based on the local properties of the model ensemble (i.e., the ensemble mean difference between m and p, the ensemble spreads of both m and p, and the covariance between m and p). The inter-model cross-validation conducted by the authors indicates that the adoption of a varying (0 to 1) α increases the optimal size of the domain over which p is calculated relative to the non-adaptive case, which always uses the same value of (approaching 1, depending on the domain size). This, in turn, leads to a larger decrease in the cross-validated prediction error relative to the use of grid-box-scale climate changes with no smoothing.
The manuscript is very well written and the development of the theory of adaptive smoothing is clear and elegant. Consequently, my suggestions for improvement are generally small. However, there is one scientific issue that requires further elaboration. This is discussed in the next section of this review. The other, mostly very minor comments follow thereafter.
MAIN COMMENT: What leads to an improvement on the grid box scale might not do the same on a larger scale.
Inspection of the precipitation change maps in Figs. 4-7 reveals an interesting pattern. On one hand, the multi-model mean increase in precipitation (as shown in the a-panels) tends to be systematically larger over mountainous regions (e.g., the Alps, western Norway, and south-eastern Iceland) than elsewhere. On the other hand, the adaptive smoothing (f-panels) tends to systematically reduce the precipitation increase in the same areas. This is, of course, a direct consequence of the fact that the precipitation increase in the surrounding areas is smaller. Still, this seems undesirable because the larger increase over mountainous regions is physically plausible. Even if the relative (per cent) increase in precipitation were the same over the mountains and the surrounding flatlands, the larger baseline precipitation over the mountains would lead to a larger absolute increase.
Although the algorithm used to find the values of α and the horizontal scale over which the predictor p is calculated is likely optimal for minimizing the grid-scale mean square errors, these features suggest that this may not be the case when the interest is on larger-scale mean values (e.g., the average precipitation change over the Alps). For such larger-scale averages, the decrease in “random noise” becomes likely less important (because there is less noise to start with) relative to the biases that result from calculating p over a relatively wide area.
While it is easy to recognize this problem, it may not be as simple to solve it. By intuition, the best solution might be a smoothing in which size of the area over p is calculated is adaptive and regionally variable (a possibility mentioned by the authors). Most likely, this area should be smaller where there are large regional variations in the multi-model mean climate change. However, as the formulation of such smoothing may be mathematically less straightforward, this falls beyond the scope of the present work.
An easier alternative worth checking might be to apply the smoothing on relative (per cent) than absolute precipitation changes, since the per cent changes are likely to show a less systematic difference between mountainous areas and their surroundings.
MINOR COMMENTS
- L126-131. Is this paragraph needed?
- L298 and 312. What is the corresponding relative decrease in the PRMSE relative to the individual cross-verifying simulations (which was the statistics used by RY)? This is relevant under the statistically indistinguishable paradigm which assumes that the real climate changes (including a contribution from internal variability) belong to the same statistical population as the model results, rather than being in the middle of this population.
- L356-357. This is unsurprising, because the values of precipitation and therefore its change are also larger in mountainous areas.
- L360. Please include the unit of precipitation change in the caption of Fig. 4.
TECHNICAL COMMENTS
- L26 and 533. Räisänen and Ylhäisi
- L96. higher resolution than
Citation: https://doi.org/10.5194/npg-2022-7-RC1 -
RC2: 'Comment on npg-2022-7', Anonymous Referee #2, 29 Mar 2022
The manuscript "Adaptive Smoothing of the Ensemble Mean of Climate Model Output for Improved Projections of Future Rainfall" provides a simple but intuitive smoothing procedure for ensemble mean of future projections. The manuscript reads well, it fits very well the scope of the NPG journal, and presents a quite well detailed discussion of the results. I have no significant remarks on its quality, I would only suggest some improvements and clarifications before being accepted for publication.
- The main differences in the smoothing procedures are mainly located along mountains, especially when adaptive methods are employed. How these differences can be related to the choice of alpha and/or to the number of grid points used for smoothing (n)? Is there any advantage in using the Gaussian filtering with respect to the exponential one? When dealing with kernel functions a widely employed smoothing function is the so-called Epanechnikov kernel, i.e., a parabolic function of di,j(k,l) in this case. Did the authors explore the possibility of using this function?It is optimal in a mean-square sense, so it would be useful for this purposes.
- How the fit parameters are related to the spatial scale of filtering? Does exist a relation between alpha and the scale as a function of the grid resolution? What is the horizon of applicability of this procedure as a function of the grid resolution?Is there any drawback depending on increasing/decreasing spatial resolution?
- Could the authors argue with more details on the choice of the weighting function wi,j in Eqs. (3)-(4)? In particular, why they choose to have 0.1 at the edge of the circle?Does this affect the results?
Minor spelling/improvements
- Page 4, line 96: "that" should be "then.
- Page 14, line 341: why n=37 is used? What is the benefit of increasing/decreasing n?
- Figs. 4-7: I would suggest the change the colorbar range for panels (a), (c)-(f) as well as to restrict the longitudinal range to the explored ones by map (i.e., avoiding white areas outside in longitude)
Citation: https://doi.org/10.5194/npg-2022-7-RC2
Interactive discussion
Status: closed
-
RC1: 'Comment on npg-2022-7', Anonymous Referee #1, 06 Mar 2022
GENERAL COMMENTS
Model projections of future climate change are expected to be the least reliable on the smallest resolved (grid box) scales, where the effects of both model errors and internal variability are maximized. Earlier studies have explored the possibility to improve the projections by smoothing the climate model output in space but have concluded that this potential is small for two reasons. First, the smoothing introduces a bias if the true climate change signal at the target locations differs from its environment. Second, multi-model ensemble means are more difficult to improve by smoothing than the output from individual models, because averaging over multiple models implicitly acts a spatial smoother.
In this manuscript, the authors show that the potential advantages of smoothing can be increased by an adaptive formulation, where the original multi-model mean climate change (m) at the target grid box is replaced by
my = m(1-α) + αp (5)
where p is a weighted average of the model projections in a surrounding region and α is an adaptive parameter. The value for α is derived theoretically and varies from grid box to grid box, whereas the size of the region over which p is calculated is the same everywhere. The novelty compared with earlier research is the introduction of α, which allows the magnitude of the smoothing to be varied based on the local properties of the model ensemble (i.e., the ensemble mean difference between m and p, the ensemble spreads of both m and p, and the covariance between m and p). The inter-model cross-validation conducted by the authors indicates that the adoption of a varying (0 to 1) α increases the optimal size of the domain over which p is calculated relative to the non-adaptive case, which always uses the same value of (approaching 1, depending on the domain size). This, in turn, leads to a larger decrease in the cross-validated prediction error relative to the use of grid-box-scale climate changes with no smoothing.
The manuscript is very well written and the development of the theory of adaptive smoothing is clear and elegant. Consequently, my suggestions for improvement are generally small. However, there is one scientific issue that requires further elaboration. This is discussed in the next section of this review. The other, mostly very minor comments follow thereafter.
MAIN COMMENT: What leads to an improvement on the grid box scale might not do the same on a larger scale.
Inspection of the precipitation change maps in Figs. 4-7 reveals an interesting pattern. On one hand, the multi-model mean increase in precipitation (as shown in the a-panels) tends to be systematically larger over mountainous regions (e.g., the Alps, western Norway, and south-eastern Iceland) than elsewhere. On the other hand, the adaptive smoothing (f-panels) tends to systematically reduce the precipitation increase in the same areas. This is, of course, a direct consequence of the fact that the precipitation increase in the surrounding areas is smaller. Still, this seems undesirable because the larger increase over mountainous regions is physically plausible. Even if the relative (per cent) increase in precipitation were the same over the mountains and the surrounding flatlands, the larger baseline precipitation over the mountains would lead to a larger absolute increase.
Although the algorithm used to find the values of α and the horizontal scale over which the predictor p is calculated is likely optimal for minimizing the grid-scale mean square errors, these features suggest that this may not be the case when the interest is on larger-scale mean values (e.g., the average precipitation change over the Alps). For such larger-scale averages, the decrease in “random noise” becomes likely less important (because there is less noise to start with) relative to the biases that result from calculating p over a relatively wide area.
While it is easy to recognize this problem, it may not be as simple to solve it. By intuition, the best solution might be a smoothing in which size of the area over p is calculated is adaptive and regionally variable (a possibility mentioned by the authors). Most likely, this area should be smaller where there are large regional variations in the multi-model mean climate change. However, as the formulation of such smoothing may be mathematically less straightforward, this falls beyond the scope of the present work.
An easier alternative worth checking might be to apply the smoothing on relative (per cent) than absolute precipitation changes, since the per cent changes are likely to show a less systematic difference between mountainous areas and their surroundings.
MINOR COMMENTS
- L126-131. Is this paragraph needed?
- L298 and 312. What is the corresponding relative decrease in the PRMSE relative to the individual cross-verifying simulations (which was the statistics used by RY)? This is relevant under the statistically indistinguishable paradigm which assumes that the real climate changes (including a contribution from internal variability) belong to the same statistical population as the model results, rather than being in the middle of this population.
- L356-357. This is unsurprising, because the values of precipitation and therefore its change are also larger in mountainous areas.
- L360. Please include the unit of precipitation change in the caption of Fig. 4.
TECHNICAL COMMENTS
- L26 and 533. Räisänen and Ylhäisi
- L96. higher resolution than
Citation: https://doi.org/10.5194/npg-2022-7-RC1 -
RC2: 'Comment on npg-2022-7', Anonymous Referee #2, 29 Mar 2022
The manuscript "Adaptive Smoothing of the Ensemble Mean of Climate Model Output for Improved Projections of Future Rainfall" provides a simple but intuitive smoothing procedure for ensemble mean of future projections. The manuscript reads well, it fits very well the scope of the NPG journal, and presents a quite well detailed discussion of the results. I have no significant remarks on its quality, I would only suggest some improvements and clarifications before being accepted for publication.
- The main differences in the smoothing procedures are mainly located along mountains, especially when adaptive methods are employed. How these differences can be related to the choice of alpha and/or to the number of grid points used for smoothing (n)? Is there any advantage in using the Gaussian filtering with respect to the exponential one? When dealing with kernel functions a widely employed smoothing function is the so-called Epanechnikov kernel, i.e., a parabolic function of di,j(k,l) in this case. Did the authors explore the possibility of using this function?It is optimal in a mean-square sense, so it would be useful for this purposes.
- How the fit parameters are related to the spatial scale of filtering? Does exist a relation between alpha and the scale as a function of the grid resolution? What is the horizon of applicability of this procedure as a function of the grid resolution?Is there any drawback depending on increasing/decreasing spatial resolution?
- Could the authors argue with more details on the choice of the weighting function wi,j in Eqs. (3)-(4)? In particular, why they choose to have 0.1 at the edge of the circle?Does this affect the results?
Minor spelling/improvements
- Page 4, line 96: "that" should be "then.
- Page 14, line 341: why n=37 is used? What is the benefit of increasing/decreasing n?
- Figs. 4-7: I would suggest the change the colorbar range for panels (a), (c)-(f) as well as to restrict the longitudinal range to the explored ones by map (i.e., avoiding white areas outside in longitude)
Citation: https://doi.org/10.5194/npg-2022-7-RC2
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