An updated assessment of past and future warming over France based on a regional observational constraint
 ^{1}CNRM, Université de Toulouse, Météo France, CNRS, Toulouse, France
 ^{2}CECI, Université de Toulouse, CERFACS, CNRS, Toulouse, France
 ^{3}MétéoFrance, Direction de la Climatologie et des Services Climatiques, Toulouse, France
 ^{1}CNRM, Université de Toulouse, Météo France, CNRS, Toulouse, France
 ^{2}CECI, Université de Toulouse, CERFACS, CNRS, Toulouse, France
 ^{3}MétéoFrance, Direction de la Climatologie et des Services Climatiques, Toulouse, France
Abstract. Building on CMIP6 climate simulations, updated global and regional observations, and recently introduced statistical methods, we provide an updated assessment of past and future warming over France. Following the IPCC AR6 and recent global scale studies, we combine model results with observations to constrain climate change at the regional scale. Over Mainland France, the forced warming in 2020 wrt 1900–1930 is assessed to be 1.66 [1.41 to 1.90] °C, i.e., in the upper range of the CMIP6 estimates, and is almost entirely humaninduced. A refined view of the seasonality of this past warming is provided through updated daily climate normals. Projected warming in response to an intermediate emission scenario is assessed to be 3.8 °C (2.9 to 4.8 °C) in 2100, and rises up to 6.7 [5.2 to 8.2] °C in a very high emission scenario, i.e., substantially higher than in previous ensembles of global and regional simulations. Winter and summer warming are expected to be about 15 % lower than, and 30 % higher than the annual mean warming, respectively, for all scenarios and time periods. This work highlights the importance of combining various lines of evidence, including model and observed data, to deliver the most reliable climate information. This refined regional assessment can feed adaptation planning for a range of activities and provides additional rationale for urgent climate action. Code is made available to facilitate replication over other areas or political entities.
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Aurélien Ribes et al.
Status: closed

CC1: 'Comment on esd20227', Xu Liu, 11 Apr 2022
Using the newly developed statistical method (Kriging for Climate Change; KCC) and observational records, this paper aims to constrain the uncertainty of IPCC model simulated past and projected future warming under various scenarios over mainland France. Authors found that anthropogenic influences dominates the warming in 2020, and projects a significant ~3.8°C and ~6.7°C warming in the end of 21 century under CMIP6 SSP245 and SSP585 scenario, respectively. This paper also compares CMIP6 with CMIP5 and regional EUROCORDEX simulations, and a thorough discussion has been made. I'm glad to say that I haven't got much to do as a reviewer of this excellent manuscript. It is wellwritten, clear, thorough, and of great scientific interest. I recommend it for publication at current form.

RC1: 'Comment on esd20227', Anonymous Referee #1, 11 Apr 2022
Using the newly developed statistical method (Kriging for Climate Change; KCC) and observational records, this paper aims to constrain the uncertainty of IPCC model simulated past and projected future warming under various scenarios over mainland France. Authors found that anthropogenic influences dominates the warming in 2020, and projects a significant ~3.8°C and ~6.7°C warming in the end of 21 century under CMIP6 SSP245 and SSP585 scenario, respectively. This paper also compares CMIP6 with CMIP5 and regional EUROCORDEX simulations, and a thorough discussion has been made. I'm glad to say that I haven't got much to do as a reviewer of this excellent manuscript. It is wellwritten, clear, thorough, and of great scientific interest. I recommend it for publication at current form.
 AC1: 'Reply on RC1', Aurélien Ribes, 09 May 2022

RC2: 'Comment on esd20227', Anonymous Referee #2, 16 Apr 2022
Title: An updated assessment of past and future warming over France based on a regional observational constraint
Authors: Ribes et al.
Summary:
This paper assesses the past and future warming over France at the regional scale. One highlight of this paper is about the usage of Kriging for climate change, a method based on Bayesian Statistics, to get the posterior estimation of the projections after “assimilating” observations, which should substantially reduce the estimation uncertainties. As a researcher working on data assimilation, it is very inspiring and enlightening to see how data assimilation methods can be used for climate projections. The paper is wellwritten and clear. It would be great if the authors can show more details about the Kriging for climate change (KCC).Recommendation:
Minor revisionMajor Comments:
 More detailed procedure describing the KCC is needed (, which can be put in the appendix). Especially how you set the prior covariance for x in eq.(2). You mentioned at Line 150 that “mu_x and Sigma_x are estimated as the sample mean and covariance of the CMPI6 model forced responses.” But how do you calculate Sigma_x exactly? How does Sigma_x look like? For data assimilation, the setting of prior error covariance requires a lot of efforts. What’s the dimension of Sigma_x. Is it diagonal or block diagonal? Does Kriging requires the calculation of inverse of Sigma_x?
 You mentioned near line 130 that “x…where each element is an entire 18502100 time series of the forced response.”, but what is the exact dimension of x? If x is large, how to you invert Sigma_x?
 Near Line 120: what’s the exact dimension of your vector y? Near line 160, you mentioned that no measurement error is assumed. Do you mean Sigma_y = 0? Can you give an explanation what’s the impact of setting Sigma_y = 0 in KCC, specially how does your influence influence the posterior?

AC2: 'Reply on RC2', Aurélien Ribes, 09 May 2022
We are very grateful to Anonymous Referee #2 (R2) for this very positive comment about our manuscript.
R2 is asking excellent questions about the KCC method. In our original submission, we did not provide much details about the method, since it is described in another published paper, and the focus of this study is applicative. But we are very much willing to provide additional details in the revised manuscript, and fully agree that this will help readers to better understand what is done. We provide some explanation below. Further details will be added to the revised manuscript.
 Dimension of x and Sigma_x:
x as defined in Eq (2) is of dimension 5x251+171 = 1426. Indeed, each vector "T" in Eq (2) is a timeseries of length 251 years (18502100), except T^{ghg}, which only covers 171 years (18502020, due to data availability). Consequently, Sigma_x is a matrix of size 1426 x 1426.  Estimation of Sigma_x:
The original manuscript said that “mu_x and Sigma_x are estimated as the sample mean and covariance of the CMIP6 model forced responses.” In practice, this is done in three steps.
i/ For each CMIP6 model considered, we estimate the forced response in each of the "T" vectors shown in Eq (2). So, we estimate the forced response in GSAT, in annual and seasonal mean temperature over France, and also the response to specific forcings (i.e., NATonly or GHGonly). We use all available members to make this calculation. As a result, we have a sample of 27 estimates of x  1 for each CMIP6 model considered.
ii/ We compute the sample mean and variance over this sample of 27 vectors. These are our estimates for mu_x and Sigma_x. This deserves a few remarks. Estimated that way, Sigma_x is not diagonal nor block diagonal  and covariances play a key role in KCC. The resulting estimate of Sigma_x is not invertible: the rank of our Sigma_x is 26, which is much smaller than its dimension 1426. But, one key point is that Sigma_x does not need being inverted.
iii/ In computing the posterior, the only matrix which needs being inverted is
S = (H Sigma_x H' + Sigma_y).
In our implementation, this matrix S is invertible, as Sigma_y is invertible itself (see below).  Vector y and estimation of Sigma_y:
Vector y is defined in Eq (3). As of 2020, we have 171 observed years for GSAT (18502020), and 122 years for the temperature over France (18992020). So the dimension of y is 171 + 122 = 293.
Regarding Sigma_y, there are in principle two sources of uncertainty at play: (i) measurement uncertainty, and (ii) internal variability (IV), i.e., variations of the temperature related to intrinsic climate variability (as opposed to forced variability). In our implementation, we assume that measurement uncertainty is null at the regional scale only (i.e., over France). But the second term, related to IV, is relatively large (i.e., we do not assume that "Sigma_y=0"), and it alone guarantees that Sigma_y is invertible. In practice, we assume IV over France to behave like an AR1 process, resulting in a multidiagonal matrix Sigma_y (this applies only to the block of Sigma_y describing France temperature).
 Dimension of x and Sigma_x:

RC3: 'Comment on esd20227', Francis Zwiers, 12 May 2022
.
Please see my attached report. I think this is an excellent paper, but I do think it would benefit from some additional discussion and from the addition of further details concerning the methodology.
With my best regards, Francis Zwiers
 AC3: 'Reply on RC3', Aurélien Ribes, 21 Jun 2022
Status: closed

CC1: 'Comment on esd20227', Xu Liu, 11 Apr 2022
Using the newly developed statistical method (Kriging for Climate Change; KCC) and observational records, this paper aims to constrain the uncertainty of IPCC model simulated past and projected future warming under various scenarios over mainland France. Authors found that anthropogenic influences dominates the warming in 2020, and projects a significant ~3.8°C and ~6.7°C warming in the end of 21 century under CMIP6 SSP245 and SSP585 scenario, respectively. This paper also compares CMIP6 with CMIP5 and regional EUROCORDEX simulations, and a thorough discussion has been made. I'm glad to say that I haven't got much to do as a reviewer of this excellent manuscript. It is wellwritten, clear, thorough, and of great scientific interest. I recommend it for publication at current form.

RC1: 'Comment on esd20227', Anonymous Referee #1, 11 Apr 2022
Using the newly developed statistical method (Kriging for Climate Change; KCC) and observational records, this paper aims to constrain the uncertainty of IPCC model simulated past and projected future warming under various scenarios over mainland France. Authors found that anthropogenic influences dominates the warming in 2020, and projects a significant ~3.8°C and ~6.7°C warming in the end of 21 century under CMIP6 SSP245 and SSP585 scenario, respectively. This paper also compares CMIP6 with CMIP5 and regional EUROCORDEX simulations, and a thorough discussion has been made. I'm glad to say that I haven't got much to do as a reviewer of this excellent manuscript. It is wellwritten, clear, thorough, and of great scientific interest. I recommend it for publication at current form.
 AC1: 'Reply on RC1', Aurélien Ribes, 09 May 2022

RC2: 'Comment on esd20227', Anonymous Referee #2, 16 Apr 2022
Title: An updated assessment of past and future warming over France based on a regional observational constraint
Authors: Ribes et al.
Summary:
This paper assesses the past and future warming over France at the regional scale. One highlight of this paper is about the usage of Kriging for climate change, a method based on Bayesian Statistics, to get the posterior estimation of the projections after “assimilating” observations, which should substantially reduce the estimation uncertainties. As a researcher working on data assimilation, it is very inspiring and enlightening to see how data assimilation methods can be used for climate projections. The paper is wellwritten and clear. It would be great if the authors can show more details about the Kriging for climate change (KCC).Recommendation:
Minor revisionMajor Comments:
 More detailed procedure describing the KCC is needed (, which can be put in the appendix). Especially how you set the prior covariance for x in eq.(2). You mentioned at Line 150 that “mu_x and Sigma_x are estimated as the sample mean and covariance of the CMPI6 model forced responses.” But how do you calculate Sigma_x exactly? How does Sigma_x look like? For data assimilation, the setting of prior error covariance requires a lot of efforts. What’s the dimension of Sigma_x. Is it diagonal or block diagonal? Does Kriging requires the calculation of inverse of Sigma_x?
 You mentioned near line 130 that “x…where each element is an entire 18502100 time series of the forced response.”, but what is the exact dimension of x? If x is large, how to you invert Sigma_x?
 Near Line 120: what’s the exact dimension of your vector y? Near line 160, you mentioned that no measurement error is assumed. Do you mean Sigma_y = 0? Can you give an explanation what’s the impact of setting Sigma_y = 0 in KCC, specially how does your influence influence the posterior?

AC2: 'Reply on RC2', Aurélien Ribes, 09 May 2022
We are very grateful to Anonymous Referee #2 (R2) for this very positive comment about our manuscript.
R2 is asking excellent questions about the KCC method. In our original submission, we did not provide much details about the method, since it is described in another published paper, and the focus of this study is applicative. But we are very much willing to provide additional details in the revised manuscript, and fully agree that this will help readers to better understand what is done. We provide some explanation below. Further details will be added to the revised manuscript.
 Dimension of x and Sigma_x:
x as defined in Eq (2) is of dimension 5x251+171 = 1426. Indeed, each vector "T" in Eq (2) is a timeseries of length 251 years (18502100), except T^{ghg}, which only covers 171 years (18502020, due to data availability). Consequently, Sigma_x is a matrix of size 1426 x 1426.  Estimation of Sigma_x:
The original manuscript said that “mu_x and Sigma_x are estimated as the sample mean and covariance of the CMIP6 model forced responses.” In practice, this is done in three steps.
i/ For each CMIP6 model considered, we estimate the forced response in each of the "T" vectors shown in Eq (2). So, we estimate the forced response in GSAT, in annual and seasonal mean temperature over France, and also the response to specific forcings (i.e., NATonly or GHGonly). We use all available members to make this calculation. As a result, we have a sample of 27 estimates of x  1 for each CMIP6 model considered.
ii/ We compute the sample mean and variance over this sample of 27 vectors. These are our estimates for mu_x and Sigma_x. This deserves a few remarks. Estimated that way, Sigma_x is not diagonal nor block diagonal  and covariances play a key role in KCC. The resulting estimate of Sigma_x is not invertible: the rank of our Sigma_x is 26, which is much smaller than its dimension 1426. But, one key point is that Sigma_x does not need being inverted.
iii/ In computing the posterior, the only matrix which needs being inverted is
S = (H Sigma_x H' + Sigma_y).
In our implementation, this matrix S is invertible, as Sigma_y is invertible itself (see below).  Vector y and estimation of Sigma_y:
Vector y is defined in Eq (3). As of 2020, we have 171 observed years for GSAT (18502020), and 122 years for the temperature over France (18992020). So the dimension of y is 171 + 122 = 293.
Regarding Sigma_y, there are in principle two sources of uncertainty at play: (i) measurement uncertainty, and (ii) internal variability (IV), i.e., variations of the temperature related to intrinsic climate variability (as opposed to forced variability). In our implementation, we assume that measurement uncertainty is null at the regional scale only (i.e., over France). But the second term, related to IV, is relatively large (i.e., we do not assume that "Sigma_y=0"), and it alone guarantees that Sigma_y is invertible. In practice, we assume IV over France to behave like an AR1 process, resulting in a multidiagonal matrix Sigma_y (this applies only to the block of Sigma_y describing France temperature).
 Dimension of x and Sigma_x:

RC3: 'Comment on esd20227', Francis Zwiers, 12 May 2022
.
Please see my attached report. I think this is an excellent paper, but I do think it would benefit from some additional discussion and from the addition of further details concerning the methodology.
With my best regards, Francis Zwiers
 AC3: 'Reply on RC3', Aurélien Ribes, 21 Jun 2022
Aurélien Ribes et al.
Data sets
Code and data of Ribes et al. (2022) Aurélien Ribes https://doi.org/10.5281/ZENODO.6029159
Aurélien Ribes et al.
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