## 6.4 Applicability step 1: different sources of input

Until now, we have an efficient emulator that correctly captures the relationship it is designed to learn. The next step to assess if the emulator is the right tool to enlarge RCM matrices is to ensure that the relationship learnt holds in a slightly different world. Neural networks might be unstable to a slight modification of the input space. I have tried to prevent such an effect in this work with two strategies. In the network architecture, the pooling layer and the Relu activation function help to ensure the stability of the emulator. On the other hand, by artificially dissociating the spatial information from the temporal information and standardising the input, I have tried to control the discrepancies between two simulations. Indeed, the aim was somehow to reduce the input space by leaving only the spatial information at the grid point scale and extracting the temporal one at the domain scale. In chapter 4 I have shown that the perfect model framework is well adapted to test the robustness of the RCM-emulator to different input sources. Therefore, I took all ALADIN63 simulations and extracted some large scales predictors that I downscaled with the emulator. In both temperature and precipitation cases, we saw that the emulator maps and local time series were always close to the RCM ones. The statistical evaluation regarding the mean or some specific quantiles maps and the entire pdfs showed similar performance on all simulations. Moreover, the differences between simulations in climate change were also reproduced in the emulated series. This result shows that the relationship learnt in a given simulation holds in other simulations from the same RCM. Besides, a short experiment presented in chapter 4 showed that the normalisation strategy is crucial to secure this result.

Nevertheless, the study of the transferability to other input sources also highlighted some emulator limitations. Indeed, we saw that the tool is not appropriate to extrapolate too far from its training set, notably regarding a warmer or colder climate. To further explore the relationship's robustness, I trained various emulators using combinations of all available simulations. It helped to draw the following conclusions. Firstly regarding the driving scenario, we concluded that training in the coldest and warmest scenarios allows downscaling more intermediate scenarios, but the inverse does not hold. Secondly, we saw that some RCM simulations are constantly warmer than others. Thus, training in a *cold* simulation does not allow reproducing the warmer simulation's warmest extremes, leading to a slight cold bias when looking at climatological means. Conversely, training in a globally warmer simulation leads to warm bias in a colder simulation. Finally, we could also observe that some simulations seem less good than others to be considered as training sets.

All these results provide some indications of how to build the best training set for the emulator. The great principle could be “the most diversified, the better”, which seems logical. At fixed computational costs, the best way to build a training set for the emulator is to downscale with an RCM the most different GCMs and the most extreme scenarios possible. Moreover, having more than one driving GCM for the training set prevents using only a too-specific simulation for calibrating the emulator and thus ensures better transferability. Finally, I have also shown that
more extended simulations are better. Indeed, I did not present the result in this
manuscript. However, a short experiment done for the EUCP project seemed to
show that 20 years of historical and 20 years of far future are the strict minima to
have a reasonable emulator. And longer is better as it explores more climate and
better the internal variability.

The strong conclusions here are that a RCM-emulator trained in a given Scenario-GCM-RCM triplet will be able to downscale all other members from the same Scenario-GCM pair. Secondly, there is quite high confidence that it can also downscale simulation from the same GCM and more intermediate scenarios. Finally, there is a good confidence that it produces accurate series when downscaling simulations from an other GCM as long as it is not too far from the training one. Therefore, using the most diversified training set is probably a good solution to prevent such a situation.

**6.5 Applicability step 2: GCM world**

Finally, the last point to validate the actual applicability of the RCM-Emulator
proposed here is its good behaviour when applied to GCM simulations. It is the *real
life* of the emulator, as all previous steps are perfect model validation. The final aim
of the RCM-emulator is to downscale GCM simulations never downscaled by the
RCM. This is definitively the most challenging point of this work. Indeed, over the
last years, various studies have raised the inconsistencies that can occur between
RCM and their driving GCM (Laprise et al, 2008; Bartók et al, 2017; Boé et al,
2020; Taranu et al, 2022). We also have been confronted with this problem when
evaluating the downscaling performed by the emulator. Indeed, as we focused only
on the downscaling function, the emulator does not reproduce GCM/RCM large
scale biases. Therefore, the RCM simulation driven by a given GCM simulation
is not an exact reference when the emulator is applied to this GCM simulation.
The emulated series needs to be coherent with its driving large scale but should
also include all the added value brought by the RCM. In both temperature and
precipitation cases, the emulator seemed to follow the chronology of the GCM
simulation it downscaled. Moreover, we saw that the biases between the emulator
and RCM are generally coherent with the RCM/GCM ones. The emulated maps
contained the complex spatial structure resulting from the RCM resolution at
daily or climatological time scales and regarding both mean states or extremes.
This result shows that the emulator includes the RCM added value on the GCM
large scale quite well. We have seen in precipitation some counter-example that
might imply an incomplete reproduction of the RCM added value. However, it is
complicated to assess whether it is an emulator error.

Consequently, it is necessary to find a proper manner to evaluate the RCM-Emulator
when it is applied to a GCM simulation. Several options could be considered.
Firstly, using a nudged simulation for the evaluation as this technique forces the
RCM large scales to respect the GCM ones. Then the RCM series should be
a better reference under the hypothesis that the nudging does not modify the
downscaling function. It is an easy test that is necessary to do soon. A second
option could be to build a perfect RCM/GCM pair. Taranu et al (2022) show that
setting up a nearly-perfect GCM-RCM with minimal large scale biases is feasible, and it could become a proper test for the emulator. The last option (in my opinion, at least) could be to apply the emulator to some reanalysis and compare its result to the observed data and the RCM downscaling. If the emulator reproduces the entire RCM downscaling function without large scale biases, the emulated series should be closer to the observations than the RCM simulation.

A fundamental question here is the soundness of those RCM/GCM biases. In this work, we somehow assumed that the large scale biases are not legitimate as the framework I set implies not learning them. This strong assumption seems to be confirmed by some recent studies (Taranu et al, 2022). In this case, an actual result from this work is that we no longer aim to complete an RCM/GCM matrix but to construct another one. Indeed we assume that the existing matrix includes inconsistent biases that we get rid of with the emulator. The emulated matrix is somehow the one we should have in the perfect world where RCMs only downscale the GCM information without transforming it. Of course, it relies on two strong assumptions that are not verified yet: the emulator captures the entire downscaling function in the RCM perfectly, and the transformation function of the RCM is for the wrong reasons. On the other hand, if the last hypothesis does not hold, then the framework I proposed to train the emulator breaks down, and it is necessary to learn also this large scale transformation.

## 6.6 More general perspectives

I believe this work opens the door to multiple studies to evaluate better, improve or apply the emulator. In the last sections, I presented some perspectives to answer different problems raised during my work. Nevertheless, I still see some ideas for further development and application.

The first point necessary to assess is the multivariate consistency of the emulator. In other words, the emulator must reproduce the exact relationship between temperature and precipitation. Most impact studies necessitate temperature and precipitation, and a real relationship must exist between them. In perfect model mode, we have seen that the emulated series follows almost perfectly the RCM one. If the relationship is realistic in the RCM, it should also be in the emulated simulation. Nevertheless, I did not watch this specifically, and it should be done. Besides, it could also be a way to verify the accuracy of downscaling a GCM simulation. A multivariate emulator is perfectly imaginable if the relationship is not well reproduced. A constraint on the joint loss could force the network to respect a good consistency between precipitation and temperature.

A second point concerns higher resolution in space and time. Indeed, in the introduction, I mentioned the existence of Convection Permitting Models with a horizontal resolution of less than 3km. Those models have notably shown an excellent ability to reproduce hourly precipitation and are necessary to study extreme and devastating precipitation changes. The high resolution of these models implies very high computational costs. RCM emulator could then be necessary
to extend the number of simulations. I have already done some preliminary tests
on a daily scale with such models. It provided good results, but the emulator
could not capture the finest spatial structure that the CPM creates. Today, I
can see two possible reasons behind this: the resolution jumps (from 150km to
2.5km) are too big as I used the same input grid as the one in this work, or
I did not have a long enough simulation (20 years in total). This transfer to
higher spatial resolution necessitates further developments but is accessible. On
the other hand, hourly prediction is another challenge. I can see two possibilities
to do it. Firstly, following the same principle as for the daily prediction. The
emulator considers each hour independently, with hourly inputs and maybe a
cosinus/sinus vector to represent the day's hour (similarly to the seasonal one
I implemented here). The big disadvantage of this option is that it implies a
good quality hourly input which the GCM might not well represent. Moreover,
it implies heavy input files and more preprocessing. The second option is to use
lower temporal resolution inputs (daily or 6 hours, for example) and also down-
scale the temporal resolution using recurrent approaches like in nowcasting exercises.

Finally, the last perspective, probably the most evident, concerns the application of
RCM emulators. If the tool is trusted, it could be used to downscale huge ensembles
of GCM simulation. It could completely change the way performing local studies of
climate change. An entirely statistical approach could be used to extract robust and
reliable messages on the local implications of global climate warming. The internal
variability could be entirely explored, and the most extreme possible events could
be studied. Moreover, I believe that a diversity of emulators based on different
statistical approaches would serve the purpose of exploring the possibilities and
extracting robust information.
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