# Energy and carbon footprint considerations for data-driven weather forecasting models

Thomas Rieutord, Clément Mignon, Emily Gleeson, Ewa K. Mcaufield

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## To cite this version:

Thomas Rieutord, Clément Mignon, Emily Gleeson, Ewa K. Mcaufield. Energy and carbon footprint considerations for data-driven weather forecasting models. 2024. meteo-05033831

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# Energy and carbon footprint considerations for data-driven weather forecasting models

Thomas Rieutord<fnref n="1" /> | Clément Mignon<fnref n="1" />,<fnref n="2" />† | Ewa McAufield<fnref n="1" /> | Emily Gleeson<fnref n="1" />

**Correspondence**

Thomas Rieutord, Met Éireann, 67/69 Glasnevin Hill, D09Y921 Dublin, Ireland
Email: thomas.rieutord@met.ie

**Present address**

†Work done during an internship at Met Éireann. Now at Ecole des Ponts, Institut Polytechnique de Paris, Cité Descartes, 8 Av. Blaise Pascal, 77420 Champs-sur-Marne, France.

**Funding information**

This research did not receive any funding

Data-driven models for weather forecasting display impressive computational speed-up. However, these gains do not include the training phase of the models. This study gathers information from the literature about training and inference to estimate their energy and carbon footprints. Despite being considerably more costly than a physics-based forecast, the training is rapidly compensated by the savings made during the inference. For a use-case corresponding to one year of use, data-driven models are estimated to consume 21 to 1272 times less energy than the physics-based model. Consequently, data-driven models bring opportunities to significantly reduce the carbon footprint of weather forecasting.

**KEYWORDS**

artificial intelligence, numerical weather prediction, carbon footprint, data-driven models

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## 1 | INTRODUCTION

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Numerical weather prediction (NWP) has been undergoing significant changes since 2022, with the emergence of forecasting systems purely based on data (the so-called data-driven forecasting systems) leveraging artificial intelligence

<footnote n="1">¹Research and Applications Division, Met Éireann, Dublin, Ireland</footnote>

<footnote n="2">²National School of Meteorology, Météo-France, University of Toulouse, Toulouse, France</footnote>
20 (Al). The first breakthrough consisted of training modern deep learning models on large meteorological datasets, such as ERA5 [1]. Independently, and a few days apart, Keisler [2] and Pathak et al. [3] released the first data-driven models (DDMs) for weather forecasting with competitive performances. Then, many systems rapidly followed, such as Pan-guWeather [4], GraphCast [5], FuXi [6], FengWu [7], AIFS [8] and NeuralGCM [9]. The first evaluation of these models confirmed the potential of DDMs in terms of forecast accuracy and speed [10]. Indeed, one of the most impressive advantages of DDMs over traditional NWP systems is the considerable computational speed-up. As a consequence of the speed-up, the energy consumption, and therefore the carbon footprint, of weather forecasting is expected to be considerably reduced. However, these claims only refer to the inference (i.e. the forecasting) phase of DDMs. Given that the training phase is notoriously more costly than the inference, including the training seems necessary to properly assess the potential computational benefits of DDMs.

30 The carbon footprint of an activity is "the measure of the exclusive total amount of emissions of carbon dioxide that is directly and indirectly caused by the activity" [11]. Here, the activity we consider is weather forecasting with DDMs and a physics-based model. For computing activities such as these, the carbon footprint is mainly due to electricity consumption [12, 13, 14]. Therefore, reporting on energy usage enables users to mindfully choose among several options and/or include carbon footprint as a target, alongside performance [15].

35 This brief article aims to review the energy claims made by six of the aforementioned DDMs (FourCastNet, Pan-guWeather, GraphCast, FengWu, AIFS, NeuralGCM), with training included, and compare these to a physics-based equivalent. Sect. 2 describes the data extracted from publicly available literature. Sect. 3 describes the methods used to estimate the energy consumption and the carbon footprints, while Sect. 4 gives the results of the estimated energy and carbon footprints. Sect. 5 discusses the limitations of this study and potential prospects. Some conclusions are drawn in Sect. 6.

## 2 | DATA

40 To estimate the energy consumption of DDMs, we need information about the computing time (for both training and inference) and the power consumption of the hardware. Details about such data are given in Sect. 2.1. Carbon footprints are then estimated from the energy consumption and the carbon intensity of the country in which the simulations could be run. Details about this are given in Sect. 2.2.

### 2.1 | Computational information

45 Computing times (for both training and inference) are taken from the references given for each DDM, and the type of GPU used. The DDMs considered in this study are global, with a resolution of under 1° and provide all the information needed (namely: the training time, the inference time, and number and type of GPU). A proportionality assumption was made to reduce the inference time to that of a deterministic 10-day forecast. All inferences are made on a single GPU. Details on where to find the data in the literature are given in Appendix A. The relevant data are summarised in Table 1.

50 The power consumption of a GPU is taken to be equal to the thermal design power (TDP) provided by the manufacturer [16]. Despite the numerous limitations of the TDP (link to the actual consumption, various measurement methods across manufacturers and so on), it has the benefit of being publicly available in hardware specifications. When the exact specification of the GPU type was not specified so that TDP could not be determined, we selected the highest TDP for that GPU type. For example, the Nvidia A100-40GB-PCIe has a TDP of 250 W and the A100-
<table><caption>**TABLE 1** Computing information considered in this study. Inference times are for 10-day deterministic forecasts on one GPU. Detailed references to the literature content are given in Appendix A.</caption><thead><tr><td>Model</td><td>Inference time (s)</td><td>Training time (s)</td><td>No. of GPUs</td><td>Type of GPU</td><td>TDP (W)</td><td>Reference</td></tr></thead><tbody><tr><td>FourCastNet</td><td>2.8</td><td>57,600</td><td>64</td><td>A100<sup>1</sup></td><td>400</td><td>[3]</td></tr><tr><td>PanguWeather</td><td>14.0</td><td>1,382,400</td><td>192</td><td>V100<sup>2</sup></td><td>300</td><td>[4]</td></tr><tr><td>GraphCast</td><td>60.0</td><td>2,419,200</td><td>32</td><td>TPUv4<sup>3</sup></td><td>192</td><td>[5]</td></tr><tr><td>FengWu</td><td>30.0</td><td>1,468,800</td><td>32</td><td>A100<sup>1</sup></td><td>400</td><td>[7]</td></tr><tr><td>AIFS</td><td>150.0</td><td>604,800</td><td>64</td><td>A100<sup>1</sup></td><td>400</td><td>[8]</td></tr><tr><td>NeuralGCM</td><td>116.0</td><td>1,814,400</td><td>256</td><td>TPUv4<sup>3</sup></td><td>192</td><td>[9]</td></tr></tbody></table>

40GB-SMX has a TDP of 400 W. Therefore, when a reference only says “A100”, we selected 400 W.

We compared the total energy consumed by a DDM to a traditional NWP counterpart. The natural baseline is the model of the European Center for Medium-range Weather Forecast (ECMWF): the Integrated Forecasting System<fnref n="1" /> (IFS). Indeed, in the literature, performances of the DDMs are usually compared to that of the IFS (see references in Table 1). Information about the energy consumption of the IFS (cycle 48r1) is available in [17]. The detailed calculations provided in Appendix A give an energy consumption $E_{ifs} = 14.4$ kWh.

## 2.2 | Carbon intensities

Information about carbon intensities is taken from the CodeCarbone Python package [18] and shown in Fig. 1. There are large differences between countries, which leads to very different impacts, even for the same energy consumption. To illustrate these differences, we chose three European countries to cover a wide range of carbon intensities: Norway (29.5 kgCO2e/MWh), Italy (226.1 kgCO2e/MWh) and Poland (739.4 kgCO2e/MWh). We also estimated the carbon footprints for China (544.4 kgCO2e/MWh) and the USA (380.0 kgCO2e/MWh), as many DDMs were trained there. Finally, we estimated the carbon footprint on the use-case scenario when the training is done in Norway (low carbon intensity) and the inference is done in Poland (high carbon intensity). This is to show a possible way to minimize the carbon footprint when running DDMs.

While the carbon footprints are measured in kilograms of carbon dioxide equivalent (kgCO2e), the meaning of this unit can be difficult to grasp. Therefore, we will base our interpretation of these values on the following equivalents, obtained from the comparator<fnref n="2" /> promoted by the French Agency for Ecological Transition (ADEME).

* Ten meals containing beef: 72.6 kgCO2e.

* Car travel (petrol) of 1200 km (Denver to Las Vegas, cross France's mainland): 250 kgCO2e.

* Plane travel of 11,650 km (Paris to New York or Tokyo to New Delhi, there and back): 1770 kgCO2e.

* The average annual carbon footprint of a French citizen: 9300 kgCO2e<fnref n="3" />.

<footnote n="1">¹A100 assumed to be A100-40GB-SMX. Specifications: https://shorturl.at/JX5Wq</footnote>

<footnote n="2">²V100 assumed to be V100-SMX2. Specifications: https://shorturl.at/g63Rj</footnote>

<footnote n="3">³TPUv4 specifications: https://cloud.google.com/tpu/docs/v4</footnote>

<footnote n="1">¹Documentation: https://www.ecmwf.int/en/publications/ifs-documentation (last visited January 31, 2025)</footnote>

<footnote n="2">²https://impactco2.fr/outils/comparateur (last visited: January 31, 2025).</footnote>

<footnote n="3">³Data from the Ministry of Environment (2019), including imported emissions: https://www.statistiques.developpement-durable.</footnote>
<figure><img src="image_3.png" /><figcaption>FIGURE 1 Carbon intensities of electricity production per country (source: [18])</figcaption></figure>

## 3 | METHODS

### 3.1 | Energy consumption estimations

We focus on the energy consumed by Graphical Processing Units (GPU) because this detailed information is present in publications. Therefore, other forms of energy consumption, such as CPU, memory, network and non-IT consumption, are not taken into account [12]. The energy E consumed by using $N_{gpus}$ with a power P for a time T is given by equation 1.

$$E = N_{gpus}PT \qquad (1)$$

The energy consumed by a DDM in making $N_{runs}$ of 10-day $N'_{mb}$-member ensemble forecasts is given by Eq. 2, where $E_{train}$ is the energy consumed during the training phase and $E_{infer}$ is the energy consumed during the inference phase for a deterministic 10-day forecast. Both $E_{train}$ and $E_{infer}$ are estimated using Eq. 1 from data collected in the literature and described in Sect. 2.1.

$$E_{DDM} = E_{train} + N'_{mb}N_{runs}E_{infer} \qquad (2)$$

The energy consumed by the IFS for making $N_{runs}$ of 10-day $N_{mb}$-member ensemble forecasts is given by Eq. 3, with $E_{ifs}$ being the energy consumed for a deterministic 10-day forecast using the IFS.

$$E_{PHY} = N_{mb}N_{runs}E_{ifs} \qquad (3)$$

We estimate $E_{PHY}$ and $E_{DDM}$ for each of the six DDMs listed in Table 1 as if they were used for one year with two runs per day ($N_{runs} = 730$) and an ensemble size equal to that of the current IFS ensemble ($N'_{mb} = N_{mb} = 51$). These
estimations are referred to as our use-case scenario. Additionally, we estimated quantities that help to answer the two questions raised in Sect. 3.1.1 and 3.1.2.

## 3.1.1 | How long to compensate training? ($N'_{mb} = N_{mb}$)

Because $E_{infer} < E_{ifs}$, DDMs make energy savings at each inference. After a large enough number of inferences, the savings compensate for the cost of the training, and the DDM becomes more energy efficient than its physics-based counterpart. We want to estimate the minimum number of days $N_{days}$ a DDM should be used to become more energy-efficient. We make the assumptions that $E_{infer} < E_{ifs}$, $N_{runs} = 2N_{days}$ (i.e. 2 runs per day) and $N'_{mb} = N_{mb}$. Then, the inequality $E_{DDM} \le E_{PHY}$ can be written as follows by inserting Eq. 2 and 3:

$$N_{days} \ge \frac{E_{train}}{2N_{mb}(E_{ifs} - E_{infer})} \qquad (4)$$

Therefore, the minimum number of days for a DDM to become more energy-efficient than the IFS is given by the term on the right-hand side of Eq. 4. It increases with $E_{train}$ (the higher the training cost, the longer the DDM will need to be used), and decreases with $E_{ifs} - E_{infer}$ (a higher energy gap between the DDM and the IFS leads to a quicker compensation).

## 3.1.2 | How large can DDM ensembles be? ($N'_{mb} > N_{mb}$)

Alternatively, the reduced cost of inference makes it possible to run very large ensembles with DDMs, which raises the question: how large can DDM ensembles be at equal (or reduced) costs? We want to estimate the maximum ensemble size $N'_{mb}$ a DDM can have without exceeding the cost of a physics-based ensemble forecast with $N_{mb}$ members. We make the assumptions that $N'_{mb} > N_{mb}$, $E_{train} > 0$ and $E_{infer} > 0$. Then, the inequality $E_{DDM} \le E_{PHY}$ can be written as $E_{train} \le N_{runs}(N_{mb}E_{ifs} - N'_{mb}E_{infer})$ by substituting in Eq. 2 and 3. This modified inequality can only be satisfied if the term on the right hand-side is positive, which means:

$$N'_{mb} < N_{mb} \frac{E_{ifs}}{E_{infer}} \qquad (5)$$

The right hand side of Eq. 5 gives the maximum DDM ensemble size beyond which it is too large to be beneficial in terms of energy.

## 3.2 | Uncertainty quantification

Using only publicly available data leads to substantial uncertainties in the given estimations of energy used to run forecasts for each model. The main sources we identify come from the terms $P$ and $T$ in Eq. 1. To estimate the range of these uncertainties, we choose three values for each term (high, medium, low).

The power consumption, $P$, is estimated from the TDP. According to [16], TDP is often between the peak power and the average power consumed during a given computation. This suggests that using $P$ =TDP, as we do in Sect. 2.1, is likely to be an overestimation. Therefore, in this study we consider the high (TDP), medium (0.75 TDP) and low (0.5 TDP) estimates for $P$ in Eq. 1.
The computational time is taken from the values given in the literature. Mostly, these values are coarse estimates (e.g. in [8] regarding the training time: “the entire process takes about one week”). As a first approach we estimate the uncertainty in the literature estimates by an arbitrary proportion of 5% of the given value (e.g., for one week, this corresponds to ±8 hours). Therefore, if the literature estimate is $T_{lit}$, the high, medium and low estimates for $T$ are 1.05$T_{lit}$, $T_{lit}$ and 0.95$T_{lit}$ respectively.

The uncertainty ranges given in Fig. 2 are obtained by considering all combinations of the three values for each term. Our use-case scenario takes $P = \text{TDP (high value)}$ and $T = T_{lit}$ (mid value).

## 3.3 | Carbon footprint estimation

According to [12], the carbon footprint, $F(c)$, of the electrical energy $E$ consumed in country $c$ is the product of the carbon intensity of electricity production in that country, $\alpha(c)$, as per Eq. 6.

$$F(c) = \alpha(c)E \qquad (6)$$

Carbon intensity units and values are described in Sect. 2.2. The carbon footprints are estimated using Eq. 6 on the energy $E_{DDM}$ and $E_{PHY}$ obtained for our use-case scenario ($N_{runs} = 730$, $N_{mb} = 51$) and for the five countries listed in Sect. 2.2.

# 4 | RESULTS

Figure 2 shows the estimated energy consumption on our use-case scenario for the six DDMs listed in Table 1. The respective share of energy consumed for the inference and the training are shown with colors. The dots show the uncertainty estimation on the total energy consumption obtained as described in Sect. 3.2. The numbers on top of the bars are ratios with the IFS energy consumption, $E_{PHY}/E_{DDM}$ (e.g. for AIFS, 108.9 means that the energy consumption of AIFS for our use-case is 108.9 times lower than that of the IFS). Firstly, the energy consumption widely depends on the model. PanguWeather and NeuralGCM have a much larger energy consumption than the other DDMs. Conversely, FourCastNet consumes noticeably less energy. Secondly, the training dominates the energy budget. The proportion of the training in the total energy consumption ranges from 87.4% (AIFS<fnref n="4" />) to 99.8% (PanguWeather) for our use-case. Thirdly, the ratios with the IFS energy consumption (numbers on top of the bars) are relatively high, despite a large variability. They range from 21 (NeuralGCM) to 1273 (FourCastNet), which means that, even with the most energy-expensive model considered, the energy consumed on our use-case is 21 times lower than that of the IFS. Moreover, an increased number of inferences (larger ensembles, longer times without re-training) will reduce the share of the training and increase the ratio with the IFS. Finally, this holds for all scenarios considered in the uncertainty quantification, with the main scenario near the upper-bound of the uncertainty window, which means that the energy consumptions are probably overestimated.

Table 2 shows the values of $E_{train}$ and $E_{infer}$ for all DDMs and their ratios with $E_{ifs}$. Note that because of the magnitude gap, the training energy is given in megawatt-hours while the inference energy is given in watt-hours. Indeed, the energy ratio between inference and training (not shown) ranges between $2.6 \cdot 10^5$ (AIFS) and $1.9 \cdot 10^7$

<footnote n="4">⁴The inference time of AIFS includes the input/output of the forecast, which might not be the case for the other models (not mentioned in the documents).</footnote>
<figure><img src="image_4.png" /><figcaption>**FIGURE 2** Energy consumption estimations for six data-driven models used for our use-case scenario of one year of use with a 51-member ensemble of 10-day forecasts performed twice a day ($N_{runs} = 730$, $N_{mb} = 51$). Bars distinguish training (blue) and inference (orange) contributions. Dots show the uncertainty estimations. The numbers on top of the bars are the ratios with the IFS energy consumption ($E_{PHY}/E_{DDM}$).</figcaption></figure>

(PanguWeather). The first two columns report the energy consumption when running an inference for a deterministic 10-day forecast on a single GPU ($E_{infer}$) and how many inferences are needed to match the energy consumed by an equivalent forecast with the IFS ($E_{ifs}/E_{infer}$). While there are some discrepancies among DDMs, inferences are all greatly cheaper in terms of energy than the IFS. Ratios range from 864 (AIFS) to more than 46,000 (FourCastNet), which confirms the considerable speed-ups reported in the literature. The two middle columns show the energy consumption estimates for the training of the DDM ($E_{train}$) and how many IFS forecasts it represents ($E_{train}/E_{ifs}$). Again, large discrepancies exist between the DDMs. The lowest training cost is 409.6 kWh (FourCastNet, 28 IFS forecasts) and the highest training cost is near 25 MWh (NeuralGCM, 1,720 IFS forecasts). The fifth column gives the minimum number of days of use after which a DDM becomes more energy-efficient than the IFS, as given by the term on the right-hand side of Eq. 4. These numbers are relatively small: 17 days of use at most (NeuralGCM), 1 day at least (FourCastNet). Therefore, the initial cost of the training is quickly compensated by the gains made during the inference. The last column gives the maximum size of DDM ensembles beyond which they are too large to be beneficial in terms of energy. These numbers are relatively large: 44k members at least (AIFS), even 2.3M for the DDM with the cheapest inference (FourCastNet). Therefore, very large ensembles are possible with DDMs while still consuming less energy than a physics-based ensemble.

Table 3 reports the estimated carbon footprints of the six DDMs for our use-case scenario corresponding to one year of use ($N_{runs} = 730$, $N_{mb} = 51$) in the five countries listed in Sect. 2.2 in addition to the case of training in Norway and inferences in Poland. The last row gives the estimated carbon footprints of the IFS if it was run in each of the five countries. As both model costs (see Fig. 2) and carbon intensities (see Fig. 1) vary significantly, the carbon footprint of a model is country- and model-dependent. The minimum carbon footprint of 11.2 kgCO2e, which is obtained when training and using FourCastNet in Norway, corresponds to less than two meals with beef. Conversely, the maximum carbon footprint of 18.5 tCO2e, which is obtained using NeuralGCM in Poland, corresponds to more than 10 return transatlantic flights. However, the carbon footprint of the IFS for the same use-case is estimated to be much higher, reaching 121 tCO2e, which is nearly 13 times the annual carbon footprint of a French citizen or 68 return transatlantic flights.
<table><caption>**TABLE 2** Main quantities on the energy consumption of data-driven models.</caption><thead><tr><th>Model</th><th><i>E</i><sub>infer</sub> (Wh)</th><th><i>E</i><sub>ifs</sub>/<i>E</i><sub>infer</sub></th><th><i>E</i><sub>train</sub> (MWh)</th><th><i>E</i><sub>train</sub>/<i>E</i><sub>ifs</sub></th><th><i>N</i><sub>days</sub></th><th>min</th><th><i>N'</i><sub>mb</sub> max</th></tr></thead><tbody><tr><td>FourCastNet</td><td>0.3</td><td>46,286</td><td>0.4</td><td>28</td><td>1</td><td></td><td>2,360,572</td></tr><tr><td>PanguWeather</td><td>1.2</td><td>12,343</td><td>22.1</td><td>1,536</td><td>15</td><td></td><td>629,486</td></tr><tr><td>GraphCast</td><td>3.2</td><td>4,500</td><td>4.1</td><td>287</td><td>3</td><td></td><td>229,500</td></tr><tr><td>FengWu</td><td>3.3</td><td>4,320</td><td>5.2</td><td>363</td><td>4</td><td></td><td>220,320</td></tr><tr><td>AIFS</td><td>16.7</td><td>864</td><td>4.3</td><td>299</td><td>3</td><td></td><td>44,064</td></tr><tr><td>NeuralGCM</td><td>6.3</td><td>2,269</td><td>24.8</td><td>1,720</td><td>17</td><td></td><td>115,714</td></tr></tbody></table>

<table><caption>**TABLE 3** Carbon footprints of our use-case ($N_{runs} = 730$, $N_{mb} = 51$) for data-driven models and IFS in different countries, in kgCO2e<fnref n="1" />. Bold numbers are commented in the text.</caption><thead><tr><th>Model</th><th>Norway</th><th>Italy</th><th>Poland</th><th>USA</th><th>China</th><th>Trained in Norway, inference in Poland</th></tr></thead><tbody><tr><td>FourCastNet</td><td><strong>11.2</strong></td><td>95.3</td><td>311.4</td><td>159.9</td><td>229.3</td><td>19.4</td></tr><tr><td>PanguWeather</td><td>587.0</td><td>5,012.9</td><td>16,387.5</td><td>8,412.0</td><td>12,063.9</td><td>618.0</td></tr><tr><td>GraphCast</td><td>112.5</td><td>960.9</td><td>3,141.1</td><td>1,612.4</td><td>2,312.4</td><td>197.5</td></tr><tr><td>FengWu</td><td>141.6</td><td>1,209.4</td><td>3,953.4</td><td>2,029.4</td><td>2,910.4</td><td>230.1</td></tr><tr><td>AIFS</td><td>130.4</td><td><strong>1,113.2</strong></td><td>3,639.0</td><td>1,868.0</td><td>2,678.9</td><td><strong>572.7</strong></td></tr><tr><td>NeuralGCM</td><td>662.5</td><td>5,656.9</td><td><strong>18,492.7</strong></td><td>9,492.7</td><td>13,613.7</td><td>830.9</td></tr><tr><td>IFS</td><td>14,201.1</td><td><strong>121,266.4</strong></td><td>396,425.3</td><td>203,492.6</td><td>291,835.2</td><td>-</td></tr></tbody></table>

flights. Therefore, the carbon footprint of DDMs is less than that of the IFS for all models and countries of operation, by a factor ranging between 6 and 10,827. Moreover, the carbon footprint of DDMs could be further reduced if the training phase is made in a country with a low carbon intensity. The last column of Table 3 illustrates this with the training in Norway (low carbon intensity) and the inference in Poland (high carbon intensity). For example, the carbon footprint of the AIFS (which has the most costly inference, as per Fig. 2) is reduced from 1.1 tCO2e if the training and inference are both done in Italy to 572.7 kgCO2e if the training is done in Norway and the inference in Poland. Such reductions are even more pronounced for the other models with cheaper inference.

## 5 | DISCUSSION

This study only estimates the energy consumed from the information publicly available in the literature. Consequently, the uncertainty is significant and our efforts made to estimate it are somewhat arbitrary. Therefore, the given estimates should only be considered as orders of magnitudes. More precise estimates could be obtained with quantitative measurements made throughout the computations [18].

Many sources of carbon footprints are unaccounted for in this study. Some of these are expected to be impactful, such as the impact of the CPUs used by the DDMs, but are not documented in publications, and therefore could not be included in our estimations. As a result, this missing source leads to an underestimation of the carbon footprints

<footnote n="1">¹Useful equivalents given in Sect. 2.2.</footnote>
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of DDMs. The carbon footprint of other sources, such as the impact of the storage, and the fabrication and recycling of hardware, will probably be similar to traditional NWP, so they are expected to have a marginal impact on the comparison. However, this expectation is only intuitive and should be backed by further studies.

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# 6 | CONCLUSION

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This study gives orders of magnitude of the carbon footprints of six data-driven models (DDMs) and a physics-based model counterpart from data publicly available in the literature. We first estimated the energy consumption of each of the six models and then their carbon footprint in five different countries. In addition to the energy savings for the inference phase, already commented in previous studies, we included the impact of the training phase. Energy costs of the training were estimated to range between 409 kWh (FourCastNet) and 24.8 MWh (NeuralGCM), which is significantly more than that of an IFS forecast (cycle 48r1): 14.4 kWh. However, as highlighted in previous studies, the inference is considerably cheaper than an IFS forecast, ranging between 0.3 Wh (FourCastNet) and 16.7 Wh (AIFS). As a result, for each DDM there exists a minimum time of use after which the cost of the training is paid back and the DDM becomes more energy-efficient than its NWP counterpart. In our use-case for one year of use with 51 members and two forecasts per day, all DDMs consumed less energy than the IFS model, by a factor 21 (NeuralGCM) to 1272 (FourCastNet). The minimum time of use to pay back the training is estimated to be relatively quick (17 days at most, with NeuralGCM). Alternatively, we estimated how large DDM ensembles could be without exceeding the energy consumption of a physics-based ensemble and it was estimated to be relatively large (beyond 44 thousand members). Therefore, very large ensembles are possible with DDMs while still consuming less energy than a physics-based ensemble. Carbon footprints were then estimated on the same use-case by multiplying the energy consumed by the carbon intensity of the country in which the computations can be performed. Large discrepancies exist between countries, amplified by the discrepancies in the energy costs across DDMs, leading to a large range of values for the carbon footprints. However, even the highest carbon footprint of the DDMs considered does not match that of the IFS, by a factor of at least 6 (at most 10,827). Moreover, the carbon footprint of DDMs could be further reduced if the training phase is done in a country that has a low carbon intensity. While several limitations have been identified in this study, such as the uncertainty in the information found in literature and the exclusive focus on GPU energy consumption, the gaps between DDMs and traditional NWP are still large. Therefore, DDMs offer opportunities to significantly reduce the carbon footprint of weather forecasting.

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## Data availability

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Data and code used in this study are freely available on this link: https://github.com/ThomasRieutord/energy-and-carbon-DDMs

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## Acknowledgements

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We would like to thank the authors of all the data-driven models for sharing the details about their computations which made this study possible. We also thank Paul Dando (ECMWF) for his help with the IFS energy consumption and Colm Clancy (Met Éireann) for his feedback on the original draft.
## Conflict of interest

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The authors declare they have no conflict of interest.

## references

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# A | APPENDIX: DETAILS ABOUT THE DATA

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Here are more details to help readers finding the data given in Table 1 and the IFS energy consumption.

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## A.1 | FourCastNet

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Data are taken from [3].

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The training time and the number of GPUs for the training is given by the sentence "The end to end training takes about 16 hours wall-clock time on a cluster of 64 Nvidia A100 GPUs." page 7. Therefore, for the training, the literature time is $T_{lit} = 16 \times 3600 = 57600$ s and $N_{gpus} = 64$.

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The inference time is given by the sentence "The FourCastNet model can compute a 100-member 24-hour forecast in 7 seconds by using a single node on the Perlmutter HPC cluster which contains 4 A100 GPUs per node." page 17. As we impose $N_{gpus} = 1$ for the inference, a 10-day lead time and a deterministic forecast for the inference, the literature time is obtained $T_{lit} = 7 \times 10 \times \frac{1}{100} \times 4 = 2.8$ s.

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The type of GPU is deduced from the sentence "With a peak power consumption of 1kW per node, we estimate this 100-member 24-hour forecast to use 8kJ of energy." page 17. The 1 kW peak power consumption indicates a TDP of 250 W per A100 GPU, which is that of the A100-40GB-PCIe.

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## A.2 | PanguWeather

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Data are taken from [4].

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The training time and the number of GPU for the training is given by the sentence "Each full training procedure takes 16 days on 192 NVIDIA Tesla-V100 GPUs." page 8. Therefore, for the training, the literature time is $T_{lit} = 16 \times 24 \times 3600 = 1382400$ s and $N_{gpus} = 192$.

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The inference time and the type of GPU are given by the sentence "In a system-level comparison, FourCastNet requires 280ms for inferring a 24-hour forecast on an NVIDIA Tesla-A100 GPU (312 TeraFLOPS), while Pangu-Weather needs 1,400ms on an NVIDIA Tesla-V100 GPU (120 TeraFLOPS)." page 12. As we impose $N_{gpus} = 1$ for the inference, a 10-day lead time and a deterministic forecast for the inference, the literature time is obtained $T_{lit} = 1.4 \times 10 = 14$ s. The value of 120 TFLOPs does not appear in the V100 data sheet, so we retain the closest one, which is the V100-SMX2. The TDP of this GPU is of 300 W.

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## A.3 | GraphCast

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Data are taken from [5].

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The training time and the number of GPU for the training is given by the sentence "Training GraphCast took roughly four weeks on 32 Cloud TPU v4 devices using batch parallelism." page 4. Therefore, for the training, the literature time is $T_{lit} = 4 \times 7 \times 24 \times 3600 = 2419200$ s and $N_{gpus} = 32$.

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The inference time and the type of GPU are given by the sentence "On a single Cloud TPU v4 device, GraphCast can generate a 0.25° resolution, 10-day forecast (at 6-hour steps) in under 60 seconds." page 26. As we impose $N_{gpus} = 1$ for the inference, a 10-day lead time and a deterministic forecast for the inference, the literature time is directly given $T_{lit} = 60$ s. According to the TPUv4 documentation, the TPD is 192 W.

## A.4 | FengWu

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Data are taken from [7].

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The training time and the number of GPU for the training is given by the sentence "FengWu is developed with Pytorch and trained with 32 Nvidia A100 GPUs in a cluster for 17 days in total." page 8. Therefore, for the training, the literature time is $T_{lit} = 17 \times 24 \times 3600 = 1468800$ s and $N_{gpus} = 32$.

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The inference time is given by the sentence "We evaluate the inference speed of FengWu on an NVIDIA Tesla-A100 GPU, which indicates that FengWu costs less than 30 seconds to generate all forecasts in the following 10 days with a six-hour interval." page 8. As we impose $N_{gpus} = 1$ for the inference, a 10-day lead time and a deterministic forecast for the inference, the literature time is directly given $T_{lit} = 30$ s.

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The TDP is confirmed to be 400 W by the sentence "With a peak power consumption of 0.4KW for an A100..." page 8.

## A.5 | AIFS

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Data are taken from [8].

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The training time and the number of GPU for the training is given by the sentence "Training is done using mixed precision (Mickevicius et al. [2018]), and the entire process takes about one week, with 64 GPUs in total." page 5. Therefore, for the training, the literature time is $T_{lit} = 7 \times 24 \times 3600 = 604800$ s and $N_{gpus} = 64$.

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The inference time is given by the sentence "Running a 10 day forecast takes approximately 2 minutes 30 seconds on a single A100 GPU, including the input and output of forecast data." page 5. As we impose $N_{gpus} = 1$ for the inference, a 10-day lead time and a deterministic forecast for the inference, the literature time is directly given $T_{lit} = 150$ s.

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The type of GPU is said to be A100, and the variation can be found on the ECMWF's HPC documentation<fnref n="5" /> (A100-40GB-SMX), which has a TDP of 400 W.

## A.6 | NeuralGCM

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Data are taken from [9], for the NeuralGCM-0.7° because its resolution is the closest to the IFS.

<footnote n="5">⁵https://confluence.ecmwf.int/display/UDOC/HPC2020%3A+GPU+usage+for+AI+and+Machine+Learning (accessed on January 31, 2025)</footnote>
All necessary information is given the Table G6, page 46. For the training, we have $T_{lit} = 3 \times 7 \times 24 \times 3600 = 1814400$ s (three weeks) and $N_{gpus} = 256$. The type of GPU is a TPUv4, with a TDP of 192 W. For inference, we have $T_{lit} = 119$ s.

## A.7 | IFS cycle 48r1

Data are taken from [17].

The cost a physics-based forecast with the IFS (cycle 48r1) is given by the sentence "For reference, one IFS Cycle 48r1 ensemble member takes about one hour to produce (excluding I/O), on 96 AMD Epyc Rome central processing units (CPUs)". More precisely, the Epyc Rome CPUs used for this computation are AMD Epyc 7742, which have a TDP of 225 W<fnref n="6" />. The energy consumed for a 10-day 1-member forecast is therefore estimated to be

$$E_{ifs} = (96 \text{ CPUs}) \times (3600 \text{ s}) \times (225 \text{ W}) \times \frac{10}{15} = 51.8 \text{ MJ} = 14.4 \text{ kWh} \quad (7)$$

<footnote n="6">⁶https://www.amd.com/en/support/downloads/drivers.html/processors/epyc/epyc-7002-series/amd-epyc-7742.html
(accessed on January 31, 2025)</footnote>