GraphCast: Learning skillful medium-range global weather forecasting

Introduction

• Traditional numerical weather prediction improves with computational resources but does not directly use increasing historical data to improve forecast models.Machine-learning weather prediction instead trains models directly from historical data, potentially improving accuracy and efficiency.Source: Introduction · pp. 1–2

GraphCast

• GraphCast produces global 10-day forecasts in under a minute on a single Google Cloud TPU v4 device and supports tropical cyclone, atmospheric river, and extreme-temperature prediction.It predicts autoregressively from the two most recent weather states on a 0.25° grid, advancing six hours per step.Source: GraphCast · p. 2
• GraphCast uses a 36.7-million-parameter encode-process-decode GNN whose multi-mesh enables efficient local and long-range information propagation across the globe.The processor applies 16 unshared GNN layers, while the encoder and decoder map between the latitude-longitude grid and the multi-mesh.Source: GraphCast · p. 4
• GraphCast was trained on 39 years of ERA5 data with an autoregressive weighted MSE objective and evaluated on held-out data from 2018 onward.Training increased the autoregressive horizon from one to 12 steps and used 32 Cloud TPU v4 devices for roughly four weeks.Source: GraphCast · p. 4

Verification methods

• Forecast skill is evaluated against HRES and ML baselines across variables, levels, and lead times using RMSE and anomaly correlation coefficient.The primary evaluation covers 69 of GraphCast’s 227 predicted variable-level combinations, excluding total precipitation because of known ERA5 biases.Source: Verification methods · p. 4
• Fair comparisons use ERA5 as GraphCast’s ground truth and an HRES-fc0 dataset for HRES, ensuring each forecast’s zeroth step is grounded consistently by recent observations.This avoids assigning HRES error caused solely by comparing its forecasts against a different initial state.Source: Verification methods · p. 5
• The verification matches data-assimilation information by evaluating GraphCast at 06z and 18z and comparing targets every 12 hours, while accounting for HRES’s shorter initialized horizons.Figures mark the transition from 06z/18z HRES comparisons through 3.5 days to 00z/12z comparisons thereafter.Source: Verification methods · p. 5

Headline-variable verification

• 7%–14% skill-score improvement over HRES occurred across all lead times for z500, the synoptic-scale pressure-distribution field.The evaluation used 10-day forecasts at 0.25° horizontal resolution and 13 vertical levels.Source: Forecast verification results · p. 5, Figure 2a

Overall verification

• 90.3% of 1,380 targets favored GraphCast over HRES, with significant outperformance on 89.9% of targets.When excluding 50 hPa, GraphCast significantly outperformed HRES on 96.9% of 1,280 targets; excluding 50 and 100 hPa, this rose to 99.7% of 1,180 targets.Source: Forecast verification results · pp. 5, 7, Figure 2 · p. 6

Vertical and regional analysis

• 96.9% of 1,280 targets excluding 50 hPa and 99.7% of 1,180 targets excluding 50 and 100 hPa significantly favored GraphCast.HRES performed better disproportionately in stratospheric regions, which had the lowest training-loss weight; the main results generally held across the globe.Source: Forecast verification results · p. 7

Blurring analysis

• 88.0% of 1,380 verification targets favored optimally blurred GraphCast over optimally blurred HRES.Increasing autoregressive steps improved longer-lead RMSE while encouraging spatially smoothed, blurrier GraphCast forecasts; HRES’s physical equations did not produce blurred predictions.Source: Forecast verification results · p. 7

Comparison with Pangu-Weather

• 99.2% of 252 presented targets favored GraphCast over Pangu-Weather, the top competing ML-based weather model.This comparison is reported in Supplements Section 6.Source: Forecast verification results · p. 7

Severe event forecasting results

• The severe-event evaluation covers tropical cyclones, atmospheric rivers, and extreme temperatures as important downstream applications not directly targeted during GraphCast training.These applications matter for human activity, including risks from injury, economic harm, precipitation, and disruption from extreme temperatures.Source: Severe event forecasting results · p. 7

Tropical cyclone tracks

• GraphCast has lower median tropical-cyclone track error than HRES over 2018–2021 and is significantly better from 18 hours to 4.75 days.Figure 3 reports bootstrapped 95% confidence intervals for the median and median paired error difference.Source: Tropical cyclone tracks · p. 7, Figure 3 · p. 8

Atmospheric rivers

• GraphCast improves atmospheric-river ivt prediction over HRES by 25% at short lead times and 10% at longer horizons.The evaluation covers coastal North America and the Eastern Pacific during cold months, despite GraphCast not being specifically trained for atmospheric rivers.Source: Figure 3 · p. 8, Atmospheric rivers · p. 9

Extreme heat and cold

• GraphCast’s precision-recall curves exceed HRES’s at 5- and 10-day extreme-temperature leads, whereas HRES performs better at 12 hours.The pattern is generally consistent across related variables, thresholds, and extreme-cold forecasting in winter.Source: Figure 3 · p. 8, Extreme heat and cold · p. 9

Effect of training data recency

• Four GraphCast variants used data beginning in 1979 and ending in 2017, 2018, 2019, or 2020, then were evaluated against HRES on 2021 data.Source: Effect of training data recency · p. 9
• The recency effect may capture changing weather trends, including ENSO-related oscillations and climate-change effects, thereby improving forecast accuracy.Periodic retraining is proposed as a way to incorporate weather patterns that change over time.Source: Effect of training data recency · p. 9
• Training GraphCast on data ending before 2021 further improves 2021 z500 skill scores over the before-2018 variant, demonstrating gains from newer training data.Figure 4 compares four training cutoffs and HRES using RMSE skill scores on 2021 test data across lead times.Source: Effect of training data recency · p. 9, Figure 4 · p. 10

• GraphCast’s forecast skill and efficiency compared with HRES show that MLWP methods are competitive with traditional weather forecasting and robust for severe-event prediction.Its severe-event performance was achieved despite not being directly trained for those events, indicating potential downstream value.Source: Conclusions · p. 10
• With 36.7 million parameters, GraphCast uses 0.25° resolution, 37 vertical levels, and 6-hour time steps, reflecting current data and engineering constraints.The authors describe GraphCast as a model family with potential to scale using greater compute and higher-resolution data.Source: Conclusions · p. 10
• GraphCast’s deterministic forecasts do not explicitly model growing long-range uncertainty, while MSE training can express uncertainty as spatially blurred predictions.The authors identify explicit uncertainty modeling as a crucial next step, especially relative to ECMWF’s stochastic ENS system for 10+ day forecasts.Source: Conclusions · p. 10
• MLWP depends critically on large quantities of high-quality data assimilated through NWP, so GraphCast should complement rather than replace established forecasting methods.Traditional methods have decades of development, rigorous real-world testing, and features not yet explored by GraphCast.Source: Conclusions · p. 11
• GraphCast’s learned-simulator approach could extend to climate, ecology, energy, agriculture, human activity, biological activity, and other complex dynamical systems.The authors argue that learned simulators trained on rich real-world data can advance machine learning in the physical sciences.Source: Conclusions · p. 11

• GraphCast’s code and trained weights are publicly available on GitHub, while the study uses ECMWF ERA5, HRES and TIGGE products and IBTrACS Version 4 under their stated licensing and attribution requirements.The ECMWF products are governed by CC BY 4.0, and IBTrACS requires reference.Source: Data and Materials Availability · p. 11

• The supplementary materials include sections S1–S9, Figures 5–53, and Tables 3–5.Source: Supplementary materials · p. 15

1. Datasets

• The study builds multiple training and evaluation datasets from subsets of ECMWF archives and IBTrACS.The paper distinguishes source archives from the datasets constructed from them.Source: §1 · p. 18

1.1. ERA5

• ERA5 supplies GraphCast data from 1979–2022 at 0.25° resolution, 6-hour intervals, and 37 pressure levels across selected variables.The archive represents global weather from 1959 onward at hourly resolution; the constructed dataset uses the 1979-01-01 to 2022-01-10 range and subsamples precipitation by six-hour accumulation.Source: §1.1 · p. 18

1.2. HRES

• HRES evaluation uses archived forecasts regridded from roughly 0.1° to 0.25° and downsampled to 6-hour intervals, with separate 10-day and 3.75-day horizons.HRES-fc0 provides initial forecast states as ground truth, using the operational forecast inputs to avoid discrepancies at short lead times.Source: §1.2 · p. 20, Figure 5 · p. 21

1.3. Tropical cyclone datasets

• Tropical-cyclone ground truth comes from IBTrACS, whose six-hourly tracks record cyclone positions, categories, and meteorological features.The HRES comparison uses TIGGE operational-tracker tracks at 0.1° resolution, parsed from forecast XML files.Source: §1.3 · p. 20

2.1. Time notation

• The notation distinguishes forecast steps, horizon, validity and initialization times, step duration, and lead time, with date-times expressed in UTC.Lead time is defined as 𝜏 = 𝑡Δ𝑑.Source: §2.1 · p. 23

2.2. General forecasting problem statement

• Forecasting is framed as learning an efficient approximation 𝜙 of the true weather dynamics Φ to predict future states over a horizon TΔ𝑑 from partial observations and past context.The model is evaluated by comparing predicted and observed trajectories, although the true weather state is unobserved.Source: §2.2 · pp. 23–24
• The study uses six-hourly data and forecasts for up to 10 days, corresponding to T = 40 forecast steps.Because Δ𝑑 is constant, forecasts can be indexed with integer time steps.Source: §2.2 · p. 24

2.3. Modeling ECMWF weather data

• ERA5 states represent surface and atmospheric weather on a 0.25° global grid with 37 pressure levels, while the model predicts 227 target variables and receives static or external inputs as context.The grid contains 721 × 1440 = 1,038,240 points; predicted targets comprise 5 surface and 6 atmospheric variable types.Source: §2.3 · p. 24

3.1. Generating a forecast

• GraphCast generates arbitrary-length forecasts autoregressively from two consecutive input states; three states did not justify their additional memory cost.Early experiments found two input states performed better than one, while adding a third provided insufficient benefit.Source: §3.1 · p. 25

3.2. Architecture overview

• GraphCast uses an encode-process-decode GNN with a multi-mesh that combines fine local edges and coarse long-range edges at generally homogeneous global resolution.The encoder maps latitude-longitude inputs to the multi-mesh, a 16-layer processor propagates information there, and the decoder maps representations back to the latitude-longitude grid.Source: §3.2 · pp. 25–26
• Under 60 seconds, GraphCast generates a 0.25°-resolution, 10-day forecast at 6-hour steps on a single Cloud TPU v4 device.ECMWF’s IFS generates a 0.1°-resolution, 10-day forecast in about an hour on an 11,664-core cluster, with varying release intervals.Source: §3.2 · p. 26

3.3. GraphCast’s graph

• At 0.25° resolution, the graph contains 1,038,240 grid nodes with 474 input features and a six-times-refined icosahedral mesh containing 40,962 nodes.The multi-mesh adds edges from all refinement levels, using lower-level nodes as hubs for longer-range communication.Source: §3.3 · pp. 26–27

3.4. Encoder

• The encoder embeds graph features and performs one Grid2Mesh message-passing step to transfer atmospheric-state information from grid nodes to mesh nodes.It uses five MLPs to embed grid nodes, mesh nodes, and the three edge types before updating edges and receiving mesh nodes.Source: §3.4 · p. 28

3.5. Processor

• The processor applies 16 unshared interaction-network layers exclusively on the full multi-mesh, enabling repeated long-distance message passing through multiscale edges.Each layer updates mesh edges and nodes with a residual connection.Source: §3.5 · p. 29

3.6. Decoder

• The decoder performs one Mesh2Grid message-passing step, then an MLP outputs 227 variables per grid node and adds the predicted difference to the input state.Mesh nodes are not updated during decoding because only grid-node representations are needed afterward.Source: §3.6 · pp. 29–30

3.7. Normalization and network parameterization

• GraphCast normalizes physical inputs by pressure-level means and standard deviations, scales edge features by the longest edge, and normalizes output differences by pressure-level standard deviations.Its MLPs use one hidden layer of size 512, swish activations, and LayerNorm except in the decoder MLP.Source: §3.7 · p. 30

4.1. Training split

• The causal split used 1979–2017 for development and 2018–2021 for testing, with no test-set access during model development.Within development, training used 1979–2015 and validation used 2016–2017; the final model excluded 1959–1978 after little preliminary benefit.Source: §4.1 · p. 31

4.2. Training objective

• GraphCast minimized a latitude-area-weighted MSE over 12-step, 3-day forecasts against ERA5 targets, using standardized per-variable-level errors and tuned loss weights.Atmospheric level weights were pressure-proportional, while surface weights were 1.0 for 2t and 0.1 for 10u, 10v, msl, and tp; total loss weight was 7.4.Source: §4.2 · pp. 31–32

4.3. Training on autoregressive objective

• The final model used autoregressive training for 12 steps, feeding each prediction into the next input and backpropagating errors through the full unrolled sequence.Loss was computed at every forecast step against its corresponding ground-truth target.Source: §4.3 · p. 32

4.4. Optimization

• Optimization used mini-batch gradient descent with batch size 32, AdamW parameters beta1 = 0.9 and beta2 = 0.95, weight decay 0.1, and gradient clipping at norm 32.Ground-truth ERA5 trajectories were sampled with replacement.Source: §4.4 · p. 33

4.5. Curriculum training schedule

• A three-phase curriculum used 1000 one-step updates, 299,000 one-step updates with cosine decay, then 11,000 updates increasing autoregressive steps from 2 to 12.The final phase increased the step count by one every 1000 updates at a fixed learning rate of 3e−7.Source: §4.5 · p. 33

4.6. Reducing memory footprint

• To fit 12-step trajectories within 32GB TPU memory, training distributed one data point per device across 32 TPUs, used bfloat16 activations, and applied gradient checkpointing.Evaluation metrics were computed with float32 precision, while checkpointing reduced memory at the cost of training speed.Source: §4.6 · p. 33

4.7. Training time

• Following the step-ramping schedule, training GraphCast took about four weeks on 32 TPU devices.Source: §4.7 · p. 33

4.8. Software and hardware stack

• The training software stack comprised JAX, Haiku, Jraph, Optax, Jaxline, and xarray.Source: §4.8 · p. 34

5.1. Training, validation, and test splits

• GraphCast models were trained on causally separated periods, with most results evaluated on 2018 and cyclone experiments extended to 2018–2021.Four models used training periods ending in 2017, 2018, 2019, and 2020 for tests through 2021; data-recency experiments used 2021.Source: §5.1 · p. 35, Figure 8 · p. 36

5.2.1. Choice of ground truth datasets

• HRES forecasts are evaluated against HRES-fc0 rather than ERA5, avoiding nonzero error at HRES’s initial forecast step.GraphCast is evaluated against ERA5 because it predicts ERA5 and takes ERA5 inputs, whereas HRES uses HRES analysis for initialization.Source: §5.2.1 · p. 35

5.2.2. Ensuring equal lookahead in assimilation windows

• GraphCast is evaluated from 06z/18z initializations and at 12-hour increments so ERA5 and HRES inputs and targets incorporate comparable +3h lookahead.At lead times of 4 days and beyond, HRES is necessarily compared at 00z/12z; this favors HRES slightly, with differences expected to remain small.Source: §5.2.2 · pp. 35–36, §5.2.3 · pp. 36–37

5.2.3. Alignment of initialization and validity times-of-day

• The protocol uses archived like-for-like HRES comparisons through 3.5 days, then switches HRES timing at the marked 3.5-day changeover.Most main results use 2018; cyclone tracking uses 2018–2021, and data-recency experiments use 2021.Source: §5.2.3 · pp. 36–37, §5.2.4 · p. 40

5.3. Evaluation metrics

• Forecast skill is quantified with latitude-weighted RMSE and ACC against each model’s ground truth, with normalized RMSE and ACC differences defining skill scores.Additional analyses use per-location, latitude, elevation, bias, and spherical-harmonic RMSE variants; spherical-harmonic RMSE is not exactly comparable to grid-based RMSE.Source: §5.3 · pp. 40–41

5.4.1. Significance tests for difference in means

• GraphCast–HRES RMSE differences are tested with paired two-sided t-tests corrected for autocorrelation, while plotted confidence intervals are approximate and skill-score intervals are conservative rather than significance tests.For lead times of at least 4 days, interpolated HRES RMSEs enable paired testing; this is conservative when systematic timing differences favor HRES.Source: §5.4.1 · p. 42, §5.4.2 · p. 43, §5.4.3 · p. 43

6. Comparison with previous machine learning baselines

• GraphCast uses Pangu-Weather ’s 00z/12z initializations and evaluation protocol for a fair comparison against identical ERA5 targets.Both models receive the same +9 hours of lookahead and are evaluated every 6 hours; HRES is omitted because its initialization provides at most +3 hours of lookahead.Source: §6 · p. 45
• 99.2% of targets favor GraphCast over Pangu-Weather, with only two z500 metrics favoring Pangu-Weather.The exceptions occur at 6- and 12-hour lead times, where GraphCast has 1.7% higher average RMSE; Figure 12 compares the models across 10 days at 6-hour steps.Source: §6 · p. 45, Figure 12 · p. 46
• GraphCast’s surface-variable error is 10–20% lower during the first several days and 7–10% lower at longer lead times.These comparisons cover 2t, 10u, 10v, and msl; the evaluation also reports z500, t500, t850, q500, u500, and v500.Source: §6 · p. 45

7.1.3. Effect of data recency on GraphCast

• Variants trained on data ending closer to the 2021 test year generally improve their skill score against HRES, although older variants can still outperform HRES for some variables.The authors speculate that recent statistical biases may act like long-term bias correction, while HRES upgrades may also affect comparisons.Source: §7.1.3 · pp. 47, 51, Figure 15 · p. 52

7.2.2. RMSE skill score by latitude and pressure level

• GraphCast’s relative skill often deteriorates near the stratosphere, at high elevations, and for selected polar, tropical, land, and near-surface regions, though some deficits improve at longer lead times.The causes may include lower loss weighting at low pressure levels, pressure-level interpolation below ground, coordinate-system difficulty, and differences between ERA5 and HRES-fc0 predictability.Source: §7.2.2 · p. 57, §7.2.4 · p. 61, §7.2.5 · p. 64

7.2.3. Biases by latitude and longitude

• GraphCast’s average per-location biases are smaller than HRES’s for most variables up to 6 days but generally exceed HRES’s later, while bias correlations reach 0.6 at 10 days.GraphCast and HRES biases are uncorrelated or weakly correlated at the shortest lead times, with correlation generally increasing over the forecast horizon.Source: §7.2.3 · p. 60, Figure 23 · p. 60, Figure 24 · p. 60

7.3.1. Multi-mesh ablation

• GraphCast benefits from multi-mesh edges for all predicted variables except beyond 5 days at 50 hPa, and they are essential for beating HRES on geopotential under 5 days.The improvement is especially pronounced for geopotential across pressure levels and mean sea-level pressure at shorter lead times.Source: §7.3.1 · p. 65, Figure 29 · p. 66

7.3.2. Effect of autoregressive training

• Training with fewer autoregressive steps trades longer-lead accuracy for shorter-lead accuracy, suggesting that models with different horizons could be combined.The full model uses 12 autoregressive steps, while variants were fine-tuned with progressively increasing step counts.Source: §7.3.2 · p. 65, Figure 30 · p. 67

7.4.1. Effect on the comparison of skill between GraphCast and HRES

• Optimal blurring rarely changes GraphCast’s ranking against HRES, generally narrowing their performance gap, but homogeneous isotropic filters can over-blur predictable local details.The filters are fitted in the spherical-harmonic domain with lead-time-specific weights, and are less effective for surface variables such as 2m temperature.Source: §7.4.1 · p. 68, §7.4.2 · p. 68

7.4.3. Transfer functions of the optimal filters

• Optimal filters attenuate short-to-mid wavelengths increasingly at longer lead times, with HRES requiring more blurring because GraphCast already blurs its predictions.The filters also compensate for GraphCast’s ERA5-resolution spectral cutoff and remove z500 artifacts near 100 km introduced by grid-to-mesh transformations.Source: §7.4.3 · p. 70, Figure 33 · p. 71

7.4.4. Relationship between autoregressive training horizon and blurring

• Longer autoregressive training reduces the benefit of optimal blurring until beyond the training horizon, yet still produces lower post-filtering RMSE than shorter-horizon training.Using a short training horizon can yield less-blurry predictions, but its higher long-lead RMSE reflects compromises beyond insufficient blurring.Source: §7.4.4 · p. 72, Figure 34 · p. 72

7.5.1. Spectral decomposition of mean squared error

• At lead times of at least 2 days, GraphCast improves on HRES across wavelengths for most variables, whereas at 12 hours to 1 day HRES can be better at approximately 200–2000 km scales.2m temperature is a notable exception to the longer-lead result; at shorter leads, GraphCast is generally better outside the stated intermediate-scale range.Source: §7.5.1 · p. 73, Figure 35 · p. 74, Figure 36 · p. 75

7.5.2. RMSE as a function of horizontal resolution

• GraphCast generally has lower RMSE than HRES across verification resolutions, before and after optimal filtering, with exceptions concentrated in specific variables, lead times, and intermediate scales.Exceptions include 2m temperature, and t500 and u500 at 12 hours, where HRES can outperform GraphCast around 0.5°–2.5° despite GraphCast performing better at 0.25°.Source: §7.5.2 · p. 76, Figure 37 · p. 77

7.5.3. Spectra of predictions and targets

• GraphCast predictions lose short-to-mid-wavelength power with lead time and show z500 peaks near 100 km, while differences between ERA5 and HRES spectra create an important evaluation caveat.The peaks are attributed to artifacts from GraphCast’s internal transformations, and short wavelengths contribute little to total signal power despite appearing prominent in relative log-scale plots.Source: §7.5.3 · p. 78, Figure 38 · p. 79

8.1.1. Evaluation protocol

• Cyclone evaluation compares GraphCast and HRES on shared IBTrACS events through 120 hours, using geodesic center-distance errors and 6-hour lead-time increments.Because both methods are evaluated against the same IBTrACS ground truth, their targets have matched lookahead; events are retained when both trackers detect a cyclone at corresponding lead times.Source: §8.1.1 · pp. 79–80

8.1.2. Statistical methodology

• Cyclone significance estimates use cyclone-level bootstrapping rather than correlated initialization-time samples, reporting both per-model confidence and confidence that GraphCast is better than HRES.The cyclone-level choice yields more conservative uncertainty bounds, with 95% confidence intervals applied to mean or median errors.Source: §8.1.2 · p. 80, Figure 39 · p. 81

8.1.3. Results

• GraphCast significantly outperforms HRES in mean cyclone track error from 2 to 5 days, while detecting a similar number of cyclones.The comparison uses conservative cyclone-level bootstrapping with 95% confidence intervals, and GraphCast is equal or better across cyclone categories, with significant advantages for categories 2 and 5.Source: §8.1.3 · pp. 81–82, Figure 39 · p. 81, Figure 41 · p. 83

8.1.4. Tracker details

• The cyclone analysis uses a modified ECMWF tracker adapted to GraphCast’s 0.25° predictions, while HRES tracks are taken directly from the TIGGE archive.The modifications include searching tracker radii, wind-steering weights, direction filters, and displacement clipping; GraphCast and HRES drop comparable numbers of cyclones.Source: §8.1.4 · pp. 82, 86, §8.1.3 · p. 82

8.2. Atmospheric rivers

• 25% at short lead times and 10% at longer horizons: GraphCast improves atmospheric-river ivt prediction over HRES.ivt is derived from predicted specific humidity and horizontal wind, and the comparison uses common pressure levels over coastal North America and the Eastern Pacific during the cold season.Source: §8.2 · pp. 86–87, Figure 44 · p. 87

8.3. Extreme heat and cold

• Extreme heat and cold are evaluated as imbalanced binary classification tasks using precision-recall curves for 2t, t850, and z500 relative to variable-, seasonal-, diurnal-, location-, and level-specific climatologies.The analysis covers hemisphere-specific warm and cold seasons over land and summarizes lead-time performance with maximum SEDI scores.Source: §8.3 · pp. 87–88, Figure 45 · p. 89, Figure 46 · p. 90

9. Forecast visualizations

• GraphCast visualizations use representative examples with median performance on 2018 for 2t, 10u, msl, z500, t850, v500, and q700.The examples span seven variables and are selected by median 2018 performance.Source: §9 · p. 91
• The 2t, 10u, and msl examples show forecasts initialized at 2018-05-05 12:00, 2018-12-22 00:00, and 2018-03-03 12:00 UTC, respectively, across 2-, 6-, and 10-day lead times.These visualizations correspond to Figures 47–49.Source: Figure 47 · p. 92, §9 · pp. 92–94, Figure 48 · p. 93
• The z500, t850, and v500 forecast visualizations show 2-, 6-, and 10-day lead times from distinct initialization times in 2018.Source: Figure 50 · p. 95, §9 · pp. 95–97, Figure 51 · p. 96