DeepMind's GraphCast waaweyn ee nidaamka warshadaha ugu fiican ee adduunka

Haku: Remi Lam (Google DeepMind) Alvaro Sanchez-Gonzalez (Google DeepMind) Matthew Willson (Google DeepMind) Peter Wirnsberger (Google DeepMind) Meire Fortunato (Google DeepMind) Ferran Alet (Google DeepMind) Suman Ravuri (Google DeepMind) Timo Ewalds (Google DeepMind) Zach Eaton-Rosen (Google DeepMind) Weihua Hu (Google DeepMind) Alexander Merose (Google Research) Stephan Hoyer (Google Research) George Holland (Google DeepMind) Oriol Vinyals (Google DeepMind) Jacklynn Stott (Google DeepMind) Alexander Pritzel (Google DeepMind) Shakir Mohamed (Google DeepMind) Peter Battaglia (Google DeepMind) Haku: Remi Lam ee Google DeepMind Alvaro Sanchez-Gonzalez ee Google DeepMind Matthew Willson ee Google DeepMind Peter Wirnsberger ee Google DeepMind Meire Fortunato ee Google DeepMind Ferran Alet ee Google DeepMind Suman Ravuri ee Google DeepMind Tim Ewalds ee Google DeepMind Zach Eaton-Rosen ee Google DeepMind Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Alexander Merose (Research Google) waxaa laga yaabaa Stephan Hoyer (Research Google) oo ka mid ah wax soo saarka George Holland ee Google DeepMind Xisaabinta Xisaabinta Xisaabinta Xisaabinta Xisaabinta Xisaabinta Xisaabinta Jacklynn Stott ee Google DeepMind Alexander Pritzel ee Google DeepMind Shakir Mohamed (Google DeepMind) Peter Battaglia ee Google DeepMind Waayo, waxaa laga yaabaa in ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka, wax soo saarka iyo wax soo saarka iyo wax soo saarka. Keywords: warbixinta, ECMWF, ERA5, HRES, simulators learning, network graph neural Haku Waxaa ku yaalaa 05:45 UTC mid-October, 2022, in Bologna, Italy, iyo Mid-Range Weather Forecasts (ECMWF) ee European Centre for Medium-Range Weather Forecasts (ECMWF) waa mid ka mid ah wax soo saarka ugu fiican ee soo saarka. Waayo, System for Integrated Forecasting (IFS) waa la soo saarka ah si ay u soo saarka soo saarka oo ka mid ah ka mid ka mid ah ka mid ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah. IFS, iyo dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhism Sida loo yaqaan "NWP" waa mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ka mid ah mid ka mid ka mid ah mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid ka mid Sida loo yaqaan 'High Resolution Forecast' (HRES) ee ECMWF, waa mid ka mid ah IFS oo loo yaqaan 'Global 10-day forecasts at 0.1° latitude/longitude resolution' oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah. Haku Waxa uu soo bandhigay in uu ku saabsan MLWP for global medium-range weather forecasting oo ku yaalaa "GraphCast", oo loo yaqaan "GraphCast", oo loo yaqaan "GraphCast", oo loo yaqaan "GraphCast", oo loo yaqaan "GraphCast", oo loo yaqaan "GraphCast", oo loo yaqaan "GraphCast" iyo "Google Cloud TPU v4" oo loo yaqaan "Google Cloud TPU v4", oo ku yaqaan "GraphCast", "GraphCast", "GraphCast", "GraphCast", "GraphCast", "GraphCast", "GraphCast", "GraphCast", "GraphCast", "GraphCast" iyo "Google Cloud TPU v4", "Google" iyo "Google" iyo "Google" GraphCast waxay ka mid ah soo saarka ugu horeysay ee warshadaha Earth, oo ay ka mid ah soo saarka ugu horeysay oo ka mid ah 6 saacadood oo ka horay, oo ay ka mid ah soo saarka ugu horeysay ee warshadaha ku yaal ah oo ka mid ah 0.25 ° latitude / longitude grid (721 × 1440), oo ku salaysan ka mid ah 28 × 28 km resolution at the equator (Figure 1a), oo ka mid ah mid ka mid ah waalka warshadaha waa mid ka mid ah qalabka warshadaha iyo atmospheric (wax yar tababarka 1). GraphCast waxaa loo isticmaali karaa sida shuruudaha network neural, oo ku yaalaa GNNs ee "code-process-decode" configuration [1], oo ka mid ah 36,7 milyan parameter. Simulators ka horay GNN-based is-simoolada [31, 26] waxaa laga yaabaa in aad u ah in ay u ahaysaa dynamics sare ee caadiga iyo nidaamaha kale modeled by shuruudaha differential partial, oo ku salaysan si ay u ahaysaa for modeling dynamics weather. Qalabka (Figure 1d) waxaa loo isticmaali karaa layer GNN ah in la isticmaali karaa variables (normalized to zero-mean unit-variance) ku yaalaa sida atributes node on the input grid to learned node attributes on an internal "multi-mesh" representation. Dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Processor (Figure 1e) waxaa loo isticmaalaa 16 layers GNN ah si ay u isticmaalaa message-passing ah ee multi-mesh, si ay u isticmaalaa si ay u isticmaalaa si ay u isticmaalaa si ay u isticmaalaa si ay u isticmaalaa in ay u isticmaalaa in ay u isticmaalaa in ay u isticmaalaa in ay u isticmaalaa in ay u isticmaalaa in ay u isticmaalaa in ay u isticmaalaa in ay u isticmaalaa in ay isticmaalaa in ay isticmaalaa in ay isticmaalaa in ay isticmaalaa in ay isticmaalaa in ay isticmaalaa. Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Waayo, waxaa loo isticmaali karaa 39 sano (1979–2017) oo loo isticmaali karaa data ugu horeysay ee archive reanalysis ERA5 [10] ee ECMWF. Sida wax soo saarka, waxaan ka mid ah wax soo saarka qiyaasta qiyaasta (MSE) ee ku yaal ah oo ka mid ah xawaaraha qiyaasta. GraphCast waxaa loo isticmaali karaa mid ka mid ah xawaaraha qiyaasta ah ee GraphCast iyo wax soo saarka ERA5 ee loo isticmaali karaa oo ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah. GraphCast ayaa ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ka mid ah oo mid ka mid ah. GraphCast ayaa ka mid ah mid ka mid Sida loo yaabaa in ay ku yaabaa in ay ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah macluumaad ka mid ah. Qalabka Verification Waayo, waxa uu soo bandhigay in ay ka mid ah wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka. Waayo, waxaa loo yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid Marka aad u baahan tahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u Qalabka dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha iyo dhismaha Qalabka dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha iyo dhismaha. Qalabka Qalabka Qalabka Waayo, GraphCast waxay ka mid ah dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Shuruudaha 2a-c wuxuu soo xigtay in ka mid ah GraphCast (shuruudaha blue) waxay ka soo xigtay HRES (shuruudaha black) on z500 (geopotential at 500 hPa) "headline" field in terms of RMSE skill score, RMSE skill score (ii.e., differential RMSE normalized between model A and baseline B defined as (RMSEA − RMSEB)/RMSEB), iyo ACC skill. Isticmaalka z500, oo ka mid ah dhismaha shuruudaha synoptic-scale, waa caadiga ah ee shuruudaha, sida ay ka mid ah wax soo saarka ah [27]. Shuruudaha waxay soo xigtay GraphCast waxay ka mid ah wax soo saarka badan oo dhan oo ka mid ah wax soo saarka ah oo ka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka dhismaha oo ku yaalaa in ay ku yaalaa dhismaha oo ku saabsan dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Marka aad u baahan tahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u Waxaan sidoo kale soo bandhigi karaa wax soo saarka GraphCast iyo model warshadaha ugu horeysay ee ML, Pangu-Weather [4], oo ka mid ah ka mid ah wax soo saarka GraphCast oo ka mid ah 99.2% ee 252 warshadaha waxay ku soo bandhigi karaa (wax yar dhererka 6 for details). Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Waayo, ka dib markii loo yaabaa in ka mid ah dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha. Qalabka Cyclone Waayo, waxaa loo yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah iyo mid ka mid ka mid ka mid ah oo mid ka mid ah mid ka mid ah mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo mid ka mid ah oo mid ah mid ka mid ah oo mid ka mid ah oo mid ah mid ka mid ah oo mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo Qalabka 3a wuxuu ka soo bandhigay GraphCast waa mid ka mid ah dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dh Riixiinta Atmosphere Qalabka dhismaha waa mid ka mid ah mid ah mid ka mid ah mid ka mid ah oo mid ka mid ah mid ah oo mid ka mid ah oo mid ah mid ka mid ah oo mid ah oo mid ka mid ah oo mid ka mid ah oo mid ah mid ka mid ah oo mid ah oo mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo mid ah oo mid ah oo mid ka mid ah oo mid ah oo mid ah oo mid ka mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo mid ah oo Qalabka dhismaha iyo dhismaha Qalabka dhismaha iyo dhismaha dhismaha ah waxaa loo yaabaa in ka mid ah macluumaadka badan oo ka mid ah dhismaha dabiiciga [19, 16, 18], oo waxay ka mid ah caawin ah oo ka mid ah macluumaadka macaamiisha. Waxaan si ay u hesho in ka mid ah dhismaha dhismaha dhismaha ah oo ka mid ah 2% ugu badan ee dhismaha dabiiciga ah oo ka mid ah maalmood, waqti, iyo bulan ee, oo ka mid ah 2 T at 12 hours, 5 days, and 10 days lead times, for land regions across the northern and southern hemisphere over summer months. We plot precision-recall curves [30] to reflect possible different trade-offs between reducing false positives (high precision) and reducing false negatives (high rec Shuruudaha 3d wuxuu ka soo bandhigay quruudaha quruudaha quruudaha quruudaha GraphCast waa ka badan HRES ee 5 iyo 10 maalmood ka horumariyo, oo ka mid ah xawaaraha GraphCast waa ka mid ah HRES ka horumariyo dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha. Qalabka Qalabka Qalabka Qalabka GraphCast waxaa laga yaabaa in ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka iyo wax soo saarka oo ka mid ah wax soo saarka iyo wax soo saarka oo ka mid ah wax soo saarka. Qalabka 4 wuxuu ku yaalaa si ay u qaadi karo wax soo saarka (waxirida by GraphCast:<2018) ee soo saarka iyo HRES, ee z500. Waayo, laakiin wax soo saarka GraphCast oo ka soo saarka oo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo ka horumariyo. Qalabka Waayo, wax soo saarka ah ee loo yaqaan 'GraphCast' oo ka mid ah 'HRES' oo ka mid ah 'MLWP' waa mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid Waayo, GraphCast waa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah Markaad ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Waxa uu ku yaalaa in la yaabaa in ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid Waayo, GraphCast waxay ka dhigi karaa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah Data iyo wax soo saarka GraphCast waxaa loo isticmaali karaa codka iyo wax soo saarka ah oo loo isticmaali karaa github https://github.com/ deepmind/graphcast. Dhamaan waxaa loo isticmaali karaa data oo loo isticmaali karaa oo loo isticmaali karaa ee European Centre for Medium Range Forecasting (ECMWF). Waxaan isticmaali karaa wax soo saarka ECMWF (wax yar) ee wax soo saarka ERA5, HRES iyo TIGGE, oo loo isticmaali karaa waxaa loo isticmaali karaa by Creative Commons Attribution 4.0 International (CC BY 4.0). Waxaan isticmaali karaa IBTrACS Version 4 ee https://www.ncei.noaa.gov/ products/international-best-track-archive and reference [13, 12] sida loo isticmaali karaa. The Earth texture in Figure 1 waxaa loo isticmaali karaa ee CC BY 4.0 ee https://www.solarsystemscope.com/ textures/. Shuruudaha Marka aad u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u QEEBE [1] Peter W Battaglia, Jessica B Hamrick, Victor Bapst, Alvaro Sanchez-Gonzalez, Vinicius Zambaldi, Mateusz Malinowski, Andrea Tacchetti, David Raposo, Adam Santoro, Ryan Faulkner, et al. 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Isticmaalka Meteorological iyo wax soo saarka sare ee wax soo saarka oo ka mid ah go'aanka oo ka mid ah go'aanka go'aanka ah ee West Coast ee North America oo ku saabsan xisaabinta satellite ssm / i. Journal of Hydrometeorology, 9(1):22-47, 2008. [24] Tung Nguyen, Johannes Brandstetter, Ashish Kapoor, Jayesh K Gupta, iyo Aditya Grover. ClimaX: A foundation model for weather and climate. arXiv preprint arXiv:2301.10343, 2023. [25] Jaideep Pathak, Shashank Subramanian, Peter Harrington, Sanjeev Raja, Ashesh Chattopad-hyay, Morteza Mardani, Thorsten Kurth, David Hall, Zongyi Li, Kamyar Azizzadenesheli, et al. Fourcastnet: a global data-driven high-resolution weather model using adaptive fourier neural operators. arXiv preprint arXiv:2202.11214, 2022. [26] Tobias Pfaff, Meire Fortunato, Alvaro Sanchez-Gonzalez, iyo Peter Battaglia. Qalabka simulatorsiga mashiinka oo ku saabsan network graph. In Conference International on Learning Representations, 2021. 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Project TIGGE iyo wax soo saarka. Bulletin of the American Meteorological Society, 97(1):49 – 67, 2016. [35] Jonathan A Weyn, Dale R Durran, iyo Rich Caruana. Haddii mashiinka waxay u arki karaa in ay ku raaxaysaa waqti? Iska loo isticmaali karaa in ay loo isticmaali karaa in ay ku raaxay 500-hPa geopotential height oo ku saabsan data warshadaha ah. Journal of Advances in Modeling Earth Systems, 11(8):2680–2693, 2019. [36] Jonathan A Weyn, Dale R Durran, iyo Rich Caruana. Nadiifinta dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha. Journal of Advances in Modeling Earth Systems, 12(9):e2020MS002109, 2020. Qalabka Data In this section, waxaan ku dhameyn kartaa dhamaadka oo loo isticmaali karaa in la helo GraphCast (Supplements Section 1.1), dhamaadka loo isticmaali karaa xawaaraha ee NWP baseline HRES, iyo HRES-fc0, oo loo isticmaali karaa sida dhamaadka dhamaadka ee HRES (Supplements Section 1.2). Markaas oo ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah 1.1 Qalabka 5 Waayo, waxa uu ku yaalaa dhismaha iyo dhismaha GraphCast, waxaan ku yaalaa dhismaha ERA5 [24]1 ee archive ECMWF, oo waa dhismaha ah ee dhismaha ah oo ku yaalaa dhismaha warshadaha global ka mid ah 1959, at 0.25° latitude/longitude resolution, iyo 1 hour increments, for hundreds of static, surface, and atmospheric variables. The ERA5 archive is based on reanalysis, which uses ECMWF's HRES model (cycle 42r1) which was operational for most of 2016 (see Table 3), within ECMWF's 4D-Var data assimilation system. Markaasadda ERA5 waa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid 1.2 Qalabka Qalabka dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha HRES waxaa loo yaabaa in ay ku yaalaa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid HRES operational forecasts Waxaan ka dibna soo bandhigiisa xawaaraha ka mid ah 0.25 ° latitude / longitude grid (wax yar ERA5's resolution) oo loo isticmaalo library Metview ee ECMWF, oo ka mid ah macluumaadka regrid default. Waxaan soo bandhigiisa xawaaraha ka mid ah 6 saacadood. Waxaa kale oo ka mid ah two groups of HRES predictions: those initialized at 00z/12z which are released for 10 day horizons, iyo those initialized at 06z/18z which are released for 3.75 day horizons. For evaluating the skill of the HRES operational forecasts, we constructed a ground truth dataset, “HRES-fc0”, based on ECMWF’s HRES operational forecast archive. This dataset comprises the initial time step of each HRES forecast, at initialization times 00z, 06z, 12z, and 18z (see Figure 5). The HRES-fc0 data is similar to the ERA5 data, but it is assimilated using the latest ECMWF NWP model at the forecast time, and assimilates observations from ±3 hours around the corresponding date and time. Note, ECMWF also provides an archive of “HRES Analysis” data, which is distinct from our HRES-fc0 dataset. The HRES Analysis dataset includes both atmospheric and land surface analyses, but is not the input which is provided to the HRES forecasts, therefore we do not use it as ground truth because it would introduce discrepancies between HRES forecasts and ground truth, simply due to HRES using different inputs, which would be especially prominent at short lead times. HRES-fc0 Waqtiga ah ee ku saabsan geopotential caadiga ah ee 850hPa (z850) iyo 925hPa (z925) waa mid ka mid ah (NaN). NaN waa mid ka mid ah mid ka mid ah 2016-2021 iyo mid ka mid ah oo ka mid ah caadiga ah oo ka mid ah xawaaraha. Tani waa in ka mid ah 0.00001% pixels ee z850 (1 pixels oo ka mid ah 10 x 1440 x 721 oo ka mid ah xawaaraha xawaaraha), 0.00000001% pixels ee z925 (1 pixels oo mid ka mid ah 10 x 1440 x 721 oo ka mid ah xawaaraha xawaaraha xawaaraha) iyo waxaa ka mid ah mid ka mid ah wax soo saarka. HRES NaN handling 1.3.Troopic Cyclone dhismaha Waayo, waxaa loo isticmaali karaa iibsiga IBTrACS [28, 29, 31, 30] si ay u dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha. Marka aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u Sida loo yaabaa, waxaa loo yaabaa in ka mid ah macluumaadka iyo macluumaadka macluumaadka. Qalabka Qalabka Qalabka Qalabka Qalabka In this section, waxaan ku yaalaa isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo (Section 2.1), si loo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo (Section 2.2), iyo loo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo isticmaalo (Section 2.3). 2.1 Qalabka Qalabka Waayo, sidoo kale waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid t: Dhammaan oo ka mid ah wax soo saarka oo ka mid ah wax soo saarka oo ka mid ah wax soo saarka oo ka mid ah wax soo saarka oo ka mid ah wax soo saarka. T: Horizon Prognosis, oo ku yaalaa qiyaasta ugu badan oo ka horumarka. d: Waayo, oo ku yaalaa waqti-waayo ee xawaaraha caadiga ah. d0: waqti ugu horeysay ee loo yaabaa, oo ku yaalaa waqti ugu horeysay ee loo yaabaa ugu horeysay ee loo yaabaa. Δd: Waqtiga dhismaha, oo ku yaala in ay ku yaalaa in ka mid ah waqti oo ka mid ah dhismaha dhismaha. τ: waqti dhismaha, oo ku yaalaa waqti dhismaha (yuu, τ = tΔd). 2.2.Saacadaha dhismaha dhismaha Waayo, Zd waxaa loo yaabaa xawaaraha caadiga ah ee xawaaraha caadiga ah ee xawaaraha caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah. Ma rabtaa in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. Xd−Δd , Xd−2Δd , ..., ka mid ah Xd. Model waa in ay ka mid ah in ay ka mid ah wax soo saarka dheeraad ah si ay u soo saarka Zd. Analogous to Equation (1), the prediction 𝑋ˆ𝑑+Δ𝑑 can be fed back into 𝜙 to autoregressively produce a full forecast, Waxaad ku dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa in ay u dhigi karaa. Qalabka waxaa laga yaabaa in ka mid ah qiyaasta 5 ah. Waayo, dhismaha dhismaha dhismaha dhismaha iyo dhismaha waxaa laga yaabaa Δd = 6 saacadood oo horumarka dhismaha ugu badan ee 10 maalmood, oo ku salaysan dhismaha T = 40 maalmood. Sida dhismaha Δd waa dhismaha mid ka mid ah dhismaha dhismaha, sidoo kale sidoo kale sidoo kale sidoo kale sidoo kale sidoo kale sidoo kale sidoo kale loo isticmaali karaa (Xt, Xt+1, . . . , Xt+T ) in ka mid ah (Xd, Xd+Δd , . . , Xd+TΔd ), si ay u hesho waqti oo ka mid ah dhismaha dhismaha. Qalabka dhismaha ECMWF For training and evaluating models, we treat our ERA5 dataset as the ground truth representation of the surface and atmospheric weather state. As described in Section 1.2, we used the HRES-fc0 dataset as ground truth for evaluating the skill of HRES. Marka aad u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u baahan yahay in ay u Waayo, waxaa loo yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid Xtii, j waa mid ka mid ah 721 × 1440 × (5 + 6 × 37) = 235, 680, 480 qiimaha. Nala soo xiriir, at the poles, the 1440 longitude points are equal, so the actual number of separate grid points is slightly smaller. Qalabka GraphCast Qalabka dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha, dhismaha iyo dhismaha. 3.1 Qalabka dhismaha Our GraphCast model waxaa loo yaabaa sida simulators one-step learned that takes the role of φ in Equation (2) and predicts the next step based on two consecutive input states. Sida loo helo equation (3), waxaan sidoo kale loo isticmaali karaa GraphCast in ay isticmaali karaa in ay soo saarka of arbitrary length, 𝑇. This is illustrated in Figure 1b,c. We found, in early experiments, that two input states yielded better performance than one, and that three did not help enough to justify the increased memory footprint. 3.2.Architectural kharashka The core architecture of GraphCast uses GNNs in an “encode-process-decode” configuration [6], as depicted in Figure 1d,e,f. GNN-based learned simulators are very effective at learning complex physical dynamics of fluids and other materials [43, 39], as the structure of their representations and computations are analogous to learned finite element solvers [1]. A key advantage of GNNs is that the input graph’s structure determines what parts of the representation interact with one another via learned message-passing, allowing arbitrary patterns of spatial interactions over any range. By contrast, a convolutional neural network (CNN) is restricted to computing interactions within local patches (or, in the case of dilated convolution, over regularly strided longer ranges). And while Transformers [48] can also compute arbitrarily long-range computations, they do not scale well with very large inputs (e.g., the 1 million-plus grid points in GraphCast’s global inputs) because of the quadratic memory complexity induced by computing all-to-all interactions. Contemporary extensions of Transformers often sparsify possible interactions to reduce the complexity, which in effect makes them analogous to GNNs (e.g., graph attention networks [49]). The way we capitalize on the GNN’s ability to model arbitrary sparse interactions is by introducing GraphCast’s internal “multi-mesh” representation, which allows long-range interactions within few message-passing steps and has generally homogeneous spatial resolution over the globe. This is in contrast with a latitude-longitude grid which induce a non-uniform distribution of grid points. Using the latitude-longitude grid is not an advisable representation due to its spatial inhomogeneity, and high resolution at the poles which demands disproportionate compute resources. Marka aad u baahan yahay in aad u baahan tahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u GraphCast’s encoder (Figure 1d) first maps the input data, from the original latitude-longitude grid, into learned features on the multi-mesh, using a GNN with directed edges from the grid points to the multi-mesh. The processor (Figure 1e) then uses a 16-layer deep GNN to perform learned message-passing on the multi-mesh, allowing efficient propagation of information across space due to the long-range edges. The decoder (Figure 1f) then maps the final multi-mesh representation back to the latitude-longitude grid using a GNN with directed edges, and combines this grid representation, 𝑌ˆ𝑡+𝑘, with the input state, 𝑋ˆ𝑡+𝑘, to form the output prediction, 𝑋ˆ𝑡+𝑘+1 = 𝑋ˆ𝑡+𝑘 + 𝑌ˆ𝑡+𝑘. Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid 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. For comparison, ECMWF’s IFS system runs on a 11,664-core cluster, and generates a 0.1° resolution, 10-day forecast (released at 1-hour steps for the first 90 hours, 3-hour steps for hours 93-144, and 6-hour steps from 150-240 hours, in about an hour of com-pute time [41]. See the HRES release details here: https://www.ecmwf.int/en/forecasts/ datasets/set-i.. 3.3. GraphCast’s graph GraphCast is implemented using GNNs in an “encode-process-decode” configuration, where the encoder maps (surface and atmospheric) features on the input latitude-longitude grid to a multi-mesh, the processor performs many rounds of message-passing on the multi-mesh, and the decoder maps the multi-mesh features back to the output latitude-longitude grid (see Figure 1). Model waxaa loo isticmaali karaan G(VG, VM, EM, EG2M, EM2G), oo ku yaalaa in ay ku yaalaa in ay ka mid ah ka mid ah qiyaasta ka mid ah. VG represents the set containing each of the grid nodes 𝑣G. Each grid node represents a vertical slice of the atmosphere at a given latitude-longitude point, 𝑖. The features associated with each grid node 𝑣G are vG,features = [x𝑡−1, x𝑡, f𝑡−1, f𝑡, f𝑡+1, c𝑖], where x𝑡 is the time-dependent weather state 𝑋𝑡 corresponding to grid node 𝑣G and includes all the predicted data variables for all 37 atmospheric levels as well as surface variables. The forcing terms f𝑡 consist of time-dependent features that can be computed analytically, and do not need to be predicted by GraphCast. They include the total incident solar radiation at the top of the atmosphere, accumulated over 1 hour, the sine and cosine of the local time of day (normalized to [0, 1)), and the sine and cosine of the of year progress (normalized to [0, 1)). The constants c𝑖 are static features: the binary land-sea mask, the geopotential at the surface, the cosine of the latitude, and the sine and cosine of the longitude. At 0.25° resolution, there is a total of 721 × 1440 = 1, 038, 240 grid nodes, each with (5 surface variables + 6 atmospheric variables × 37 levels) × 2 steps + 5 forcings × 3 steps + 5 constant = 474 input features. Grid nodes Waayo, waxaa laga yaabaa in ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah oo mid ah mid ka mid ah mid ah oo mid ka mid ah mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ka mid ah oo mid ka mid ah. Mesh nodes Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Mesh edges Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah. EG2M are unidirectional edges that connect sender grid nodes to receiver mesh nodes. An edge 𝑒G2M 𝑣G→𝑣M is added if the distance between the mesh node and the grid node is smaller s r or equal than 0.6 times5 the length of the edges in mesh 𝑀6 (see Figure 1) which ensures every grid node is connected to at least one mesh node. Features eG2M,features are built the same way as those for 𝑣G→𝑣M s r the mesh edges. This results on a total of 1,618,746 Grid2Mesh edges, each with 4 input features. Grid2Mesh edges EM2G are unidirectional edges that connect sender mesh nodes to receiver grid nodes. For each grid point, we find the triangular face in the mesh 𝑀6 that contains it and add three Mesh2Grid edges of the form 𝑒M2G 𝑣M→𝑣G, to connect the grid node to the three mesh nodes adjacent s r to that face (see Figure 1). Features eM2G,features are built on the same way as those for the mesh 𝑣M→𝑣G s r edges. This results on a total of 3,114,720 Mesh2Grid edges (3 mesh nodes connected to each of the 721 × 1440 latitude-longitude grid points), each with four input features. Mesh2Grid edges 3.4 Qalabka Shuruudaha codsiga waa in la soo saarka data in wax soo saarka latent ee processor, oo waa in la soo saarka exclusively on multi-mesh. Sida loo isticmaalo codsiyada, waxaan ka soo bandhigi karaa in ay ka mid ah wax soo saarka, wax soo saarka, wax soo saarka, wax soo saarka, wax soo saarka iyo wax soo saarka. Embedding the input features Next, in order to transfer information of the state of atmosphere from the grid nodes to the mesh nodes, we perform a single message passing step over the Grid2Mesh bipartite subgraph GG2M(VG, VM, EG2M) connecting grid nodes to mesh nodes. This update is performed using an interaction network [5, 6], augmented to be able to work with multiple node types [2]. First, each of the Grid2Mesh edges are updated using information from the adjacent nodes, Grid2Mesh GNN Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah: Qalabka dhismaha iyo dhismaha iyo dhismaha dhismaha iyo dhismaha dhismaha iyo dhismaha dhismaha iyo dhismaha dhismaha, dhismaha dhismaha iyo dhismaha dhismaha iyo dhismaha dhismaha, dhismaha dhismaha dhismaha iyo dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha, dhismaha dhismaha dhismaha. After updating all three elements, the model includes a residual connection, and for simplicity of the notation, reassigns the variables, 3.5 Qalabka The processor is a deep GNN that operates on the Mesh subgraph GM (VM, EM) which only contains the Mesh nodes and and the Mesh edges. Note the Mesh edges contain the full multi-mesh, with not only the edges of 𝑀6, but all of the edges of 𝑀5, 𝑀4, 𝑀3, 𝑀2, 𝑀1 and 𝑀0, which will enable long distance communication. A single layer of the Mesh GNN is a standard interaction network [5, 6] which first updates each of the mesh edges using information of the adjacent nodes: Multi-mesh GNN Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah: And after updating both, the representations are updated with a residual connection and for simplicity of the notation, also reassigned to the input variables: The previous paragraph describes a single layer of message passing, but following a similar approach to [43, 39], we applied this layer iteratively 16 times, using unshared neural network weights for the MLPs in each layer. 3.6 Qalabka Shuruudaha ee decoder waa in la soo saarka wax soo saarka si ay u soo saarka, iyo si ay u soo saarka. Analogous to the Grid2Mesh GNN, the Mesh2Grid GNN performs a single message passing over the Mesh2Grid bipartite subgraph GM2G(VG, VM, EM2G). The Grid2Mesh GNN is functionally equivalent to the Mesh2Grid GNN, but using the Mesh2Grid edges to send information in the opposite direction. The GNN first updates each of the Grid2Mesh edges using information of the adjacent nodes: Mesh2Grid GNN Markaas ka dib markii ay u soo dejisan wax soo saarka, waxaa laga yaabaa in la soo saarka wax soo saarka oo ay ku saabsan wax soo saarka iyo wax soo saarka. Waxaad ka mid ah ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Waxaad ka mid ah in la soo bandhigay, oo ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah: Sida loo yaabaa, waxaa loo isticmaali karaa in ay u isticmaali karaa macluumaadka macluumaadka. Output function Markaas ka mid ah [43, 39], xawaaraha ugu soo saarka, X ̈t + 1, waxaa loo isticmaali karaa ka mid ah xawaaraha per-node, Y ̈t , ee xawaaraha dhismaha for all node grid, 3.7 Normalization iyo network parameterization Sidaas [43, 39], waxaan ku habboonay intaa oo dhan. Waayo, waxaan ku habboonay mid ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah. Input normalization Sida loo yaqaan 'Yt' waa mid ka mid ah Xt+1, waxaan ka mid ahay in ka mid ah Xt+1, waxaan ka mid ahay in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid ah in ka mid Output normalization Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Neural network parameterizations Qalabka Details This section provides details pertaining to the training of GraphCast, including the data split used to develop the model (Section 4.1), the full definition of the objective function with the weight associated with each variable and vertical level (Section 4.2), the autoregressive training approach (Section 4.3), optimization settings (Section 4.4), curriculum training used to reduce training cost (Section 4.5), technical details used to reduce the memory footprint of GraphCast (Section 4.6), training time (Section 4.7) and the software stacked we used (Section 4.8). 4.1 Qalabka Qalabka To mimic real deployment conditions, in which the forecast cannot depend on information from the future, we split the data used to develop GraphCast and data used to test its performance “causally”, in that the “development set” only contained dates earlier than those in the “test set”. The development set comprises the period 1979–2017, and the test set contains the years 2018–2021. Neither the researchers, nor the model training software, were allowed to view data from the test set until we had finished the development phase. This prevented our choices of model architecture and training protocol from being able to exploit any information from the future. Marka aad u baahan tahay in ay ku saabsan wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka, wax soo saarka iyo wax soo saarka, wax soo saarka iyo wax soo saarka. 4.2 Qalabka Qalabka GraphCast was trained to minimize an objective function over 12-step forecasts (3 days) against ERA5 targets, using gradient descent. The training objective is defined as the mean square error (MSE) between the target output 𝑋 and predicted output 𝑋ˆ, Kuuma τ ∈ 1 : Ttrain waa xawaaraha caadiga ah oo ku salaysan Ttrain auto-regresive. 𝑑0 ∈ 𝐷batch represent forecast initialization date-times in a batch of forecasts in the training set, j ∈ J waxaa loo yaqaan 'variable' iyo 'pressure level' oo ku saabsan variables atmospheric. E.g. J ={z1000, z850, . . . , 2 T, MsL}, i ∈ G0.25◦ waa xawaaraha (latitude iyo longitude) ee grid, x ̈d0+τ iyo xd0+τ waa mid ka mid ah xawaaraha iyo xawaaraha caadiga ah ee mid ka mid ah qalabka, xawaaraha, iyo xawaaraha caadiga,j,i j,i s j waa mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. wj waa dhismaha dhismaha dhismaha dhismaha, 𝑎𝑖 is the area of the latitude-longitude grid cell, which varies with latitude, and is normalized to unit mean over the grid. In order to build a single scalar loss, we took the average across latitude-longitude, pressure levels, variables, lead times, and batch size. We averaged across latitude-longitude axes, with a weight proportional to the latitude-longitude cell size (normalized to mean 1). We applied uniform averages across time and batch. Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah oo mid ka mid ah mid ka mid ah oo mid ka mid ah oo mid ka mid ah mid ka mid ah oo mid ka mid ah mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo mid ka mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah oo mid ah mid ka mid ah oo mid ka mid ah oo mid ah oo mid ka mid ah. 4.3 Qalabka on auto-regresive objective In order to improve our model’s ability to make accurate forecasts over more than one step, we used an autoregressive training regime, where the model’s predicted next step was fed back in as input for predicting the next step. The final GraphCast version was trained on 12 autoregressive steps, following a curriculum training schedule described below. The optimization procedure computed the loss on each step of the forecast, with respect to the corresponding ground truth step, error gradients with respect to the model parameters were backpropagated through the full unrolled sequence of model iterations (i.e., using backpropagation-through-time). 4.4 Qalabka optimization Waayo, sidoo kale waxaa loo yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid 4.5. Curriculum training schedule Qalabka ugu horeysay ayaa ku yaalaa in ay ka mid ah 1000 maalmood dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhism 4.6. Reducing memory footprint To fit long trajectories (12 autoregressive steps) into the 32GB of a Cloud TPU v4 device, we use several strategies to reduce the memory footprint of our model. First, we use batch parallelism to distribute data across 32 TPU devices (i.e., one data point per device). Second, we use bfloat16 floating point precision to decrease the memory taken by activations (note, we use full-precision numerics (i.e. float32) to compute performance metrics at evaluation time). Finally, we use gradient check-pointing [11] to further reduce memory footprint at the cost of a lower training speed. 4.7 Qalabka Waayo, ka dib markii loo yaabaa in ka mid ah shuruudaha auto-regresive, sida loo yaabaa ka hor, GraphCast ayaa ka mid ah 4 toddobaad ah oo ka mid ah 32 TPU-ga. 8.Software iyo Hardware Stack Waxaan isticmaali karaa JAX [9], Haiku [23], Jraph [17], Optax, Jaxline [4] iyo xarray [25] in la soo saarka iyo dhismaha modelka. 5. Verification methods This section provides details on our evaluation protocol. Section 5.1 details our approach to splitting data in a causal way, ensuring our evaluation tests for meaningful generalization, i.e., without leveraging information from the future. Section 5.2 explains in further details our choices to evaluate HRES skill and compare it to GraphCast, starting from the need for a ground truth specific to HRES to avoid penalizing it at short lead times (Section 5.2.1), the impact of ERA5 and HRES using different assimilation windows on the lookahead each state incorporates (Section 5.2.2), the resulting choice of initialization time for GraphCast and HRES to ensure that all methods benefit from the same lookahead in their inputs as well as in their targets (Section 5.2.3), and finally the evaluation period we used to report performance on 2018 (Section 5.2.4). Section 5.3 provides the definition of the metrics used to measure skill in our main results, as well as metrics used in complementary results in the Supplements. Finally, Section 5.4 details our statistical testing methodology. 5.1 Qalabka, Validation, iyo Test splits Waayo, waxaa loo isticmaali karaa protocollan oo ku yaalaa xafiisyada horumarinta (Section 4.1), waxaan ku habboonay 4 version of GraphCast, oo dhan oo ka mid ah waqti badan. Waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah 5.2. Qalabka GraphCast iyo HRES 5.2.1. Choice of ground truth datasets GraphCast waxaa la soo saarka in ay ku yaalaa data ERA5 iyo in ay ka heli karaa data ERA5 si loo yaabaa; waxaan sidoo kale loo isticmaali karaa ERA5 si ay u yaalaa modelka. Haddii loo yaabaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay ku yaalaa in ay 5.2.2 Waqtiga ugu caawin ah ee xayawaanka xayawaanka Sida loo yaqaan Section 1, HRES wuxuu soo bandhigi karaa wax soo saarka 4 +/-3h ee ka mid ah 00z, 06z, 12z iyo 18z (waana 18z waa mid ka mid ah 18:00 UTC ee shuruudaha Zulu), laakiin ERA5 waxay isticmaalaa 2 +9h/-3h ee ka mid ah 00z iyo 12z, ama mid ka mid ah 2 +3h/-9h ee ku mid ah 06z iyo 18z. Si kastaba ha ahaatee, sidoo kale sidoo kale sidoo kale sidoo kale sidoo kale ka mid ah Figure 9 for illustration. GraphCast waxaa loo yaabaa in ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah 5.2.3. Qalabka initialization iyo wax soo saarka-day Sida loo yaqaan oo ku yaal ah, soo bandhigiisa ah ee HRES waa in ay ku yaalaa GraphCast loo isticmaalo 06z iyo 18z initializations, iyo oo ka mid ah ka mid ah ka mid ah ka mid ah 12h, oo waa in ka mid ah ka mid ah 06z iyo 18z. Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Marka aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. Whenever we plot RMSE and other evaluation metrics as a function of lead time, we indicate with a dotted line the 3.5 day changeover point where we switch from evaluating HRES on 06z/18z to evaluating on 00z/12z. At this changeover point, we plot both the 06z/18z and 00z/12z metrics, showing the discontinuity clearly. 5.2.4 Waqtiga ah Markaad ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid 5.3 Qalabka Qalabka We quantify the skillfulness of GraphCast, other ML models, and HRES using the root mean square error (RMSE) and the anomaly correlation coefficient (ACC), which are both computed against the models’ respective ground truth data. The RMSE measures the magnitude of the differences between forecasts and ground truth for a given variable indexed by 𝑗 and a given lead time 𝜏 (see Equation (20)). The ACC, L𝑗,𝜏 , is defined in Equation (29) and measures how well forecasts’ differences from climatology, i.e., the average weather for a location and date, correlate with the ground truth’s differences from climatology. For skill scores we use the normalized RMSE difference between model 𝐴 and baseline 𝐵 as (RMSE𝐴 − RMSE𝐵)/RMSE𝐵, and the normalized ACC difference as (ACC𝐴 − ACC𝐵)/(1 − ACC𝐵). Dhismaha oo dhan waxaa loo isticmaali karaa float32 si ay u isticmaali karaa farxad dynamic native of the variables, oo ka mid ah normalization. . We quantified forecast skill for a given variable, 𝑥 𝑗, and lead time, 𝜏 = 𝑡Δ𝑑, using a latitude-weighted root mean square error (RMSE) given by Root mean square error (RMSE) where • d0 ∈ Deval waxay ku yaalaa dhismaha ugu horeysay ee dhismaha ugu horeysay ee dhismaha dhismaha, • 𝑗 ∈ 𝐽 index variables and levels, e.g., 𝐽 = {z1000, z850, . . . , 2 T, MsL}, • i ∈ G0.25◦ waa xawaaraha (latitude iyo longitude) ee grid, • x ̈d0+τ iyo xd0+τ waa mid ka mid ah qiimeynta iyo cilmi-baarista oo ka mid ah mid ka mid ah xafiisyada, xafiisyada, iyo xafiisyada, QEEBE J,I • ai waa alaabta la qalajiyeyaalka xayawaanka la xawaaraha-gawaaraha xayawaanka (gawaarida ka mid ah xayawaanka ah ee xayawaanka) oo waa la xayawaanka xayawaanka. Sida loo yaqaan 'Rocket Root' waa mid ka mid ah oo ka mid ah in la mid ah oo ka mid ah in la mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah. Waayo, waxaa laga yaabaa in ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah. Root mean square error (RMSE), spherical harmonic domain. Sidaas, fd0+τ iyo fd0+τ waxaa laga yaabaa oo ka mid ah coefficients ee dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha j,l,m j,l,m Qalabka dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha iyo dhismaha. Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah: Root mean square error (RMSE), per location. Waxaan sidoo kale soo xigtay RMSE by latitude kaliya: ku yaabaa (G0.25◦ ) Átha = 1440 waa badan oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah 0.25 °. Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah: Root mean square error (RMSE), by surface elevation. ku yaqaan ll waa mid ka mid ah function indicator. Qalabka waxaa loo yaabaa sida Mean bias error (MBE), per location. Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Root-mean-square per-location mean bias error (RMS-MBE). Sida loo yaabaa, waxaa laga yaabaa in ay ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Correlation of per-location mean bias errors. Qalabka dhismaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha ugu horeysay ee shuruudaha. where 𝐶𝑑0+𝜏 is the climatological mean for a given variable, level, latitude and longitude, and for the day-of-year containing the validity time 𝑑0 + 𝜏. Climatological means were computed using ERA5 data between 1993 and 2016. All other variables are defined as above. 5.4 Qalabka Statistics 5.4.1.Test Significance for difference in midabka Waayo, waxaa loo isticmaali karaa in ay ka mid ah mid ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah. Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid Qalabka 5 oo ka mid ah wax soo saarka wax soo saarka ah ee wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka wax soo saarka. 5.2.2 Qalabka dhismaha Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Waayo, waxaan u hesho diferensiyada Waxaa loo isticmaali karaa si ay u hesho null in ay E[diff-RMSE( j, τ, d0)] = 0 in ka mid ah alterna-tive two-sided. Waayo, by our stationarity assumption this expectation does not depend on d0. Sida loo yaabaa in Section 5.2.3, oo ka mid ah 4 maalmood oo ka badan, waxaan sidoo kale ka mid ah dhismaha HRES ka mid ah 00z iyo 12z dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Waxaan isticmaali karaa in ay u isticmaali karaa in ay u isticmaali karaa hipotesis null E[diff-RMSEinterp( j, τ, d0)] = 0, oo uu u isticmaali karaa d0 si ay u isticmaali karaa warshad stagnation on the differences. If we further assume that the HRES RMSE time series itself is stationary (or at least close enough to stationary over a 6 hour window) then E[diff-RMSEinterp( j, τ, d0)] = E[diff-RMSE( j, τ, d0)] and the interpolated differences can also be used to test deviations from the original null hypothesis that E[diff-RMSE( j, τ, d0)] = 0. Sida loo yaqaan 'HREs RMSEs' waxay ka mid ah wax soo saarka, waxaa loo yaqaan 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs RMSEs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' iyo 'HREs' 5.4.3. Intervals dhismaha ee RMSEs Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid These confidence intervals make a stationarity assumption for the separate GraphCast and HRES RMSE time series, which as stated above is a stronger assumption that stationarity of the differences and is violated somewhat. Thus these single-sample confidence intervals should be treated as approximate; we do not rely on them in our significance statements. 5.4.4. Intervals dhismaha oo ka mid ah macluumaadka RMSE Sida loo yaabaa t-testi oo ku yaalaa Section 5.4.1 waxaan sidoo kale sidoo kale loo yaqaan 'intervals of confidence for the true difference in RMSEs', laakiin waxaa loo yaqaan 'intervals of confidence for the true RMSE skill score', oo ku yaqaan 'intervals of confidence for the true difference is normalized by the true RMSE of HRES': A confidence interval for this quantity should take into account the uncertainty of our estimate of the true HRES RMSE. Let [𝑙diff, 𝑢diff] be our 1 − 𝛼/2 confidence interval for the numerator (difference in RMSEs), and [𝑙HRES, 𝑢HRES] our 1 − 𝛼/2 confidence interval for the denominator (HRES RMSE). Given that 0 < 𝑙𝐻𝑅𝐸𝑆 in every case for us, using interval arithmetic and the union bound we obtain a conservative 1 − 𝛼 confidence interval Waayo, waxaan soo bandhigay la xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka xayawaanka. 6. Comparison with previous machine learning baselines To determine how GraphCast’s performance compares to other ML methods, we focus on Pangu-Weather [7], a strong MLWP baseline that operates at 0.25° resolution. To make the most direct comparison, we depart from our evaluation protocol, and use the one described in [7]. Because published Pangu-Weather results are obtained from the 00z/12z initializations, we use those same initializations for GraphCast, instead of 06z/18z, as in the rest of this paper. This allows both models to be initialized on the same inputs, which incorporate the same amount of lookahead (+9 hours, see Sections 5.2.2 and 5.2.3). As HRES initialization incorporates at most +3 hours lookahead, even if initialized from 00z/12z, we do not show the evaluation of HRES (against ERA5 or against HRES-fc0) in this comparison as it would disadvantage it. The second difference with our protocol is to report performance every 6 hours, rather than every 12 hours. Since both models are evaluated against ERA5, their targets are identical, in particular, for a given lead time, the target incorporates +3 hours or +9 hours of lookahead for both GraphCast and Pangu-Weather, allowing for a fair comparison. Pangu-Weather[7] reports its 7-day forecast accuracy (RMSE and ACC) on: z500, T 500, T 850, Q 500, U 500, v 500, 2 T, 10 U, 10 v, and MsL. Sida loo yaabaa in Qalabka 12, GraphCast (Lines Blue) waa ugu fiican Pangu-Weather [7] (Lines Red) at 99.2% of targets. For the surface variables (2 T, 10 U, 10 v, MsL), error of GraphCast in the first few days is around 10-20% lower, and over the longer lead times plateaus to around 7-10% lower error. The only two (of the 252 total) metrics on which Pangu-Weather outperformed GraphCast was z500, at lead times 6 and 12 hours, where GraphCast had 1.7% higher average RMSE (Figure 12a,e). Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Dhismaha ugu badan oo ka mid ah dhismaha ka mid ah dhismaha ka mid ah dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha, dhismaha 7.1 Results Details for variables dheeraad ah 7.1.1 RMSE iyo ACC Qalabka 13 waxay ku yaalaa Qalabka 2a-b iyo waxay ku sooja RMSE iyo qalabka RMSE ku saabsan HRES for GraphCast iyo HRES on a combination of 12 highlight variables. Qalabka 14 waxay ku sooja ACC iyo qalabka ACC ku saabsan HRES for GraphCast iyo HRES on the same a combination of 12 variables and complements Qalabka 2c. Qalabka Qalabka ACC waa qalabka ACC ku saabsan model A iyo baseline B as (ACCA − ACCB)/(1 − RMSEB). 7.1.2. Results of Significance Test for RMSE comparisons Qalabka 5 waxay ku saabsan wax soo saarka oo ku yaal ah oo ka mid ah macluumaadka macluumaadka ee macluumaadka macluumaadka ee macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka macluumaadka 7.1.3. Effect of data recency on GraphCast An important feature of MLWP methods is they can be retrained periodically with the most recent data. This, in principle, allows them to model recent weather patterns that change over time, such as the ENSO cycle and other oscillations, as well as the effects of climate change. To explore how the recency of the training data influences GraphCast’s test performance, we trained four variants of GraphCast, with training data that always began in 1979, but ended in 2017, 2018, 2019, and 2020, respectively (we label the variant ending in 2017 as “GraphCast:<2018”, etc). We evaluated the variants, and HRES, on 2021 test data. Figure 15 shows the skill and skill scores (with respect to HRES) of the four variants of GraphCast, for several variables and complements Figure 4a. There is a general trend where variants trained to years closer to the test year have generally improved skill score against HRES. The reason for this improvement is not fully understood, though we speculate it is analogous to long-term bias correction, where recent statistical biases in the weather are being exploited to improve accuracy. It is also important to note that HRES is not a single NWP across years: it tends to be upgraded once or twice a year, with generally increasing skill on z500 and other fields [18, 22, 19, 20, 21]. Markaas ka mid ah, GraphCast:<2018 iyo GraphCast:<2019, si kastaba ha ahaatee, waxaa laga yaabaa wax soo saarka ah oo ka mid ah HRES oo ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah ka mid ah. 7.2 Qalabka dhismaha 7.2.1 RMSE by qiyaasta Waayo, waxaa laga yaabaa in aad u baahan tahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. 7.2.2. RMSE skill score by latitude and pressure level In Figuur 19, waxaan bixiyaan dhismaha normalized RMSE ka mid ah GraphCast iyo HRES, sida wax soo saarka oo ka mid ah heerka dhismaha iyo latitude. Waxaan bixiyaan kaliya 13 heerka dhismaha ka mid ah WeatherBench [41] oo ka mid ah waxaan bixiyaan HRES. On these plots, we indicate at each latitude the mean pressure of the tropopause, which separates the troposphere from the stratosphere. We use values computed for the ERA-15 dataset (1979-1993), given in Figure 1 of [44]. These will not be quite the same as for ERA5 but are intended only as a rough aid to interpretation. We can see from the scorecard in Figure 2 that GraphCast performs worse than HRES at the lowest pressure levels evaluated (50hPa). Figure 19 shows that the pressure level at which GraphCast starts to get worse is often latitude-dependent too, in some cases roughly following the mean level of the tropopause. Waayo, waxaan loo isticmaali karaa wax soo saarka dhismaha badan oo ka mid ah wax soo saarka dhismaha badan oo ka mid ah wax soo saarka dhismaha ah oo ka mid ah wax soo saarka dhismaha ah oo ka mid ah wax soo saarka dhismaha dhismaha ah oo ka mid ah wax soo saarka dhismaha dhismaha. 7.2.3 Biases by latitude iyo longitude In Figures 20 to 22, we plot the mean bias error (MBE, or just ‘bias’, defined in Equation (26)) of GraphCast as a function of latitude and longitude, at three lead times: 12 hours, 2 days and 10 days. Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Waayo, waxa uu ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah. We also computed a correlation coefficient between GraphCast and HRES’ per-location mean bias errors (defined in Equation (27)), which is plotted as a function of lead time in Figure 24. We can see that GraphCast and HRES’ biases are uncorrelated or weakly correlated at the shortest lead times, but the correlation coefficient generally grows with lead time, reaching values as high as 0.6 at 10 days. 7.2.4. qiimeeyaasha RMSE by latitude iyo longitude Markaas ka mid ah Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Q Shuruudaha ugu horeysay ee HRES ee ku saabsan GraphCast waa mid ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah oo ka mid ah caadiga ah. In 12 saacadood iyo 2 maalmood ka mid ah GraphCast iyo HRES waxaa la aasaasay at 06z/18z initialization iyo xawaaraha, laakiin in 10 maalmood ka mid ah 10 maalmood ka mid ah GraphCast at 06z/18z iyo HRES at 00z/12z (x. 7.2.5. RMSE Skill Score ka mid ah xawaaraha sare Marka aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Waayo, GraphCast waxaa la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay in la aasaasay. Variables using pressure-level coordinates are interpolated below ground when the pressure level exceeds surface pressure. GraphCast is not given any explicit indication that this has happened and this may add to the challenge of learning to forecast at high surface elevations. In further work using pressure-level coordinates we propose to provide additional signal to the model indicating when this has happened. Sida loo yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. 7.3 GraphCast ablations waaweyn 7.3.1 Qalabka Multi-Mesh Marka aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u Shuruudaha 29 (panel ka mid ah) wuxuu soo bandhigay tababarka soo bandhigay GraphCast iyo model ablated. GraphCast waxay ka mid ah tababarka soo bandhigay multi-mesh for all predicted variables, oo ka mid ah waqti-baaran oo ka badan 5 maalmood ka badan 50 hPa. Imtixaanka waa mid ka mid ah in geopotential oo ka mid ah xawaaraha xawaaraha sare ee 5 maalmood ka badan 5 maalmood. Tababarka mid ah wuxuu soo bandhigay tababarka soo bandhigay model ablated iyo HRES, iyo tababarka mid ka mid ah soo bandhigay GraphCast iyo HRES, si ay u soo bandhigay in multi-mesh waa mid ka mid ah in GraphCast in ay ka mid ah HRES on geopot 7.3.2 Dhammaan oo ku haboon autoregressive Waayo, sidoo kale waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah oo mid ka mid ah. 7.4 Qalabka optimum 7.4.1. Imtixaanka in la soo bandhigiisa ka hor GraphCast iyo HRES Markaaskii 31 iyo 32 waxaan soo bandhigay RMSE ee HRES iyo GraphCast ka hor iyo ka dib markii loo isticmaali karaa dhismaha optimum ee mid ka mid ah model. 7.4.2. Filtering methodology We chose filters which minimize RMSE within the class of linear, homogeneous (location invariant), isotropic (direction invariant) filters on the sphere. These filters can be applied easily in the spherical harmonic domain, where they correspond to multiplicative filter weights that depend on the total wavenumber, but not the longitudinal wavenumber [12]. Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid Waxaan ka dibna soo bandhigay cadaadiga ah f ̈d0+τ by a filter weight bτ, which is independent of j,l,m j,l the longitudinal wavenumber m. The filter weights were fitted using least-squares to minimize average square error, as computed in the spherical harmonic domain: Waxaan isticmaali karaa data ka 2017 si ay u isticmaali karaa wax soo saarka ah, oo ay ka mid ah wax soo saarka ah ee 2018 oo ka mid ah wax soo saarka. Ka dib markii ay si ay u isticmaali karaa wax soo saarka, waxaan soo saarka MSE ee warshad dhismaha dhismaha dhismaha dhismaha, sida loo soo saarka Ecuation (22). Sida loo isticmaali karaa filters kala duwan ee cadaadis kasta, dhismaha dhismaha waxaa la isticmaali karaa si ay u isticmaali karaa dhismaha kala duwan ee dhismaha. While this method is fairly general, it also has limitations. Because the filters are homogeneous, they are unable to take into account location-specific features, such as orography or land-sea boundaries, and so they must choose between over-blurring predictable high-resolution details in these locations, or under-blurring unpredictable high-resolution details more generally. This makes them less effective for some surface variables like 2 T, which contain many such predictable details. Future work may consider more complex post-processing schemes. Markaad ka mid ah in ay ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah oo mid ka mid ah mid ka mid ah oo mid ka mid ah mid ka mid ah mid ka mid ah oo mid ka mid ah mid ka mid ah oo mid ah mid ka mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ka mid ah mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah 7.4.3. Transfer functions of the optimal filters The filter weights are visualized in Figure 33, which shows the ratio of output power to input power for the filter, on the logarithmic decibel scale, as a function of wavelength. (With reference to Equation (35), this is equal to 20 log10(𝑏𝜏 ) for the wavelength 𝐶𝑒/𝑙 corresponding to total wavenumber 𝑙.) Markaas ka mid ah HRES iyo GraphCast, waxaan noqon doonaa in ay ka mid ah in MSE si ay u qiyaasta in ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah oo ka mid ah. We can see that HRES generally requires more blurring than GraphCast, because GraphCast’s predictions already blur to some extent (see Section 7.5.3), whereas HRES’ do not. Filters optimum waa ka mid ah in la mid ah, si ay u dhiso biaska spectral ee xawaaraha GraphCast iyo HRES. Sidaas, oo ka mid ah badan oo ka mid ah daawada ee our ERA5 data set, spectrum ka mid ah oo ka mid ah oo ka badan 62km oo ka mid ah oo ka mid ah 0.28125◦ resolution ee ERA5. GraphCast waxay ka mid ah in la mid ah in la mid ah in la mid ah this cutoff. Waxaan sidoo kale ku yaalaa in ay ka mid ah ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah. 7.4.4. Relationship between autoregressive training horizon and blurring In Figuur 34 waxaa loo isticmaali karaa wax soo saarka of optimum blurring si ay u arki karaa xanuunka ka mid ah dhismaha autoregressive iyo blurring of GraphCast's xawaaraha oo ka badan leh. Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid Waxaad ka mid ah in la soo xiriir oo ka mid ah wax soo saarka horisont ah oo ka mid ah wax soo saarka post-processing, sida wax soo saarka optimaal, laakiin sidoo kale sidoo kale sidoo kale ka mid ah wax soo saarka horisont ah oo ka mid ah wax soo saarka horisontada oo ka mid ah wax soo saarka horisontada oo ka mid ah wax soo saarka horisontada oo ka mid ah wax soo saarka. Marka aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. 7.5 Qalabka Analysis 7.5.1.Dhammaan spectraal ee dhismaha midabka quruuska ah Waayo, waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. oo lmax = 719 oo ku saabsan Equation (22). Dhammaan qiyaastii ka mid ah qiyaastii l waa mid ka mid ah qiyaastii Ce / l, oo Ce waa mid ka mid ah qiyaastii Earth. Waayo, waxaa loo yaqaan 'Histograms' (Histograms) iyo 'Histograms' (Histograms) waxaa loo yaqaan 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' (Histograms) iyo 'Histograms' Waayo, ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah. At shorter lead times of 12 hours to 1 day, for a number of variables (including z500, T500, T850 and U500) HRES has greater skill than GraphCast at scales in the approximate range of 200-2000km, with GraphCast generally having greater skill outside this range. 7.5.2. RMSE as a function of horizontal resolution Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid The RMSEs between truncated predictions and targets can be obtained via cumulative sums of the mean error powers 𝑆 𝑗,𝜏(𝑙) defined in Equation (37), according to Figure 37 shows that in most cases GraphCast has lower RMSE than HRES at all resolutions typically used for forecast verification. This applies before and after optimal filtering (see Section 7.4). Exceptions include 2 meter temperature at a number of lead times and resolutions, T 500 at 12 hour lead times, and U 500 at 12 hour lead times, where GraphCast does better at 0.25° resolution but HRES does better at resolutions around 0.5◦ to 2.5◦ (corresponding to shortest wavelengths of around 100 to 500 km). In particular we note that the native resolution of ERA5 is 0.28125◦ corresponding to a shortest wavelength of 62km, indicated by a vertical line in the plots. HRES-fc0 targets contain some signal at wavelengths shorter than 62km, but the ERA5 targets used to evaluate GraphCast do not, natively at least (see Section 7.5.3). In Figure 37 we can see that evaluating at 0.28125◦ resolution instead of 0.25° does not significantly affect the comparison of skill between GraphCast and HRES. 7.5.3. Spectra of predictions and targets Qalabka 38 waxay soo bandhigay xisaabooyinka awoodda ee xawaaraha GraphCast, xawaaraha ERA5 iyo HRES-fc0. Markaas ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Differences between HRES and ERA5 Waayo, waxaa laga yaabaa in ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka. Blurring in GraphCast Waayo, waxaan ku yaalaa in ay ku salaysan oo kale oo kale oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka iyo wax soo saarka iyo wax soo saarka iyo wax soo saarka. Peaks for GraphCast around 100km wavelengths Markaas ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Waayo, GraphCast waxay ku yaalaa in ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka ah oo ka mid ah wax soo saarka iyo wax soo saarka. 8.1 Qalabka Cyclone Tropical In this section, waxaan soo xiriir in ay isticmaali karaa protocolls warshadaha (Supplements Section 8.1.1) iyo analyzes statistical significance (Supplements Section 8.1.2), si ay u soo saarka wax soo saarka (Supplements Section 8.1.3), iyo ku saabsan our tracker iyo wax soo saarka oo ka mid ah ECMWF (Supplements Section 8.1.4). 8.1.1. Evaluation protocol The standard way of comparing two tropical cyclone prediction systems is to restrict the comparison to events where both models predict the existence of a cyclone. As detailed in Supplements Section 5.2.2, GraphCast is initialized from 06z and 18z, rather than 00z and 12z, to avoid giving it a lookahead advantage over HRES. However, the HRES cyclone tracks in the TIGGE archive [8] are only initialized at 00z and 12z. This discrepancy prevents us from selecting events where the initialization and lead time map to the same validity time for both methods, as there is always a 6h mismatch. Instead, to compare HRES and GraphCast on a set of similar events, we proceed as follows. We consider all the dates and times for which our ground truth dataset IBTrACS [29, 28] identified the presence of a cyclone. For each cyclone, if its time is 06z or 18z, we make a prediction with GraphCast starting from that date, apply our tracker and keep all the lead times for which our tracker detects a cyclone. Then, for each initialization time/lead time pairs kept for GraphCast, we consider the two valid times at +/-6h around the initialization time of GraphCast, and use those as initialization time to pick the corresponding HRES track from the TIGGE archive. If, for the same lead time as GraphCast, HRES detects a cyclone, we include both GraphCast and HRES initialization time/lead time pairs into the final set of events we use to compare them. For both methods, we only consider predictions up to 120 hours. Waayo, waxaan soo xigtay xigtay oo ku saabsan xigtay ugu horeysay (e.g., IBTrACS), si ay u xigtay xigtay xigtay oo ku yaqaan Section 5.2.2 of Supplements, i.e. xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay xigtay Waayo, xawaaraha ka mid ah mid ka mid ah dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha 8.1.2 Qalabka dhismaha Qalabka dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha 1. Waxaa ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid Markaas ka mid ah dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Waayo, waxa uu u baahan tahay in ay ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah oo mid ah mid ka mid ah. Sida loo yaabaa, waxaa loo yaabaa in ka mid ah 50 (50, 100, 150) ee Cyclone A, (300, 200) ee Cyclone B iyo (100, 100) ee Cyclone C, oo A waxay ka mid ah macluumaadka. 8.1.3. Results In Supplements Figure 3a-b, we chose to show the median error rather than the mean. This decision was made before computing the results on the test set, based on the performance on the validation set. On the years 2016–2017, using the version of GraphCast trained on 1979–2015, we observed that, using early versions of our tracker, the mean track error was dominated by very few outliers and was not representative of the overall population. Furthermore, a sizable fraction of these outliers were due to errors in the tracking algorithm rather than the predictions themselves, suggesting that the tracker was suboptimal for use with GraphCast. Because our goal is to assess the value of GraphCast forecast, rather than a specific tracker, we show median values, which are also affected by tracking errors, but to a lesser extent. In figure Figure 40 we show how that the distribution of both HRES and GraphCast track errors for the test years 2018–2021 are non-gaussian with many outliers. This suggests the median is a better summary statistic than the mean. Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Because of well-known blurring effects, which tend to smooth the extrema used by a tracker to detect the presence of a cyclone, ML methods can drop existing cyclones more often than NWPs. Dropping a cyclone is very correlated with having a large positional error. Therefore, removing from the evaluation such predictions, where a ML model would have performed particularly poorly, could give it an unfair advantage. Sida loo yaabaa, waxaan ku yaalaa in uu ka mid ah wax soo saarka super-parameter-searched (x.Supplements Section 8.1.4) waxay ka caawinayaa in ka mid ah oo ka mid ah cyclones sida HRES.Supplements Figure 41 wuxuu ku yaalaa in ay ka mid ah wax soo saarka (2018-2021), GraphCast iyo HRES ka mid ah oo ka mid ah oo ka mid ah cyclones, si ay u caawinayaa in ay ka mid ah wax soo saarka ugu caawin ah. Qalabka Qalabka 42 iyo 43 soo dejisan dhismaha midabka iyo dhismaha caadiga ah sida wax soo saarka oo ka mid ah waqti caadiga ah, oo ku yaal ah oo ka mid ah dhismaha ah waxaa loo yaqaan Saffir-Simpson Hurricane Wind Scale [47], iyo dhismaha 5 waa mid ka mid ah dhismaha caadiga ah oo ka mid ah dhismaha caadiga ah (wax, waxaan isticmaali karaa dhismaha 0 in ka mid ah dhismaha caadiga ah). Waxaan sidoo kale ka heli karaa in ka mid ah ama ugu fiican ee dhismaha caadiga ah oo ka mid ah dhismaha. 8.1.4 Tracker xawaaraha Marka aad u isticmaali karaa in ay u isticmaali karaa GraphCast waxaa loo isticmaali karaa si ay u isticmaali karaa ECMWF's tracker [35]. Sida loo isticmaali karaa in ay isticmaali karaa 0.1° HRES, waxaan sidoo kale u isticmaali karaa in ay isticmaali karaa macluumaad ka mid ah macluumaadka macluumaadka macluumaadka sida loo isticmaali karaa in ay isticmaali karaa in ay GraphCast. Si kastaba ha ahaatee, macluumaadka macluumaadka waxaa laga yaabaa, oo loo yaabaa in ay isticmaali karaa macluumaadka macluumaadka macluumaadka ka mid ah 0.25° oo ka mid ah 0.1°. Waayo, waxaan ka dibna soo bandhigiisa in la soo bandhigiisa ah oo ka mid ah ECMWF, ka dib markii la soo bandhigiisa in la soo bandhigiisa iyo wax soo bandhigiisa. Sida loo yaabaa in ay ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ECMWF tracker Waayo, waxaa loo yaabaa in ay ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah Ka dib markii loo yaabaa in ay ku yaalaa xafiisyada horumarka ugu horumarka ah oo ka mid ah 445 km ka horumarka ugu horumarka ugu horumarka ah (MsL) oo ka mid ah 445 km ka horumarka ugu horumarka ah. 1. Vorticity check: the maximum vorticity at 850 hPa within 278 km of the local minima is larger than 5 · 10−5 s−1 for the Northern Hemisphere, or is smaller than −5 · 10−5s−1 for the Southern Hemisphere. Vorticity can be derived from horizontal wind (U and v). Qalabka dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha dhismaha Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka Qalabka If no minima satisfies all those conditions, the tracker considers that there is no cyclone. ECMWF’s tracker allows cyclones to briefly disappear under some corner-case conditions before reappearing. In our experiment with GraphCast, however, when a cyclone disappear, we stop the tracking. Waayo, sidoo kale waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ka mid ah. Our modified tracker Marka aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan tahay in aad u baahan yahay in aad u baahan tahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay in aad u baahan yahay. Waxaan sidoo kale ka heli karaa parameter this si aad u baahan tahay si aad u aragto badan oo ka mid ah macluumaadka: 278 × f for f in 0.25, 0.375, 0.5, 0.625, 0.75, 1.0 (wax yar). 3. Qalabka soo saarka ee ECMWF waxaa loo isticmaali karaa soo saarka 50-50 ka mid ah extrapolation linear iyo vectators dhererka dhererka. In our case where wind is predicted at 0.25° resolution, we found wind steering to sometimes obstacle estimates. This is not surprising because the wind is not a spatially smooth field, and the tracker is probably tailored to leverage 0.1° resolution predictions. So, we hyper-parameter searched the weighing among the following options: 0.0, 0.1, 0.33, 0.5 (value original). Sidaas, waxaan ka mid ah u baahan tahay in ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah Markaas oo ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Waayo, waxaan sidoo kale soo xigtay in ka mid ah wax soo saarka hyper-parameter, oo ka mid ah wax soo saarka ah oo loo isticmaali karaa GraphCast ayaa ka caawinayaa in ka mid ah oo ka mid ah oo ka mid ah HRES. 8.2 Qalabka dhismaha Waayo, GraphCast waxay ka heli karaa IvT oo ka mid ah wax soo saarka caadiga ah ee caadiga ah ee caadiga ah (IvT) waxaa loo isticmaali karaa si ay u isticmaali karaa in ay soo saarka caadiga ah ee caadiga ah ee caadiga ah [38, 37]. Haddii GraphCast waxay ka soo saarka IvT si ay u soo saarka caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah (U, v), sidoo kale sidoo kale sidoo kale sidoo kale sidoo kale sidoo kale loo isticmaali karaa in ka mid ah caadiga caadiga ah ee caadiga ah ee caadiga ah ee caadiga ah [38]: oo g = 9,80665 m/s2 waa xawaaraha ka mid ah gravity ka hor, pb = 1000 hPa waa xawaaraha ugu badan, iyo pt = 300 hPa waa xawaaraha ugu badan. Waayo, waxaa loo yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid Sida loo isticmaali karaa in ay ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah Sida loo yaqaan wax soo saarka ugu horeysay [10], Qalabka 44 waxay ku yaalaynay macluumaadka iyo macluumaadka RMSE ka mid ah ee North America iyo Eastern Pacific (nga 180°W ilaa 110°W xawaaraha, iyo 10°N ilaa 60°N xawaaraha) oo ka hor (Jan-April iyo Oct-Dec 2018), oo ku yaaladaha iyo ka horumariyo oo ay ka mid ah xawaaraha caadiga ah. 8.3 Qalabka dhismaha iyo dhismaha Waayo, sidoo kale waxaa laga yaabaa in ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. Marka loo yaabaa in ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah oo mid ah mid ka mid ah mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ka mid ah oo mid ah mid ka mid ah oo mid ah mid ka mid ah oo mid ah mid ka mid ah mid ah oo mid ah mid ka mid ah oo mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid Waayo, waxaa loo yaabaa in ka mid ah wax soo saarka ah oo ka mid ah soo saarka ah oo ka mid ah 2 T [35, 32], iyo T 850, z500 oo ka mid ah oo ka mid ah ECMWF si ay u isticmaalaa in ay soo saarka ah [34]. Si kastaba ha soo saarka ah [32], oo ka mid ah wax soo saarka ah oo ka mid ah June, July, iyo August oo ka mid ah wax soo saarka ah oo ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah mid ah mid ka mid ah Qalabka visualization In this final section, waxaan bixiyaan mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah mid ka mid ah. QEEBE [1] Ferran Alet, Adarsh Keshav Jeewajee, Maria Bauza Villalonga, Alberto Rodriguez, Tomas Lozano-Perez, iyo Leslie Kaelbling. 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