raw · 12550 bytes
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 | """Stage `climate`: seasonal insolation → temperature, 3-cell winds + monsoons, moisture transport → rain.""" from __future__ import annotations import numpy as np from scipy import sparse from . import ocean as OC from .config import params from .graph import bicgstab_jacobi, distance_to, gradient, nearest_source, pmap, smooth_km from .grid import rowdot_at from .sphere import east_north, latlon_to_xyz, rotate_about, tangent_dir S0 = 1361.0 SEA_FREEZE_C = -1.8 # the exported SST never goes below sea water's freezing point (ice-covered sea) SEASONS = ("jun", "dec", "eq") DEFAULTS = { "t_a": -55.2, "t_b": 0.3206, "t_c": -2.974e-4, "land_seasonal": 0.45, "land_summer": 0.9, "continentality_summer_max": 1.5, "ocean_seasonal": 0.15, "continentality_km": 1500.0, "continentality_max": 1.8, "lapse_c_per_km": 6.5, "current_c": 4.0, "current_reach_km": 600.0, "current_leak_km": 150.0, "heat_transport_km": 300.0, "hadley_edge_deg": 20.0, "ferrel_edge_deg": 55.0, "itcz_shift_deg": 8.0, "trade_u": -6.0, "trade_v": 2.0, "westerly_u": 8.0, "westerly_v": 1.0, "polar_u": -4.0, "polar_v": 1.0, "monsoon_k": 1.0, "monsoon_length_km": 1500.0, "monsoon_speed_scale": 6000.0, "coriolis_min_deg": 20.0, "coriolis_span_deg": 50.0, "base_rate": 0.25, "conv_rate": 2.0, "front_rate": 0.8, "front_lat_deg": 40.0, "front_width_deg": 10.0, "itcz_width_deg": 8.0, "oro_rate": 20.0, "subsidence": 0.2, "min_rate": 0.05, "cc_per_c": 0.07, "recycle": 0.83, "eddy_k_m2s": 2.2e6, "eddy_wind_ms": 8.0, "global_mean_mm": 1000.0, "lock": False, "lock_at": [0.0, 0.0], "lock_day_c": 120.0, "lock_night_c": -200.0, "lock_wind_ms": 10.0, "lock_melt_c": 0.0, "lock_melt_width_c": 25.0, } def t_of_q(q, P): """Radiative-equilibrium-like surface temperature (°C) from insolation (W/m²); quadratic fit to Earth-like zonal means for a 20° tilt: equator 27, 45° ≈ 15, 60° ≈ 3, pole ≈ −22 (concave: damps polar-day summers).""" return P["t_a"] + P["t_b"] * q + P["t_c"] * q * q def declinations(tilt): return {"jun": tilt, "dec": -tilt, "eq": 0.0} def insolation(lat, decl): """Daily-mean top-of-atmosphere insolation (W/m²).""" phi = np.radians(np.clip(lat, -89.9999, 89.9999)) d = np.radians(decl) h0 = np.arccos(np.clip(-np.tan(phi) * np.tan(d), -1.0, 1.0)) return S0 / np.pi * (h0 * np.sin(phi) * np.sin(d) + np.cos(phi) * np.cos(d) * np.sin(h0)) def zonal_mean(g, f, bin_deg=2.0): b = np.floor((g.lat + 90.0) / bin_deg).astype(np.int64) s = np.bincount(b, weights=f * g.area_km2) w = np.bincount(b, weights=g.area_km2) return (s / np.maximum(w, 1e-12))[b] def current_anomaly(g, land, P): """Subtropical gyres: cold water off west coasts, warm off east coasts; leaks onto coastal land.""" if not land.any(): return np.zeros(g.n) d, src = nearest_source(g, np.flatnonzero(land)) e, _ = east_north(g.xyz) east_comp = np.sum(tangent_dir(g.xyz, g.xyz[np.maximum(src, 0)]) * e, axis=1) band = np.sin(np.radians((np.clip(np.abs(g.lat), 10.0, 50.0) - 10.0) * 4.5)) a = -P["current_c"] * np.sign(east_comp) * band * np.exp(-d / P["current_reach_km"]) a[land] = 0.0 return smooth_km(g, a, P["current_leak_km"]) def temperatures(g, z, land, P, tilt, cur=None): decl = declinations(tilt) Q = {s: insolation(g.lat, d) for s, d in decl.items()} q_ann = (Q["jun"] + Q["dec"] + 2 * Q["eq"]) / 4 t_ann = t_of_q(q_ann, P) dist_ocean = distance_to(g, ~land) if (~land).any() else np.full(g.n, 1e4) cont = np.clip(1.0 + dist_ocean / P["continentality_km"], 1.0, P["continentality_max"]) cur = current_anomaly(g, land, P) if cur is None else cur lapse = -P["lapse_c_per_km"] * np.maximum(z, 0.0) / 1000.0 def season(s): raw = t_of_q(Q[s], P) land_resp = np.where(raw > t_ann, P["land_summer"] * np.minimum(cont, P["continentality_summer_max"]), P["land_seasonal"] * cont) # land heats faster in summer (dry, low heat capacity) resp = np.where(land, land_resp, P["ocean_seasonal"]) return smooth_km(g, t_ann + resp * (raw - t_ann) + cur, P["heat_transport_km"]) + lapse return dict(zip(SEASONS, pmap(season, SEASONS))), dist_ocean def biotemperature(tmean, trange, n=12): ph = np.linspace(0.0, 2 * np.pi, n, endpoint=False) t = np.asarray(tmean)[:, None] + (np.asarray(trange)[:, None] / 2) * np.sin(ph)[None, :] return np.clip(t, 0.0, 30.0).mean(axis=1) def band_winds(g, itcz_lat, P): """3-cell surface winds (m/s) relative to the thermal equator.""" phi = g.lat - itcz_lat a = np.abs(phi) sgn = np.where(phi >= 0, 1.0, -1.0) s1 = 0.5 * (1 + np.tanh((a - P["hadley_edge_deg"]) / 3.0)) s2 = 0.5 * (1 + np.tanh((a - P["ferrel_edge_deg"]) / 4.0)) u = (1 - s1) * P["trade_u"] + (s1 - s2) * P["westerly_u"] + s2 * P["polar_u"] v = sgn * (-(1 - s1) * P["trade_v"] + (s1 - s2) * P["westerly_v"] - s2 * P["polar_v"]) e, n = east_north(g.xyz) return u[:, None] * e + v[:, None] * n def monsoon_winds(g, T_s, land, P): """Thermal lows over hot land / highs over cold land, flow deflected by Coriolis.""" anom = np.where(land, T_s - zonal_mean(g, T_s), 0.0) press = -P["monsoon_k"] * smooth_km(g, anom, P["monsoon_length_km"]) flow = -gradient(g, press) theta = np.radians(P["coriolis_min_deg"] + P["coriolis_span_deg"] * np.abs(np.sin(np.radians(g.lat)))) return rotate_about(g.xyz, flow, -np.sign(g.lat) * theta) * P["monsoon_speed_scale"] def _rate(per_1000km, spacing_km): return 1.0 - np.exp(-np.maximum(per_1000km, 0.0) * spacing_km / 1000.0) def eddy_mixing(g, P): """kappa · (nbr − I): the per-step eddy mixing with the neighbours — the same for every season (build once).""" kappa = P["eddy_k_m2s"] / (P["eddy_wind_ms"] * g.spacing_km * 1000.0) nbr = sparse.csr_matrix((1.0 / g.counts[g.src], (g.src, g.dst)), shape=(g.n, g.n)) return kappa * (nbr - sparse.identity(g.n, format="csr")) def precipitation(g, wind, T, z, land, itcz_lat, P, mixing=None): """Steady-state moisture transport along the wind on the cell graph; returns rain (relative units). mixing: eddy_mixing(g, P), when several seasons share it.""" t = g.edge_tangents out = np.maximum(rowdot_at(wind, g.src, t), 0.0) tot = np.bincount(g.src, weights=out, minlength=g.n) frac = np.where(tot[g.src] > 0, out / np.maximum(tot[g.src], 1e-12), 0.0) Tm = sparse.csr_matrix((frac, (g.dst, g.src)), shape=(g.n, g.n)) stay = (tot <= 0).astype(np.float64) upslope = np.maximum(np.sum(wind * gradient(g, np.maximum(z, 0.0) / 1000.0), axis=1), 0.0) conv = P["conv_rate"] * np.exp(-((g.lat - itcz_lat) / P["itcz_width_deg"]) ** 2) * np.clip((T - 10.0) / 20.0, 0, 1) subs = P["subsidence"] * np.exp(-((np.abs(g.lat - itcz_lat) - P["hadley_edge_deg"]) / 6.0) ** 2) front = P["front_rate"] * np.exp(-((np.abs(g.lat - itcz_lat) - P["front_lat_deg"]) / P["front_width_deg"]) ** 2) per = np.maximum(P["base_rate"] + conv + front + P["oro_rate"] * upslope - subs, P["min_rate"]) r = _rate(per, g.spacing_km) evap = np.where(land, 0.0, np.exp(P["cc_per_c"] * (np.clip(T, -2.0, 35.0) - 25.0))) # per advection step (one cell, time h/U): rain out, move downwind, eddy-mix with neighbours mix = eddy_mixing(g, P) if mixing is None else mixing eye = sparse.identity(g.n, format="csr") keep = sparse.diags(1.0 - r) recyc = sparse.diags(np.where(land, P["recycle"] * r, 0.0)) # land evapotranspiration returns rain system = (eye - (Tm @ keep + sparse.diags(stay) @ keep) - mix - recyc).tocsr() W, info = bicgstab_jacobi(system, evap, evap / np.maximum(r, 1e-6), 1.0 / system.diagonal(), 1e-7, 5000) if info != 0: raise ValueError(f"precipitation: moisture solve did not converge (info={info})") return r * np.maximum(W, 0.0) def run_locked(ctx, g, z, land, P) -> dict: """One face always to the sun: temperature by sun angle, no seasons; surface wind from night to the sun point.""" sub = latlon_to_xyz(*P["lock_at"]) mu = np.maximum(g.xyz @ sub, 0.0) t = P["lock_night_c"] + (P["lock_day_c"] - P["lock_night_c"]) * mu ** 0.25 lapse = -P["lapse_c_per_km"] * np.maximum(z, 0.0) / 1000.0 T = smooth_km(g, t, P["heat_transport_km"]) + lapse dist_ocean = distance_to(g, ~land) if (~land).any() else np.full(g.n, 1e4) wind = P["lock_wind_ms"] * tangent_dir(g.xyz, np.broadcast_to(sub, g.xyz.shape)) rain = np.exp(-((T - P["lock_melt_c"]) / P["lock_melt_width_c"]) ** 2) # meltwater and frost in the twilight ring k = P["global_mean_mm"] / max(np.sum(rain * g.area_km2) / g.area_km2.sum(), 1e-12) out = {} for s in SEASONS: out[f"wind_{s}"] = wind.astype(np.float32) out[f"P_{s}"] = rain * k out[f"T_{s}"] = T out["P_ann"] = rain * k out["T_mean"] = T out["T_range"] = np.zeros(g.n) out["T_min"] = T out["biotemp"] = biotemperature(T, out["T_range"]) out["PET"] = 58.93 * out["biotemp"] out["dist_ocean_km"] = dist_ocean return out def _still_ocean(g, t_mean): """No circulation (ocean disabled, locked world): zero currents/upwelling/productivity, SST = T_mean.""" z = np.zeros(g.n, np.float32) return {"current": np.zeros((g.n, 3), np.float32), "current_speed": z, "sst": np.asarray(t_mean, np.float32), "upwelling": z.copy(), "productivity": z.copy()} def run(ctx) -> dict: g = ctx.grid P = params(ctx.cfg, "climate", DEFAULTS) tilt = float(ctx.cfg["planet"]["tilt_deg"]) (z,) = ctx.need("elevation_eroded_m") z = z.astype(np.float64) water = ctx.data.get("open_water", ctx.data.get("ocean")) # big inland basins are water to the air land = ~np.asarray(water) if water is not None else z > 0 O = params(ctx.cfg, "ocean", OC.DEFAULTS) if P["lock"]: out = run_locked(ctx, g, z, land, P) out.update(_still_ocean(g, out["T_mean"])) return out sea = ~land coupled = bool(O["enabled"]) and bool(sea.any()) T, dist_ocean = temperatures(g, z, land, P, tilt, cur=np.zeros(g.n) if coupled else None) decl = declinations(tilt) def season_wind(s): itcz = P["itcz_shift_deg"] * decl[s] / max(tilt, 1e-9) wind = band_winds(g, itcz, P) return wind + monsoon_winds(g, T[s], land, P) if s != "eq" else wind winds = dict(zip(SEASONS, pmap(season_wind, SEASONS))) if coupled: # one pass: winds from current-free temperatures, then currents carry heat day = float(ctx.cfg["planet"]["day_hours"]) w_ann = (winds["jun"] + winds["dec"] + 2 * winds["eq"]) / 4 u = OC.currents(g, sea, w_ann, O, day) T_eq = (T["jun"] + T["dec"] + 2 * T["eq"]) / 4 T_s = OC.sst(g, sea, u, T_eq, O) cur = smooth_km(g, np.where(sea, T_s - T_eq, 0.0), P["current_leak_km"]) T, _ = temperatures(g, z, land, P, tilt, cur=cur) out = {} mixing = eddy_mixing(g, P) rain = dict(zip(SEASONS, pmap(lambda s: precipitation(g, winds[s], T[s], z, land, P["itcz_shift_deg"] * decl[s] / max(tilt, 1e-9), P, mixing), SEASONS))) del mixing for s in SEASONS: out[f"wind_{s}"] = winds[s].astype(np.float32) ann = (rain["jun"] + rain["dec"] + 2 * rain["eq"]) / 4 k = P["global_mean_mm"] / max(np.sum(ann * g.area_km2) / g.area_km2.sum(), 1e-12) for s in SEASONS: out[f"P_{s}"] = rain[s] * k out[f"T_{s}"] = T[s] out["P_ann"] = ann * k out["T_mean"] = (T["jun"] + T["dec"] + 2 * T["eq"]) / 4 out["T_range"] = np.abs(T["jun"] - T["dec"]) out["T_min"] = np.minimum(T["jun"], T["dec"]) out["biotemp"] = biotemperature(out["T_mean"], out["T_range"]) out["PET"] = 58.93 * out["biotemp"] out["dist_ocean_km"] = dist_ocean if coupled: sst_c = np.where(sea, np.maximum(T_s, SEA_FREEZE_C), out["T_mean"]) w_up = OC.upwelling(g, sea, w_ann, O, day) out.update({"current": u.astype(np.float32), "current_speed": np.linalg.norm(u, axis=1).astype(np.float32), "sst": sst_c.astype(np.float32), "upwelling": w_up.astype(np.float32), "productivity": OC.productivity(g, sea, w_up, z, out["T_range"], sst_c, O).astype(np.float32)}) else: out.update(_still_ocean(g, out["T_mean"])) return out |