Improve visualizations: adaptive scales, revert z-score to std normalization

- MSRM/TPI/roughness/anomalies: revert z-score (x-mean)/std to std normalization x/std
  to preserve contrast and visibility of linear features (paths, ditches, trenches)
- MSRM: adaptive scales based on resolution, archaeological weight combination
- TPI: extend from 2 to 4 scales (3m/15m/50m/200m) with weighted combination
- Hillshade: 8 directions instead of 4, altitude 35° instead of 30°
- LRM: adaptive sigma based on resolution
- Openness: doubled radius (100m instead of 50m)
- Roughness: multi-scale (3m fine + 15m broad) instead of single 5x5 window
- Anomalies: uses MSRM multi-scale relief instead of single LRM 15m
- Wavelet: 8 adaptive scales, std normalization, archaeological weights
- Remove svf (Sky-View Factor) and local_dominance visualizations
- Add AVIF format support (default), quality 98
- Add multi-resolution support (-r 0.5,0.2)
- Improve Ctrl+C handling for immediate process termination
- Update rendering.py descriptions for all modified visualizations

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>
This commit is contained in:
Jacquin Antoine
2026-05-14 23:12:08 +02:00
parent ac56ba8084
commit d334892880
8 changed files with 344 additions and 180 deletions

View File

@ -250,7 +250,7 @@ def _filter_nanaware(arr, filter_func, *args, use_gpu=True, **kwargs):
def generate_hillshade(dem_file, basename, vis_dir, resolution, shared=None):
"""Generate multi-directional hillshade with contrast enhancement — GPU if available.
Combines 4-direction hillshade (NW, NE, SW, SE) with slope shading.
Combines 8-direction hillshade with slope shading for balanced illumination.
Applies percentile normalization and gamma correction to restore
contrast lost by averaging multiple azimuths.
"""
@ -279,8 +279,9 @@ def generate_hillshade(dem_file, basename, vis_dir, resolution, shared=None):
sin_slope = xp.sin(slope)
cos_slope = xp.cos(slope)
azimuts = [315, 45, 225, 135]
altitude = 30
# 8 azimuths for balanced illumination (eliminates directional bias)
azimuts = [0, 45, 90, 135, 180, 225, 270, 315]
altitude = 35 # Higher altitude for better micro-relief detection
hillshades = []
alt_rad = xp.radians(xp.array(altitude))
@ -297,7 +298,6 @@ def generate_hillshade(dem_file, basename, vis_dir, resolution, shared=None):
combined = 0.7 * combined_hillshade + 0.3 * slope_shaded
# Contrast enhancement: percentile stretch + gamma
# Averaging 4 azimuths flattens contrast — this restores it
combined_np = to_cpu(combined)
nan_mask = shared.nan_mask if shared else np.isnan(to_cpu(dem_np) if HAS_GPU else dem_np)
valid = combined_np[~nan_mask]
@ -415,7 +415,11 @@ def generate_curvature(dem_file, basename, vis_dir, resolution, shared=None):
# ============================================================
def generate_lrm(dem_file, basename, vis_dir, resolution, shared=None):
"""Local Relief Model - deviation from local mean (GPU if available)."""
"""Local Relief Model - deviation from local mean (GPU if available).
Kernel sigma adapts to resolution: finer kernel at higher resolution
to capture micro-relief details. At 0.5m/px: 15m, at 0.2m/px: ~5m.
"""
gpu_tag = " [GPU]" if HAS_GPU else ""
logger.info(f" → Local Relief Model{gpu_tag}...")
t0 = time.time()
@ -429,7 +433,10 @@ def generate_lrm(dem_file, basename, vis_dir, resolution, shared=None):
else:
dem_np, transform, crs = _read_dem(dem_file)
nan_mask = np.isnan(dem_np)
local_mean = _filter_nanaware(dem_np, xp_gaussian_filter, sigma=15/resolution)
# Adapt sigma to resolution: standard 15m at 0.5m, finer at higher res
sigma_m = max(5.0, 15.0 * 0.5 / resolution)
logger.info(f" LRM sigma={sigma_m:.1f}m (résolution {resolution}m/px)")
local_mean = _filter_nanaware(dem_np, xp_gaussian_filter, sigma=sigma_m / resolution)
lrm = dem_np - local_mean
lrm[nan_mask] = np.nan
_save_tif(output, lrm.astype(np.float32), transform, crs)
@ -473,7 +480,7 @@ def generate_svf(dem_file, basename, vis_dir, resolution, shared=None):
angles = np.linspace(0, 2 * np.pi, n_dirs, endpoint=False)
dx_dir = np.cos(angles)
dy_dir = np.sin(angles)
max_dist = int(50 / res)
max_dist = int(100 / res)
padded = xp.pad(dem, max_dist, mode='constant', constant_values=xp.nan)
svf = xp.zeros_like(dem)
@ -520,6 +527,7 @@ def generate_openness(dem_file, basename, vis_dir, resolution, positive=True, sh
- Positive openness: max zenith angle (angle from vertical to highest visible terrain)
- Negative openness: max nadir angle (angle from vertical down to lowest terrain)
Result is averaged across all 8 directions.
Ray radius adapts to resolution: 100m for better detection of large enclosures.
"""
name = "positive_openness" if positive else "negative_openness"
gpu_tag = " [GPU]" if HAS_GPU else ""
@ -548,7 +556,7 @@ def generate_openness(dem_file, basename, vis_dir, resolution, positive=True, sh
angles = np.linspace(0, 2 * np.pi, n_dirs, endpoint=False)
dx_dir = np.cos(angles)
dy_dir = np.sin(angles)
max_dist = int(50 / res)
max_dist = int(100 / res)
padded = xp.pad(dem, max_dist, mode='constant', constant_values=xp.nan)
openness_sum = xp.zeros_like(dem)
@ -646,7 +654,11 @@ def generate_local_dominance(dem_file, basename, vis_dir, resolution, shared=Non
def generate_mslrm(dem_file, basename, vis_dir, resolution, shared=None):
"""Multi-Scale Relief Model (MSRM) - LRM at 5 scales combined (GPU if available)."""
"""Multi-Scale Relief Model (MSRM) - LRM at adaptive scales combined (GPU if available).
Scales adapt to resolution. Std normalization per scale.
Weighted combination favoring archaeologically relevant scales (5-25m).
"""
gpu_tag = " [GPU]" if HAS_GPU else ""
logger.info(f" → Multi-Scale Relief Model (MSRM){gpu_tag}...")
t0 = time.time()
@ -662,7 +674,18 @@ def generate_mslrm(dem_file, basename, vis_dir, resolution, shared=None):
dem_np, transform, crs = _read_dem(dem_file)
nan_mask = np.isnan(dem_np)
sigmas = [5, 10, 25, 50, 100]
# Adaptive scales: finer at higher resolution
min_scale = max(2.0, resolution * 4)
candidate_scales = [2, 5, 10, 20, 50, 100, 200]
sigmas = [s for s in candidate_scales if s >= min_scale]
# Archaeological weights: favor 5-25m range (ditches, enclosures, tumulus)
scale_weights = {
2: 0.8, 5: 2.0, 10: 1.8, 20: 1.5, 50: 1.0, 100: 0.6, 200: 0.4,
}
weights = np.array([scale_weights.get(s, 1.0) for s in sigmas])
logger.info(f" MSRM échelles: {sigmas}m")
lrm_stack = []
for sigma in sigmas:
@ -673,16 +696,19 @@ def generate_mslrm(dem_file, basename, vis_dir, resolution, shared=None):
local_mean = _filter_nanaware(dem_np, xp_gaussian_filter, sigma=sigma_px)
lrm = dem_np - local_mean
lrm[nan_mask] = np.nan
# Std normalization: x / std — preserves sign and contrast better than z-score
valid_lrm = lrm[~nan_mask]
lrm_std = max(np.nanstd(valid_lrm), 0.01) if len(valid_lrm) > 0 else 0.01
lrm_norm = lrm / lrm_std
lrm_stack.append(lrm_norm.astype(np.float32))
lrm = lrm / lrm_std
lrm_stack.append(lrm.astype(np.float32))
# Weighted combination
lrm_array = np.array(lrm_stack)
weights_3d = weights[:, np.newaxis, np.newaxis]
with np.errstate(invalid='ignore', divide='ignore'):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', message='Mean of empty slice')
mslrm = np.sqrt(np.nanmean(lrm_array ** 2, axis=0))
mslrm = np.sqrt(np.nansum((lrm_array ** 2) * weights_3d, axis=0) / np.sum(weights))
mslrm[nan_mask] = np.nan
_save_tif(output, mslrm.astype(np.float32), transform, crs)
logger.info(f" ✓ MSRM terminé ({time.time()-t0:.1f}s){gpu_tag}")
@ -696,7 +722,8 @@ def generate_tpi(dem_file, basename, vis_dir, resolution, shared=None):
"""Multi-Scale Topographic Position Index (GPU if available).
TPI = elevation - mean(neighborhood).
Computed at fine (5m) and broad (100m) scales.
Computed at 4 scales with std normalization and weighted combination.
Weights favor fine and medium scales (archaeologically relevant).
"""
gpu_tag = " [GPU]" if HAS_GPU else ""
logger.info(f" → TPI multi-échelle{gpu_tag}...")
@ -713,29 +740,34 @@ def generate_tpi(dem_file, basename, vis_dir, resolution, shared=None):
dem_np, transform, crs = _read_dem(dem_file)
nan_mask = np.isnan(dem_np)
fine_size = int(5 / resolution)
if fine_size % 2 == 0:
fine_size += 1
if shared:
fine_mean = _filter_nanaware_from_filled(shared, xp_uniform_filter, size=fine_size)
else:
fine_mean = _filter_nanaware(dem_np, xp_uniform_filter, size=fine_size)
tpi_fine = dem_np - fine_mean
tpi_fine[nan_mask] = np.nan
# 4 scales: fine (3m), medium (15m), broad (50m), landscape (200m)
scales_m = [3, 15, 50, 200]
weights = [1.5, 2.0, 1.2, 0.5] # Favor medium scales (ditches, enclosures)
broad_size = int(100 / resolution)
if broad_size % 2 == 0:
broad_size += 1
if shared:
broad_mean = _filter_nanaware_from_filled(shared, xp_uniform_filter, size=broad_size)
else:
broad_mean = _filter_nanaware(dem_np, xp_uniform_filter, size=broad_size)
tpi_broad = dem_np - broad_mean
tpi_broad[nan_mask] = np.nan
tpi_stack = []
for scale_m, weight in zip(scales_m, weights):
size = max(3, int(scale_m / resolution))
if size % 2 == 0:
size += 1
if shared:
local_mean = _filter_nanaware_from_filled(shared, xp_uniform_filter, size=size)
else:
local_mean = _filter_nanaware(dem_np, xp_uniform_filter, size=size)
tpi = dem_np - local_mean
tpi[nan_mask] = np.nan
# Std normalization — preserves sign and contrast better than z-score
valid = tpi[~nan_mask]
tpi_std = max(np.nanstd(valid), 0.01) if len(valid) > 0 else 0.01
tpi = tpi / tpi_std
tpi_stack.append(tpi.astype(np.float32))
fine_std = max(np.nanstd(tpi_fine[~nan_mask]), 0.01) if np.any(~nan_mask) else 0.01
broad_std = max(np.nanstd(tpi_broad[~nan_mask]), 0.01) if np.any(~nan_mask) else 0.01
tpi_combined = 0.6 * (tpi_fine / fine_std) + 0.4 * (tpi_broad / broad_std)
# Weighted combination
tpi_array = np.array(tpi_stack)
weights_3d = np.array(weights)[:, np.newaxis, np.newaxis]
with np.errstate(invalid='ignore', divide='ignore'):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', message='Mean of empty slice')
tpi_combined = np.nansum(tpi_array * weights_3d, axis=0) / np.sum(weights)
tpi_combined[nan_mask] = np.nan
_save_tif(output, tpi_combined.astype(np.float32), transform, crs)
@ -756,7 +788,7 @@ def generate_sailore(dem_file, basename, vis_dir, resolution, shared=None):
"""SAILORE - Self-Adaptive Improved Local Relief Model (GPU if available).
Kernel size adapts to local slope: flat areas get larger kernels,
steep areas get smaller kernels.
steep areas get smaller kernels. Scales adapt to resolution.
"""
gpu_tag = " [GPU]" if HAS_GPU else ""
logger.info(f" → SAILORE (LRM adaptatif){gpu_tag}...")
@ -778,8 +810,13 @@ def generate_sailore(dem_file, basename, vis_dir, resolution, shared=None):
slope_deg = np.degrees(slope)
slope_deg[nan_mask] = np.nan
sigma_min = 2.0 / resolution
sigma_max = 25.0 / resolution
# Adaptive scales: finer at higher resolution
sigma_min_m = max(1.0, 2.0 * 0.5 / resolution) # 2m at 0.5, ~5m at 0.2
sigma_mid_m = max(5.0, 13.5 * 0.5 / resolution) # 13.5m at 0.5, ~33m at 0.2
sigma_max_m = max(5.0, 25.0 * 0.5 / resolution) # 25m at 0.5, ~62m at 0.2
sigma_min = sigma_min_m / resolution
sigma_max = sigma_max_m / resolution
sigma_mid = (sigma_min + sigma_max) / 2
slope_norm = np.clip(slope_deg / 30.0, 0, 1)
if shared:
@ -822,7 +859,11 @@ def generate_sailore(dem_file, basename, vis_dir, resolution, shared=None):
# ============================================================
def generate_roughness(dem_file, basename, vis_dir, resolution, shared=None):
"""Surface roughness - standard deviation of elevation in a window (GPU-accelerated)."""
"""Surface roughness - multi-scale standard deviation (GPU-accelerated).
Combines fine (3m) and broad (15m) roughness for better detection
of archaeological features at multiple scales.
"""
gpu_tag = " [GPU]" if HAS_GPU else ""
logger.info(f" → Rugosité de surface{gpu_tag}...")
t0 = time.time()
@ -838,20 +879,43 @@ def generate_roughness(dem_file, basename, vis_dir, resolution, shared=None):
dem_np, transform, crs = _read_dem(dem_file)
nan_mask = np.isnan(dem_np)
window_size = int(5 / resolution)
if window_size % 2 == 0:
window_size += 1
# Fine roughness (3m window)
fine_size = max(3, int(3 / resolution))
if fine_size % 2 == 0:
fine_size += 1
# Vectorized std: sqrt(E[X²] - (E[X])²) via uniform_filter (NaN-aware)
if shared:
local_mean = _filter_nanaware_from_filled(shared, xp_uniform_filter, size=window_size)
# For local_mean_sq, we need to filter filled², not filled
local_mean_sq = _filter_nanaware(shared.filled.astype(np.float64)**2, xp_uniform_filter, size=window_size)
local_mean_sq[shared.nan_mask] = np.nan
fine_mean = _filter_nanaware_from_filled(shared, xp_uniform_filter, size=fine_size)
fine_mean_sq = _filter_nanaware(shared.filled.astype(np.float64)**2, xp_uniform_filter, size=fine_size)
fine_mean_sq[shared.nan_mask] = np.nan
else:
local_mean = _filter_nanaware(dem_np.astype(np.float64), xp_uniform_filter, size=window_size)
local_mean_sq = _filter_nanaware(dem_np.astype(np.float64)**2, xp_uniform_filter, size=window_size)
roughness = np.sqrt(np.maximum(local_mean_sq - local_mean * local_mean, 0))
fine_mean = _filter_nanaware(dem_np.astype(np.float64), xp_uniform_filter, size=fine_size)
fine_mean_sq = _filter_nanaware(dem_np.astype(np.float64)**2, xp_uniform_filter, size=fine_size)
roughness_fine = np.sqrt(np.maximum(fine_mean_sq - fine_mean * fine_mean, 0))
roughness_fine[nan_mask] = np.nan
# Broad roughness (15m window)
broad_size = max(3, int(15 / resolution))
if broad_size % 2 == 0:
broad_size += 1
if shared:
broad_mean = _filter_nanaware_from_filled(shared, xp_uniform_filter, size=broad_size)
broad_mean_sq = _filter_nanaware(shared.filled.astype(np.float64)**2, xp_uniform_filter, size=broad_size)
broad_mean_sq[shared.nan_mask] = np.nan
else:
broad_mean = _filter_nanaware(dem_np.astype(np.float64), xp_uniform_filter, size=broad_size)
broad_mean_sq = _filter_nanaware(dem_np.astype(np.float64)**2, xp_uniform_filter, size=broad_size)
roughness_broad = np.sqrt(np.maximum(broad_mean_sq - broad_mean * broad_mean, 0))
roughness_broad[nan_mask] = np.nan
# Std normalization per scale then weighted combination
fine_valid = roughness_fine[~nan_mask]
broad_valid = roughness_broad[~nan_mask]
fine_std = max(np.nanstd(fine_valid), 0.01) if len(fine_valid) > 0 else 0.01
broad_std = max(np.nanstd(broad_valid), 0.01) if len(broad_valid) > 0 else 0.01
roughness = 0.7 * roughness_fine / fine_std + 0.3 * roughness_broad / broad_std
roughness[nan_mask] = np.nan
roughness = to_cpu(roughness)
@ -868,7 +932,11 @@ def generate_roughness(dem_file, basename, vis_dir, resolution, shared=None):
# ============================================================
def generate_anomalies(dem_file, basename, vis_dir, resolution, shared=None):
"""Statistical anomaly detection - z-score of local relief + Local Moran's I — GPU if available."""
"""Statistical anomaly detection - std-normalized multi-scale relief + Local Moran's I — GPU if available.
Uses MSRM (multi-scale LRM) instead of single-scale LRM for better detection
of anomalies at all scales.
"""
gpu_tag = " [GPU]" if HAS_GPU else ""
logger.info(f" → Détection anomalies statistiques{gpu_tag}...")
t0 = time.time()
@ -880,30 +948,60 @@ def generate_anomalies(dem_file, basename, vis_dir, resolution, shared=None):
crs = shared.crs
dem_np = shared.dem_np
nan_mask = shared.nan_mask
lrm = shared.lrm_15.copy()
else:
dem_np, transform, crs = _read_dem(dem_file)
nan_mask = np.isnan(dem_np)
lrm_mean_val = _filter_nanaware(dem_np, xp_gaussian_filter, sigma=15 / resolution)
lrm = dem_np - lrm_mean_val
# Multi-scale LRM: compute MSRM-like combined relief
min_scale = max(2.0, resolution * 4)
candidate_scales = [2, 5, 10, 20, 50, 100]
sigmas = [s for s in candidate_scales if s >= min_scale]
lrm_stack = []
for sigma in sigmas:
sigma_px = sigma / resolution
if shared:
local_mean = _filter_nanaware_from_filled(shared, xp_gaussian_filter, sigma=sigma_px)
else:
local_mean = _filter_nanaware(dem_np, xp_gaussian_filter, sigma=sigma_px)
lrm = dem_np - local_mean
lrm[nan_mask] = np.nan
# Std normalization — preserves contrast better than z-score
valid_lrm = lrm[~nan_mask]
lrm_std = max(np.nanstd(valid_lrm), 0.01) if len(valid_lrm) > 0 else 0.01
lrm_norm = lrm / lrm_std
else:
lrm_norm = lrm
lrm_stack.append(lrm_norm.astype(np.float32))
valid_lrm = lrm[~nan_mask]
lrm_mean = np.nanmean(valid_lrm) if len(valid_lrm) > 0 else 0
lrm_std = max(np.nanstd(valid_lrm), 0.01) if len(valid_lrm) > 0 else 0.01
z_score = (lrm - lrm_mean) / lrm_std
# Weighted RMS combination (favor 5-25m scales)
scale_weights = {2: 0.8, 5: 2.0, 10: 1.8, 20: 1.5, 50: 1.0, 100: 0.6}
weights = np.array([scale_weights.get(s, 1.0) for s in sigmas])
lrm_array = np.array(lrm_stack)
weights_3d = weights[:, np.newaxis, np.newaxis]
with np.errstate(invalid='ignore', divide='ignore'):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', message='Mean of empty slice')
msrm = np.sqrt(np.nansum((lrm_array ** 2) * weights_3d, axis=0) / np.sum(weights))
msrm[nan_mask] = np.nan
window = int(10 / resolution)
# Std normalization of MSRM — preserves contrast better than z-score
valid_msrm = msrm[~nan_mask]
msrm_std = max(np.nanstd(valid_msrm), 0.01) if len(valid_msrm) > 0 else 0.01
z_score = msrm / msrm_std
# Local Moran's I for spatial clustering
window = max(3, int(10 / resolution))
if window % 2 == 0:
window += 1
if shared:
local_mean = _filter_nanaware_from_filled(shared, xp_uniform_filter, size=window)
local_mean_z = _filter_nanaware_from_filled(shared, xp_uniform_filter, size=window)
else:
local_mean = _filter_nanaware(z_score, xp_uniform_filter, size=window)
z_mean = np.nanmean(valid_lrm) if len(valid_lrm) > 0 else 0
z_std = max(np.nanstd(z_score[~nan_mask]), 0.01) if np.any(~nan_mask) else 0.01
morans_i = z_score * (local_mean - z_mean) / z_std
local_mean_z = _filter_nanaware(z_score, xp_uniform_filter, size=window)
z_mean_global = np.nanmean(z_score[~nan_mask]) if np.any(~nan_mask) else 0
z_std_global = max(np.nanstd(z_score[~nan_mask]), 0.01) if np.any(~nan_mask) else 0.01
morans_i = z_score * (local_mean_z - z_mean_global) / z_std_global
anomaly_score = np.abs(z_score) * np.sign(morans_i)
anomaly_score[nan_mask] = np.nan
@ -922,7 +1020,13 @@ def generate_anomalies(dem_file, basename, vis_dir, resolution, shared=None):
def generate_wavelet(dem_file, basename, vis_dir, resolution, shared=None):
"""Mexican Hat wavelet multi-scale analysis (GPU if available).
CWT 2D at multiple scales to detect circular features.
CWT 2D at multiple scales adapted to resolution.
- At 0.5m/px: [1, 2, 5, 10, 20, 50, 100]m
- At 0.2m/px: [0.5, 1, 2, 5, 10, 20, 50, 100]m
- Higher resolution = more fine scales available
Uses std normalization per scale and weighted combination
with emphasis on archaeologically relevant scales (2-50m).
"""
gpu_tag = " [GPU]" if HAS_GPU else ""
logger.info(f" → Ondelette Mexican Hat multi-échelle{gpu_tag}...")
@ -941,7 +1045,25 @@ def generate_wavelet(dem_file, basename, vis_dir, resolution, shared=None):
nan_mask = np.isnan(dem_np)
filled, _ = _fill_nans(dem_np.astype(np.float64))
scales = [2, 5, 10, 20, 50]
# Adapt scales to resolution: finer scales available at higher resolution
min_scale = max(resolution * 2, 1.0)
candidate_scales = [0.5, 1, 2, 5, 10, 20, 50, 100]
scales = [s for s in candidate_scales if s >= min_scale]
# Weights favor archaeological scales (2-50m: ditches, enclosures, tumulus)
scale_weights = {
0.5: 0.6, # Fine texture
1.0: 0.8, # Micro-relief
2.0: 1.5, # Small ditches, paths — key scale
5.0: 2.0, # Fossés, small enclosures — key archaeological scale
10.0: 1.8, # Medium structures
20.0: 1.5, # Large enclosures, tumulus
50.0: 1.0, # Very large enclosures
100.0: 0.6, # Landscape-level features
}
weights = np.array([scale_weights.get(s, 1.0) for s in scales])
logger.info(f" Échelles CWT: {scales}m (résolution {resolution}m/px)")
wavelet_stack = []
for scale_m in scales:
@ -954,15 +1076,21 @@ def generate_wavelet(dem_file, basename, vis_dir, resolution, shared=None):
from scipy.ndimage import gaussian_laplace
response = -gaussian_laplace(filled, sigma=sigma_px)
response[nan_mask] = np.nan
# Std normalization: scale by standard deviation to make scales comparable
valid = response[~nan_mask]
std_val = max(np.nanstd(valid), 0.01) if len(valid) > 0 else 0.01
response = response / std_val
wavelet_stack.append(response)
# Weighted RMS: sqrt(sum(w * x²) / sum(w))
# Preserves contrast at key archaeological scales
stack = np.array(wavelet_stack)
weights_3d = weights[:, np.newaxis, np.newaxis]
with np.errstate(invalid='ignore', divide='ignore'):
with warnings.catch_warnings():
warnings.filterwarnings('ignore', message='Mean of empty slice')
combined = np.sqrt(np.nanmean(np.array(wavelet_stack) ** 2, axis=0))
combined = np.sqrt(np.nansum((stack ** 2) * weights_3d, axis=0) / np.sum(weights))
combined[nan_mask] = np.nan
_save_tif(output, combined.astype(np.float32), transform, crs)