SnowEx Model Results.

Key findings

• On unseen sites at 30 m the RMSE is 0.58 m, 7% higher than predicting the training sites' mean depth (0.56 m). It beats the mean at 4 of 7 sites.
• Across block sizes the unseen-site RMSE runs from 0.52 to 0.64 m.
• Scored the old way, on a random pixel split, R² is 0.34 at 30 m.
• With all 31 inputs, least squares is unstable: each amplitude ratio is exactly amplitude 2 minus amplitude 1, and the fitted model gave errors of thousands of metres at a new site. The three ratio inputs are left out for this model.

One map per site, from models that never saw that site (random forest). Sites are listed from lowest to highest error. RMSE is the typical error. Bias is the average error: right of centre means the model predicts too much snow. Pattern r is how well the deep and shallow places line up (1 is perfect). Open 3D shows LiDAR, the predictions and the error on the terrain.

Each input’s share of the model’s total importance (0–1; all inputs sum to 1). Measured on the held-out sites by shuffling one input and seeing how much the error rises, averaged over linear regression. Bars are scaled to the most important input.

RMSE by block size · metres, lower is better

Unseen sites, averaged over the held-out sites. The lowest unseen-site error in each row is marked.

RMSE at each held-out site · 30 m

Sorted from lowest to highest linear regression error. Bias is the average error; R² compares with that site's own mean depth.

Other scores by block size

Limits

• Labels are absolute snow depth while one radar pair measures about a week of change, so terrain and canopy dominate these baselines.
• Mean R² is not a headline number here. R² compares a model with the held-out site's own mean depth, so a site with a narrow range of depths and an error in overall level scores far below zero (Grand Mesa 2020 ≈ −11, Fraser ≈ −2) and dominates the average. RMSE, error vs predicting the mean and median R² are reported instead; mean R² is listed in the full table.
• Values are block means of the 3 m archive, not native-resolution radar.

Key findings

• On unseen sites at 30 m the RMSE is 0.59 m, 7% higher than predicting the training sites' mean depth (0.56 m). It beats the mean at 2 of 7 sites.
• Across block sizes the unseen-site RMSE runs from 0.52 to 0.64 m.
• Scored the old way, on a random pixel split, R² is 0.65 at 30 m.
• A single tree is clearly worse than the random forest's 300 trees on the same inputs (0.49 m at 30 m).

One map per site, from models that never saw that site (random forest). Sites are listed from lowest to highest error. RMSE is the typical error. Bias is the average error: right of centre means the model predicts too much snow. Pattern r is how well the deep and shallow places line up (1 is perfect). Open 3D shows LiDAR, the predictions and the error on the terrain.

Each input’s share of the model’s total importance (0–1; all inputs sum to 1). Measured on the held-out sites by shuffling one input and seeing how much the error rises, averaged over decision tree. Bars are scaled to the most important input.

RMSE by block size · metres, lower is better

Unseen sites, averaged over the held-out sites. The lowest unseen-site error in each row is marked.

RMSE at each held-out site · 30 m

Sorted from lowest to highest decision tree error. Bias is the average error; R² compares with that site's own mean depth.

Other scores by block size

Limits

• Labels are absolute snow depth while one radar pair measures about a week of change, so terrain and canopy dominate these baselines.
• Mean R² is not a headline number here. R² compares a model with the held-out site's own mean depth, so a site with a narrow range of depths and an error in overall level scores far below zero (Grand Mesa 2020 ≈ −11, Fraser ≈ −2) and dominates the average. RMSE, error vs predicting the mean and median R² are reported instead; mean R² is listed in the full table.
• Values are block means of the 3 m archive, not native-resolution radar.

Key findings

• Random pixel splits overstate skill, and more so at coarser blocks: scored the old way, R² rises from 0.63 at 3 m to 0.90 at 99 m, while on unseen sites the median R² stays between −0.14 and +0.09.
• On unseen sites the random forest's RMSE is 0.45–0.57 m, 10–13% lower than predicting the training sites' mean depth.
• Most error is each site's overall snow amount: in the gradient-boosting maps the bias runs from −0.40 m (Little Cottonwood) to +0.66 m (Grand Mesa). The spatial pattern is partly captured: correlation 0.82 at Mores Creek, 0.69 at Dry Creek and 0.64 at Banner Summit, about 0.2 at Fraser and Little Cottonwood.
• The models barely use the radar: at 30 m terrain carries 0.75 of the importance, canopy 0.18 and radar 0.07, and unwrapped phase almost none. Removing every radar input does not raise the random forest's error (0.48 m without, 0.49 m with). One radar pair measures about a week of change, while the labels are absolute depth.
• Gradient boosting is worse than the random forest in this run (RMSE 0.55 m vs 0.49 m at 30 m), mostly at Grand Mesa, so its extra complexity is not justified.
• Grand Mesa's five 2017 surveys are excluded. About 70% of those rows have no canopy input and most of their radar scenes are HH-only; scored on them, the models showed no skill (pattern correlation 0.05 in a 6,000-row check). Excluding them slightly raised the error at the other six sites (0.49 to 0.51 m).

One map per site, from models that never saw that site (random forest). Sites are listed from lowest to highest error. RMSE is the typical error. Bias is the average error: right of centre means the model predicts too much snow. Pattern r is how well the deep and shallow places line up (1 is perfect). Open 3D shows LiDAR, the predictions and the error on the terrain.

Each input’s share of the model’s total importance (0–1; all inputs sum to 1). Measured on the held-out sites by shuffling one input and seeing how much the error rises, averaged over random forest and gradient boosting. Bars are scaled to the most important input.

RMSE by block size · metres, lower is better

Unseen sites, averaged over the held-out sites. The lowest unseen-site error in each row is marked.

RMSE at each held-out site · 30 m

Sorted from lowest to highest random forest error. Bias is the average error; R² compares with that site's own mean depth.

Other scores by block size

Limits

• Labels are absolute snow depth while one radar pair measures about a week of change, so terrain and canopy dominate these baselines.
• Mean R² is not a headline number here. R² compares a model with the held-out site's own mean depth, so a site with a narrow range of depths and an error in overall level scores far below zero (Grand Mesa 2020 ≈ −11, Fraser ≈ −2) and dominates the average. RMSE, error vs predicting the mean and median R² are reported instead; mean R² is listed in the full table.
• Each block appears once per matched radar pair; prediction maps average those pairs.
• Values are block means of the 3 m archive, not native-resolution radar.

Key findings

• Random pixel splits overstate skill, and more so at coarser blocks: R² rises from 0.54 to 0.78 the old way while it falls on unseen sites.
• Most error is each site's overall snow amount (bias up to ±0.5 m). The spatial pattern is partly captured: correlation 0.5–0.75 at Mores Creek, Dry Creek and Banner Summit, about 0.1 at Grand Mesa.
• The models barely use the radar: terrain and canopy carry almost all of the importance, and re-referenced unwrapped phase almost none. One radar pair measures about a week of change, while the labels are absolute depth.
• Elevation does not transfer between sites: at Banner Summit the model over-predicts valleys by 0.3 m and under-predicts ridges, because each site has its own snow-elevation gradient.
• Random forest and gradient boosting are statistically tied, so the extra complexity of boosting is not justified here.

One map per site, from models that never saw that site (random forest). Sites are listed from lowest to highest error. RMSE is the typical error. Bias is the average error: right of centre means the model predicts too much snow. Pattern r is how well the deep and shallow places line up (1 is perfect). Open 3D shows LiDAR, the predictions and the error on the terrain.

Each input’s share of the model’s total importance (0–1; all inputs sum to 1). Measured on the held-out sites by shuffling one input and seeing how much the error rises, averaged over random forest and gradient boosting. Bars are scaled to the most important input.

RMSE by block size · metres, lower is better

Unseen sites, averaged over the held-out sites. The lowest unseen-site error in each row is marked.

RMSE at each held-out site · 30 m

Sorted from lowest to highest random forest error. Bias is the average error; R² compares with that site's own mean depth.

Other scores by block size

Limits

• Labels are absolute snow depth while one radar pair measures about a week of change, so terrain and canopy dominate these baselines.
• Mean R² is pulled down by Fraser (≈ −2); medians and bias-removed errors give the fuller picture.
• Each block appears once per matched radar pair; prediction maps average those pairs.
• Values are block means of the 3 m archive, not native-resolution radar.