Station-Density Confidence Mask

Spatially modulating the CNN’s influence by gauge support.

CPC-UNI is built from a global gauge network. In Indonesia, that network is concentrated in Java; many islands have one or zero contributing stations. When the CNN is trained against CPC, it learns whatever CPC happens to say in those data-poor cells - which may be a regional climatology rather than a true local field.

The confidence mask is a per-pixel weight in $[0, 1]$ that scales the CNN’s influence by local gauge density. Where gauges are dense, the CNN gets full weight. Where gauges are absent, the CNN gets zero weight and the output reverts to pure LSEQM.

The input is the gauge network (top); the output is a smooth confidence field that is high over Java and the denser clusters and near-zero over the sparsely gauged east:

Figure 1: Top: the BMKG / CPC gauge network (Java-heavy, sparse east). Bottom: the resulting station-density confidence field. Demonstration on the Indonesia run.

Construction

Count: Stations are assigned to CPC 0.5 deg cells. Each cell gets a raw count.
Smooth: A Gaussian kernel with $\sigma = 1.0$ cell ($\approx$ 55 km at 0.5 deg) blurs the counts to avoid hard cell boundaries.
Saturate: The smoothed count is divided by a saturation parameter (default 2) and clipped to 1.0. This is the confidence value.
Regrid: Linear interpolation from 0.5 deg to the 0.1 deg working grid.

The saturation parameter

Warning

saturation_count defines how many smoothed stations per 0.5 deg cell are needed for full confidence.

saturation_count = 1: any station presence gives full confidence. This can be too aggressive when a single station’s record is noisy.
saturation_count = 2 (recommended for Indonesia’s ~180-station network): a balanced middle ground. The Bali example config uses this value.
saturation_count = 3: conservative. Outside Java, the CNN barely contributes.
saturation_count = 5+: very conservative; effectively disables the CNN outside the densest clusters.

The shipped Indonesia config sets this to 2, acknowledged as a sensitivity parameter that was not formally optimized.

The choice directly controls how far the CNN reaches. The curve below shows the effective blend weight as a function of smoothed station count for three saturation values: lowering it from 3 to 2 lets the CNN activate beyond Java without forcing full weight on single-station cells.

Figure 2: Effective blend weight vs smoothed station count for three saturation settings. Lowering 3 to 2 lets the CNN activate beyond Java. Demonstration on the Indonesia run.

How it interacts with the blend

The CNN does not get a constant weight - it gets confidence * (1 - blend_alpha). With blend_alpha = 0.70:

Local confidence	LSEQM share	CNN share
0.0 (no stations nearby)	1.00	0.00
0.5 (some support)	0.85	0.15
1.0 (dense network)	0.70	0.30

See Blending for the exact formula.

In the Indonesia run this plays out exactly as the construction predicts: mean confidence at gauge sites is highest over Jawa (0.36) and drops to roughly 0.12 to 0.20 elsewhere. Even at the peak the CNN share is modest - confidence of 0.36 means the CNN contributes about 11% of the field there, and far less in the sparse east.

Figure 3: Mean station-density confidence at gauge sites, by island. Jawa (0.36) dominates; the sparsely gauged islands sit near 0.12 to 0.20, so the CNN is gated down toward the east. Demonstration on the Indonesia run.

Implementation

src/station_density.py - build_confidence_mask(). The mask is computed once and cached as output/station_density/confidence_mask_station_density.nc4.

--- title: "Station-Density Confidence Mask" description: "Spatially modulating the CNN's influence by gauge support." --- CPC-UNI is built from a global gauge network. In Indonesia, that network is concentrated in Java; many islands have one or zero contributing stations. When the CNN is trained against CPC, it learns whatever CPC happens to say in those data-poor cells - which may be a regional climatology rather than a true local field. The confidence mask is a per-pixel weight in $[0, 1]$ that scales the CNN's influence by local gauge density. Where gauges are dense, the CNN gets full weight. Where gauges are absent, the CNN gets zero weight and the output reverts to pure LSEQM. The input is the gauge network (top); the output is a smooth confidence field that is high over Java and the denser clusters and near-zero over the sparsely gauged east: ![Top: the BMKG / CPC gauge network (Java-heavy, sparse east). Bottom: the resulting station-density confidence field. Demonstration on the Indonesia run.](../images/methodology/density_maps.png){#fig-density-maps fig-align="center"} ## Construction 1. **Count:** Stations are assigned to CPC 0.5 deg cells. Each cell gets a raw count. 2. **Smooth:** A Gaussian kernel with $\sigma = 1.0$ cell ($\approx$ 55 km at 0.5 deg) blurs the counts to avoid hard cell boundaries. 3. **Saturate:** The smoothed count is divided by a saturation parameter (default 2) and clipped to 1.0. This is the confidence value. 4. **Regrid:** Linear interpolation from 0.5 deg to the 0.1 deg working grid. ## The saturation parameter ::: {.callout-warning} `saturation_count` defines how many smoothed stations per 0.5 deg cell are needed for full confidence. - `saturation_count = 1`: any station presence gives full confidence. This can be too aggressive when a single station's record is noisy. - `saturation_count = 2` (recommended for Indonesia's ~180-station network): a balanced middle ground. The Bali example config uses this value. - `saturation_count = 3`: conservative. Outside Java, the CNN barely contributes. - `saturation_count = 5+`: very conservative; effectively disables the CNN outside the densest clusters. The shipped Indonesia config sets this to 2, acknowledged as a sensitivity parameter that was not formally optimized. ::: The choice directly controls how far the CNN reaches. The curve below shows the effective blend weight as a function of smoothed station count for three saturation values: lowering it from 3 to 2 lets the CNN activate beyond Java without forcing full weight on single-station cells. ![Effective blend weight vs smoothed station count for three saturation settings. Lowering 3 to 2 lets the CNN activate beyond Java. Demonstration on the Indonesia run.](../images/methodology/density_alpha.png){#fig-density-alpha fig-align="center"} ## How it interacts with the blend The CNN does not get a constant weight - it gets `confidence * (1 - blend_alpha)`. With `blend_alpha = 0.70`: | Local confidence | LSEQM share | CNN share | |:----------------:|:-----------:|:---------:| | 0.0 (no stations nearby) | 1.00 | 0.00 | | 0.5 (some support) | 0.85 | 0.15 | | 1.0 (dense network) | 0.70 | 0.30 | See [Blending](blending.qmd) for the exact formula. In the Indonesia run this plays out exactly as the construction predicts: mean confidence at gauge sites is highest over Jawa (0.36) and drops to roughly 0.12 to 0.20 elsewhere. Even at the peak the CNN share is modest - confidence of 0.36 means the CNN contributes about 11% of the field there, and far less in the sparse east. ![Mean station-density confidence at gauge sites, by island. Jawa (0.36) dominates; the sparsely gauged islands sit near 0.12 to 0.20, so the CNN is gated down toward the east. Demonstration on the Indonesia run.](../images/methodology/confidence_by_region.png){#fig-confidence-region fig-align="center"} ## Implementation `src/station_density.py` - `build_confidence_mask()`. The mask is computed once and cached as `output/station_density/confidence_mask_station_density.nc4`.