=== versions ===
python 3.12.0 | pykrige 1.7.3 | numpy 2.5.4 | pandas 3.0.6 | geopandas 1.2.0 | pyreadr 0.5.7 | rasterio 1.5.2

=== AURN NO2 annual means, 2025 ===
158 stations report NO2; 143 have >= 75% data capture
ratified to: {'2026-06-30': 154, '2026-03-31': 1}
                     count  mean   min   max
location_type                               
Rural Background        12   5.0   1.5  10.7
Suburban Background      3   9.9   6.5  16.4
Suburban Industrial      2  14.1  13.8  14.4
Urban Background        59  13.5   4.2  24.8
Urban Industrial         6  13.2   9.3  21.7
Urban Traffic           60  20.4   8.3  34.8

kept 74 background stations: mean 12.0, sd 5.2, range 1.5 to 24.8 ug/m3
nearest-neighbour distance: median 17.9 km, max 217.8 km

=== variogram fits (PyKrige, distances in km) ===
spherical    partial sill  11.69  range  342.9 km  nugget 18.84  -> nugget/sill 0.62
exponential  partial sill  14.65  range  636.1 km  nugget 18.55  -> nugget/sill 0.56
gaussian     partial sill  10.02  range  333.1 km  nugget 20.94  -> nugget/sill 0.68
lag centres (km): [40, 100, 162, 228, 288, 352, 412, 478, 542, 607, 668, 727]
semivariance:    [20.9, 25.9, 21.2, 30.8, 31.6, 31.4, 22.7, 36.7, 31.5, 28.2, 27.8, 17.1]

=== prediction grid ===
330 x 610 cells of 2 km, 60,917 on land

=== ordinary kriging ===
spherical model, 0.5 s for 201,300 cells
land cells: predicted NO2 6.9 to 15.8 ug/m3; kriging SD 4.6 to 5.7 (median 4.9)

=== IDW (power 2) ===
land cells: 1.5 to 24.8 ug/m3
kriging minus IDW over land: mean -0.51, 5th to 95th percentile -2.6 to +1.8 ug/m3

=== leave-one-out cross-validation, 74 background stations (ug/m3) ===
                RMSE   MAE  bias     r
IDW p=2         4.80  4.03  0.98  0.45
OK spherical    4.80  3.93  0.07  0.38
OK exponential  4.80  3.91  0.07  0.38
IDW p=1         4.82  3.94  0.68  0.43
OK gaussian     4.93  4.04  0.04  0.32
IDW p=3         5.05  4.29  1.05  0.44
Global mean     5.26  4.18 -0.00   NaN
OK spherical: mean standardised error +0.01, SD of standardised error 1.00 (1.0 = kriging variance is well calibrated)
share of stations inside the 95% kriging interval: 95%

largest kriging errors:
                 site             type  observed   OK  IDW p=2  OK error
   Southampton Centre Urban Background      21.3 10.4     10.8     -10.9
Manchester Piccadilly Urban Background      23.6 12.9     15.9     -10.7
    London Hillingdon Urban Background      24.8 14.2     15.8     -10.6
            Ladybower Rural Background       4.5 14.8     15.0      10.3
         High Muffles Rural Background       3.8 12.5     12.7       8.7
    London Bloomsbury Urban Background      23.5 14.9     18.1      -8.6

60 roadside stations: observed mean 20.4, background kriging at the same points 12.1 ug/m3 (under-prediction 8.3)

=== Sentinel-5P column at the stations ===
background stations: Pearson r = 0.75, NO2 = 2.09 + 0.169 x column (umol/m2)
roadside stations:   Pearson r = 0.40

LOOCV including the satellite covariate:
                          RMSE   MAE  bias     r
Regression only (S5P)     3.53  2.82  0.01  0.73
Regression kriging (S5P)  3.59  2.80  0.00  0.72
OK spherical              4.80  3.93  0.07  0.38
IDW p=2                   4.80  4.03  0.98  0.45
OK exponential            4.80  3.91  0.07  0.38
IDW p=1                   4.82  3.94  0.68  0.43
OK gaussian               4.93  4.04  0.04  0.32
IDW p=3                   5.05  4.29  1.05  0.44
Global mean               5.26  4.18 -0.00   NaN
residual variogram: partial sill 3.64, range 465.9 km, nugget 9.37

saved GeoTIFFs and loocv_scores.csv to output
figures written