mpspline

Python implementation of mass-preserving equal-area quadratic splines for harmonizing soil profiles to standard depth intervals.

Port of the mpspline2 R package by Lauren O'Brien, based on the method of Bishop et al. (1999), as generalized in Malone et al. (2009).

Installation

pip install mpspline

Quick Start

from mpspline import mpspline

# Single profile
result = mpspline({
    'horizons': [
        {'hzname': 'A', 'upper': 0, 'lower': 20, 'clay': 24.5},
        {'hzname': 'B', 'upper': 20, 'lower': 50, 'clay': 35.2},
    ]
}, output_type='wide')
print(result)  # {'clay_0_5': 21.4, 'clay_5_15': 27.8, ...}

Usage

Pass a dict for a single profile or a list for multiple profiles.

1. Single Profile (Wide Format)

from mpspline import mpspline

# Single profile (returns dict)
result = mpspline({
    'cokey': 12345,
    'horizons': [
        {'hzname': 'A', 'upper': 0, 'lower': 20, 'clay': 24.5},
        {'hzname': 'B', 'upper': 20, 'lower': 50, 'clay': 35.2},
    ]
}, output_type='wide')
print(result)
# {'cokey': 12345, 'clay_0_5': 22.6, 'clay_5_15': 24.1, 'clay_15_30': 29.9, ...}

2. Multiple Profiles (Long Format - Default)

profiles = [
    {
        'cokey': 1001,
        'horizons': [
            {'hzname': 'A', 'upper': 0, 'lower': 15, 'clay': 18.5},
            {'hzname': 'Bt1', 'upper': 15, 'lower': 45, 'clay': 35.0},
            {'hzname': 'Bt2', 'upper': 45, 'lower': 80, 'clay': 32.5},
        ]
    },
    {
        'cokey': 1002,
        'horizons': [
            {'hzname': 'Ap', 'upper': 0, 'lower': 20, 'clay': 15.2},
            {'hzname': 'Bw', 'upper': 20, 'lower': 50, 'clay': 28.4},
            {'hzname': 'C', 'upper': 50, 'lower': 100, 'clay': 25.0},
        ]
    },
]

# Returns DataFrame with columns: [cokey, var_name, upper, lower, value]
df_long = mpspline(profiles, var_name=['clay'])
print(df_long[['cokey', 'var_name', 'upper', 'lower', 'value']].head())

Output:

 cokey var_name  upper  lower      value
  1001     clay      0      5  16.168706
  1001     clay      5     15  19.762784
  1001     clay     15     30  31.118765
  1001     clay     30     60  36.090372
  1001     clay     60    100  31.251860

3. Multiple Profiles (Wide Format)

# Returns DataFrame with flattened columns: [cokey, clay_0_5, clay_5_15, ...]
df_wide = mpspline(profiles, var_name=['clay'], output_type='wide')
print(df_wide[['cokey', 'clay_0_5', 'clay_5_15', 'clay_15_30']].head())

Output:

 cokey  clay_0_5  clay_5_15  clay_15_30
  1001 16.168706  19.762784   31.118765
  1002 12.784555  14.721798   22.437913

4. Advanced Modes (1cm Resolution)

# Get high-resolution predictions at every 1cm interval
df_1cm = mpspline(profiles, var_name=['clay'], mode='1cm')
print(df_1cm[['cokey', 'var_name', 'depth', 'value']].head())

Output:

 cokey var_name  depth      value
  1001     clay      0  15.935577
  1001     clay      1  15.974431
  1001     clay      2  16.090996
  1001     clay      3  16.285271
  1001     clay      4  16.557255

Parameters

Parameter	Type	Default	Description
obj	dict or list	Required	Profile(s) with a 'horizons' key
var_name	str or list	None	Properties to harmonize (all numeric if None)
target_depths	list	GlobalSoilMap	Depth intervals as (top, bottom). Default: [(0,5), (5,15), (15,30), (30,60), (60,100), (100,200)]
lam	float	0.1	Smoothing parameter (0.01=smooth, 1.0=fit data closely)
vlow	float	0.0	Minimum constraint for values
vhigh	float	1000.0	Maximum constraint for values
parallel	bool	False	Use multiprocessing for multiple profiles
batch_size	int	100	Profiles per batch
strict	bool	False	Raise exceptions on validation errors (False = skip)

Horizon Input Format

Required fields:

• Depth: upper and lower (or top and bottom) in cm
• Properties: numeric fields to harmonize

Optional:

• hzname: horizon name

Example:

{
    'hzname': 'Ap',
    'upper': 0,
    'lower': 20,
    'clay': 24.5,
    'sand': 42.3,
}

Examples

# Custom depth intervals
result = mpspline(profile, target_depths=[(0, 10), (10, 30), (30, 60)])

# Adjust smoothing (0.01=smooth, 1.0=closer to data)
result = mpspline(profile, lam=0.01)

# Constrain values to realistic ranges
result = mpspline(profile, var_name=['clay'], vlow=0, vhigh=100)

# Parallel processing for many profiles
df = mpspline(profiles, parallel=True, batch_size=500)

# Only process specific properties
df = mpspline(profiles, var_name=['clay', 'sand'])

# Error handling: skip bad profiles or raise errors
df = mpspline(profiles, strict=False)  # Skip problematic profiles
try:
    df = mpspline(profiles, strict=True)  # Raise on errors
except ValueError as e:
    print(f"Validation error: {e}")

Troubleshooting

Horizons not ordered by depth: Horizons must be sequential with no gaps or overlaps.

# Wrong
{'upper': 0, 'lower': 30}, {'upper': 20, 'lower': 50}

# Right
{'upper': 0, 'lower': 20}, {'upper': 20, 'lower': 50}

Values outside expected ranges: Use vlow and vhigh to constrain predictions:

result = mpspline(profile, vlow=0, vhigh=100)

Processing is slow: Enable parallel processing:

df = mpspline(profiles, parallel=True, batch_size=500)

How it works

The algorithm fits a mass-preserving equal-area quadratic spline to horizon data. This converts discrete observations at varying depths to standard depth intervals while preserving the average value across each depth range.

See the algorithm documentation for details.

References

• O'Brien, L. (2025). mpspline2: Mass-Preserving Spline Functions for Soil Data. R package version 0.1.9. https://doi.org/10.32614/CRAN.package.mpspline2
• Bishop, T.F.A., McBratney, A.B., & Laslett, G.M. (1999). Modelling soil attribute depth functions with equal-area quadratic smoothing splines. Geoderma, 89(3-4), 185-208. https://doi.org/10.1016/S0016-7061(99)00003-8
• Malone, B.P., McBratney, A.B., & Minasny, B. (2009). Mapping continuous depth functions of soil carbon storage and available water capacity. Geoderma, 154(3-4), 138-152. https://doi.org/10.1016/j.geoderma.2009.10.007

License

GPL 3.0