Master’s Thesis Research Monograph
Author: Nnaemeka Ndubuisi
Institution / Project: Wetland_Thesis_2026
Date of Compilation & Verification: October 4,
2026
Methodological Status: Formally Verified &
Cryptographically Frozen
COMPLETE METHODOLOGICAL ARCHITECTURE
┌─────────────────────────┐ ┌─────────────────────────┐ ┌─────────────────────────┐
│ Chapter 1 │ │ Chapter 2 │ │ Chapter 3 │
│ Population Filtering │────>│ Spatial Delineation │────>│ Wetland Targets │
│ (13,994 -> 5,003 Stn) │ │ (5,556 Catchments; │ │ (W01 Area Fraction; │
│ (DOC & TOC Y3 Tiers) │ │ 937 Monitored DAGs) │ │ W02 Simplex Shares) │
└─────────────────────────┘ └─────────────────────────┘ └─────────────────────────┘
│
┌───────────────────────────────────────────────────────────────────────────┘
│
▼
┌─────────────────────────────────────────────────────────────────────────────────────────┐
│ PREDICTOR ENGINEERING SUBSYSTEM │
│ ┌───────────────────────┐ ┌───────────────────────┐ ┌─────────────────────────────┐ │
│ │ Chapter 4 │ │ Chapter 5 │ │ Chapter 6 │ │
│ │ Hydrochemistry │ │ Terrain Structure │ │ Hydroclimate │ │
│ │ DOC/TOC Endpoints, │ │ MERIT Area, Slope, │ │ CHELSA P, PET, Temp, │ │
│ │ pH, Water Temp │ │ Elevation Range │ │ Aridity (Synchronized) │ │
│ └───────────────────────┘ └───────────────────────┘ └─────────────────────────────┘ │
│ │ │ │ │
│ └───────────────────────────┼─────────────────────────────┘ │
│ ▼ │
│ ┌───────────────────────┐ │
│ │ Chapter 7 │ │
│ │ Land Cover Context │ │
│ │ 7 Terrestrial B03 │ │
│ │ (Exact vs 2023 Sens.) │ │
│ └───────────────────────┘ │
│ │ │
│ ▼ │
│ ┌───────────────────────┐ │
│ │ Chapter 8 │ │
│ │ Soil Context (B04) │ │
│ │ (Investigated, Scaled,│ │
│ │ Formally Non-Adopted)│ │
│ └───────────────────────┘ │
└─────────────────────────────────────────────────────────────────────────────────────────┘
│
▼
┌─────────────────────────────────────────────────────────────────────────────────────────┐
│ Chapter 9 │
│ Integrated Predictor Matrix (OP002_V2 & OP003) │
│ - 10 Tables, 57,988 Row Realizations, 152 Schema Columns Categorized │
│ - 5,087,208 Field-by-Field Read-Back Comparisons (Zero Mismatches) │
│ - Core Predictor Matrix: X_core = [ X_chem , X_terrain , X_climate , X_landcover ] │
│ - Strict Prohibition of Global Pre-Imputation; Retention of Raw Missing Values │
└─────────────────────────────────────────────────────────────────────────────────────────┘
│
▼
┌─────────────────────────────────────────────────────────────────────────────────────────┐
│ Chapter 10 │
│ Analysis & Modelling Architecture (AM001 - AM002B) │
│ - Paired Three-Way Comparison Protocol: Chem vs Context vs Combined (Delta-Loss) │
│ - Equal-Catchment Sample Weighting (w = 1.0 per catchment) │
│ - 5-Fold Geographic Holdouts with 100 km Geodesic Outlet Buffer Guard │
│ - Three Fixed Estimators: Null Weighted Mean, Shallow Tree (d=3), Extra Trees (256 tr)│
│ - Native Multi-Output Simplex Regression (Sum = 1.0, >= 0 Preserved Mathematically) │
│ - External Lower Saxony Validation Domain Remains 100% Sealed & Untouched │
└─────────────────────────────────────────────────────────────────────────────────────────┘| Chapter | Stage Identifier | Core Construct | Source Authority | Sample Population | Final Disposition |
|---|---|---|---|---|---|
| 1 | 01_Population_Filtering |
Global River Monitoring Cohorts | UNEP GEMStat Archive | 13,994 raw stations \(\to\) 5,003 unique stations in \(Y3\) | ADOPTED |
| 2 | 02_Spatial |
Topographic Catchment Hydrography | MERIT Hydro (3-arcsec) | 5,556 catchments; 937 monitored DAG components | ADOPTED |
| 3 | 03_Wetland_Targets |
\(W01\) Area Fraction & \(W02\) Simplex | GLWD v2 + PALSAR + MERIT | \(N = 4,523\) DOC (\(4,444\) defined); \(N = 2,715\) TOC (\(2,670\) defined) | ADOPTED |
| 4 | 04_Hydrochemistry |
DOC, TOC, in-situ pH, Water Temp | GEMStat (Stage HP007) |
DOC: 4,523 records; TOC: 2,715 records (Lower/Upper scenarios) | ADOPTED |
| 5 | 05_Other_Predictors / B01 |
Terrain Area, Slope, Relief | MERIT Hydro Topography | 5,556 catchments (100% complete, geodesic weighting) | ADOPTED |
| 6 | 05_Other_Predictors / B02 |
Atmospheric Water Balance (\(P, PET, AI\)) | CHELSA V2.1 Climatology | 5,556 catchments (Exact-year synchronized, 100% complete) | ADOPTED |
| 7 | 05_Other_Predictors / B03 |
7 Terrestrial Land Cover Fractions | Copernicus 100m Annual | 5,556 catchments (Exact-Year + 2023-from-2022 recovery) | ADOPTED |
| 8 | 05_Other_Predictors / B04 |
Mineral Clay Content & Soil pH | ISRIC SoilGrids 250m v2.0 | 34,395 GeoTIFFs acquired (16.26 GiB); mega-basin scaling wall | NOT ADOPTED |
| 9 | 05_Other_Predictors / OP002 |
Unified Predictor Matrix \(\mathbf{X}\) | OP002 V2 & OP003 Closure | 10 tables, 57,988 rows, 152 schema columns, zero imputation | CLOSED / SEALED |
| 10 | 06_Analysis_Modelling |
Machine Learning & Spatial CV | AM001–AM002B Protocol |
5 Geographic Folds, 100 km Buffer, Extra Trees Multioutput | PREREGISTERED |
A central impediment in macroscopic fluvial biogeochemistry is the vulnerability of global water-quality datasets to sampling biases, inconsistent analytical methodologies, and arbitrary data-pruning workflows. In many published global syntheses, monitoring stations are cherry-picked based on subjective completeness criteria, single-day “grab” concentrations are conflated with multi-decadal mean states, or detection-limit values are arbitrarily replaced by constant fractions (such as \(\text{DL}/2\) or \(0\)).
Block 01_Population_Filtering establishes an immutable,
mathematically reproducible foundation for the entire thesis. It defines
how the raw global monitoring holdings of the United Nations Environment
Programme (UNEP) GEMS/Water database were audited, filtered, and
structured into robust, multi-year temporal tiers
before any catchment boundaries were delineated or
wetland targets consulted.
The geographic scope was bounded to the Northern Hemisphere (\(\text{Latitude} > 0^\circ\)) to align with pan-Arctic, temperate, and tropical wetland-carbon dynamics while eliminating southern-hemisphere seasonal inversion artifacts. * The raw database contained 13,994 unique monitoring stations across 36 countries. * Duplicate metadata entries (stations with identical spatial coordinates but alternative agency identifiers) were mapped and unified to eliminate coordinate conflicts.
To ensure that dissolved and total organic carbon observations
represent true integrated catchment drainage signals, waterbodies were
pruned by strictly filtering GEMStat Waterbody_Type
metadata: * Excluded: Lakes, reservoirs, impoundments,
wetlands, groundwater wells, and estuarine mixing zones. *
Retained: Strictly lotic, freshwater stream and river
channels (River / Stream).
In aquatic biogeochemistry, organic carbon is separated into operational fractions based on filtration through a \(0.45\,\mu\text{m}\) (or \(0.7\,\mu\text{m}\)) membrane: 1. Dissolved Organic Carbon (\(\text{DOC}\)): The filtrate fraction. In natural boreal and temperate catchments, DOC typically constitutes \(85\text{--}95\%\) of total organic carbon, driven primarily by soil leaching, peat drainage, and humic/fulvic acid mobilization. 2. Total Organic Carbon (\(\text{TOC}\)): Unfiltered water, comprising both dissolved carbon and particulate organic carbon (\(\text{TOC} = \text{DOC} + \text{POC}\)). In high-gradient, agricultural, or heavily eroded catchments, particulate organic carbon pulses during storm runoff can cause TOC to diverge substantially from DOC.
Methodological Mandate: DOC and TOC are never pooled into an ad-hoc “generic carbon” variable. They are treated as strictly independent, parallel analytical branches throughout all subsequent spatial, predictor, and modeling stages.
All concentration records were standardized to mass concentration of carbon: \[C_{\text{carbon}} \quad \text{expressed in } \mathrm{mg\ C \cdot L^{-1}}\] Reported units of \(\mu\text{g/L}\), \(\text{g/m}^3\), or molar units (\(\text{mmol C/L}\)) were converted using exact physical conversion constants. Impossible extreme physical outliers (e.g., negative concentrations or values exceeding \(500\,\mathrm{mg/L}\) without industrial point-source flags) were flagged during automated read-back QA.
Surface water chemistry exhibits extreme temporal variability across hydro-meteorological events (snowmelt pulses, summer low-flow baseflow, autumn storms). A single-year monitoring snapshot often reflects anomalous dry or wet years rather than the climatological state of the catchment.
To establish persistent hydrochemical regimes, monitoring stations were classified into three hierarchical temporal tiers based on the number of unique calendar years with valid carbon measurements:
TEMPORAL TIER TAXONOMY
Years of Record: 0 1 2 3 4+
|-------|-------|---------------|--------------->
Status: [ EXCLUDED ] Tier Y2 Tier Y3 (PRIMARY) Tier Y4 (STRICT)
(>= 2 years) (>= 3 years) (>= 4 years)| Temporal Tier | Definition | DOC Station Records | DOC Unique Catchments | TOC Station Records | TOC Unique Catchments | Primary Analytical Role |
|---|---|---|---|---|---|---|
| \(Y2\) | \(\ge 2\) unique calendar years | 4,948 | 4,895 | 3,083 | 3,034 | Broad sensitivity analysis |
| \(Y3\) | \(\ge 3\) unique calendar years | 4,523 | 4,477 | 2,715 | 2,674 | Primary Thesis Analysis Cohort |
| \(Y4\) | \(\ge 4\) unique calendar years | 4,134 | 4,097 | 2,353 | 2,318 | High-stringency robustness check |
A substantial fraction of surface water chemistry observations are subject to analytical detection limits, producing censored data: 1. Left-Censored Data (\(< \text{DL}\)): The true concentration is below the laboratory detection limit \(\text{DL}\). 2. Right-Censored Data (\(> \text{UL}\)): The concentration exceeds the upper calibration range \(\text{UL}\). 3. Exact Point-Identified Data: The concentration is directly measured between limits.
In standard environmental literature, researchers frequently substitute \(< \text{DL}\) with \(\text{DL}/2\) or \(0\). In statistical hydrology, this practice is well-documented to: - Artificially truncate variance. - Induce false correlation with independent covariates. - Systematically distort spatial relationships in pristine headwater catchments with very low organic carbon concentrations.
To preserve mathematical rigor without data leakage, censored observations are represented as identification intervals \([L_i, U_i]\): * For exact grabs: \(L_i = U_i = C_{\text{observed}}\). * For left-censored grabs: \(L_i = 0\), \(U_i = \text{DL}\). * For right-censored grabs: \(L_i = \text{UL}\), \(U_i = +\infty\) (or capped at maximum physical plausibility).
From these intervals, two parallel, bounding scenario features are extracted for each station: 1. Lower-Endpoint Scenario (\(C_{\text{lower}}\)): Evaluates the conservative lower bound of carbon export (\(L_i = 0\) for censored values). 2. Upper-Endpoint Scenario (\(C_{\text{upper}}\)): Evaluates the maximum potential carbon concentration (\(U_i = \text{DL}\) for censored values).
Core Rule: In downstream modeling, \(C_{\text{lower}}\) and \(C_{\text{upper}}\) are evaluated as alternative bounding data scenarios, never as simultaneous collinear features.
A major question addressed during population filtering was whether
sample-aligned river discharge (\(Q\),
\(\text{m}^3/\text{s}\)) could be
incorporated alongside water chemistry. An exhaustive audit of the
13,994 station metadata records revealed: * Only 55 unique
stations (< 0.4%) contain any entry in the metadata
Discharge column. * Only 52 of these
stations are in the numerical \(Y2\) cohort. * Crucially, this metadata
field is a single, static station attribute (e.g.,
historical mean discharge from original station commissioning),
not continuous time-series flow matched to carbon grab
dates. * Sample-aligned discharge is completely absent from
global GEMStat river holdings.
As established in methodology audits, attempting to merge external gauging networks (such as GRDC) causes catastrophic geographic attrition (losing \(>85\text{--}90\%\) of stations) and biases the population entirely to Western Europe and the United States. Atmospheric water balance controls (\(P, \text{PET}, AI\)) from Block B02 are therefore adopted to represent hydrological yield without geographic collapse.
In fluvial biogeochemistry, the chemical composition of stream water at a sampling point represents the spatially integrated flux of all upstream terrestrial and riparian processes. Approximating catchment context with arbitrary circular buffers around monitoring stations introduces severe geomorphic errors: 1. Circular buffers capture adjacent valleys and downstream floodplains that never drain to the sampling station. 2. Buffers omit distant headwaters and alpine ridges that contribute the vast majority of water, dissolved organic matter, and sediment.
To achieve physical fidelity, Block 02_Spatial
delineates the exact topographic contributing catchment
for every qualified monitoring station using high-resolution,
hydrologically conditioned elevation data.
Catchment boundaries were delineated using MERIT
Hydro (Multi-Error-Removed Improved-Terrain Hydrography;
Yamazaki et al., 2019): * Resolution: 3-arcsecond grid
cells (\(\approx 90\text{ m} \times 90\text{
m}\) at the equator; finer at high boreal latitudes). *
Conditioning: Integrates the MERIT DEM with
high-resolution water body datasets (GWD-LR, SWBD) and removes
vegetation canopy height biases, stripe noise, and absolute speckle
errors. * Hydrographic Layers: - dir: Flow
direction rasters based on the D8 flow routing algorithm. -
upa: Flow accumulation / upstream drainage area rasters
(\(\text{km}^2\)). - elv:
Hydro-enforced hydrologic digital elevation model.
Raw coordinates reported by environmental monitoring agencies frequently exhibit minor GPS inaccuracies or reference road bridges adjacent to, rather than inside, the active channel. Placing a pour-point even one 90m pixel off the true streamline can result in delineating a tiny 1-pixel local drainage rather than a \(10,000\,\text{km}^2\) river basin.
The outlet snapping algorithm followed strict hydrological rules: 1.
Local Search Window: Examined the flow accumulation
(upa) grid within a radial distance of up to \(500\text{ m}\). 2. Upstream Area
Matching: Snapped the station coordinates to the nearest stream
pixel whose modeled upstream drainage area matched the reported agency
drainage area within strict tolerances (\(<
15\%\) area discrepancy). 3. The V023W/X Spatial QC
Filter: Stations with confirmed irreconcilable area mismatches
or coordinate mislocations were systematically flagged
(spatial_qc_confirmed_catchment_mismatch = True). These
stations (\(n=2\) in the primary
cohort) were retained for transparency but isolated to permit
high-stringency sensitivity audits.
From the snapped pour-point cell \((r_0, c_0)\), catchment delineation proceeded by recursive upstream traversal: \[\Omega_{\text{catchment}} = \left\{ (r, c) \;\middle|\; \text{Path}(r, c \to r_0, c_0) \text{ follows valid D8 flow directions} \right\}\] * Extracted catchments were converted to two synchronized spatial representations: 1. Scientific Bitmasks: Binary rasters matching the native MERIT Hydro tile tiling structure for exact cell-by-cell raster overlays. 2. Vector Polygons: Boundary shapefiles with densified geodesic coordinates for geometric spatial operations. * Global Output: Delineated exactly 5,556 authoritative catchments across the Northern Hemisphere.
Monitoring networks do not consist of isolated catchments; river basins form hierarchical branching networks where headwater monitoring stations drain into mid-reach stations, which in turn drain into downstream estuarine gauges.
The global hydrographic connectivity among the 5,556 catchments is formalized as a Directed Acyclic Graph (DAG): \[G = (V, E)\] * Nodes (\(V\)): The set of 5,556 monitored catchment units (\(|V| = 5,556\)). * Directed Edges (\(E\)): The set of directed flow connections (\(|E| = 4,619\)). A directed edge \((u, v) \in E\) indicates that catchment \(u\) discharges directly into catchment \(v\) without passing through any intermediate monitored station.
Automated topological audits confirmed the structural integrity of the stream network graph: * Acyclicity: Zero circular loops or back-flowing edges (\(\text{Cycles} = 0\)). * Completeness: Every edge represents a physically verified hydrologic connection along the MERIT Hydro river network.
NESTED DRAINAGE TOPOLOGY (DAG COMPONENT)
[Station A] (Headwater 1) [Station B] (Headwater 2)
\ /
\ /
▼ ▼
[Station C] (Mid-Reach Junction)
│
▼
[Station D] (Terminal River Basin Outlet)By computing the connected components of the undirected projection of \(G\), the global catchment network was partitioned into 937 independent monitored-hierarchy components: * Each component represents an isolated, physically self-contained river basin system that discharges into the sea or an endorheic sink. * In the primary \(Y3\) cohort: - DOC stations span 672 distinct hierarchy components (largest group contains 311 nested catchments, corresponding to major continental river networks like the Mississippi or Danube). - TOC stations span 484 distinct hierarchy components (largest group contains 273 catchments).
The most critical methodological consequence of Block
02_Spatial is the indivisibility
principle: > Methodological Mandate: In any
spatial cross-validation scheme, all catchments belonging to the same
monitored-hierarchy component must remain in the same validation
fold.
If nested stations were partitioned randomly, a downstream station (Station D) could be placed in the test set while its headwaters (Stations A, B, and C) were placed in the training set. Because Station D’s water is literally composed of the upstream water, a machine learning model would simply interpolate the training headwater signals, artificially inflating performance metrics while concealing catastrophic failure in true ungauged basins.
In earth system models and regional hydrology, wetlands are frequently represented as static binary masks or aggregated into a single generic “wetland” percentage. However, the biogeochemical influence of wetlands on fluvial carbon export is governed by two fundamentally distinct spatial characteristics: 1. Wetland Abundance (\(W01\)): How much of the upstream catchment is occupied by inundated, waterlogged, or saturated environments capable of generating dissolved organic matter? 2. Wetland Typology & Composition (\(W02\)): What types of wetlands dominate? A catchment covered by peat bogs mobilizes vast quantities of recalcitrant, highly aromatic humic acids, whereas a catchment dominated by open lacustrine surfaces acts primarily as a carbon sink and processing reactor with substantial photo-oxidation.
Block 03_Wetland_Targets rigorously operationalizes
these constructs into mathematically coherent, independent response
variables.
\(W01\) represents the areal fraction of the total topographic catchment occupied by mapped wetland environments: \[W01 = \frac{A_{\text{wetland}}}{A_{\text{catchment}}} = \frac{\sum_{i \in \Omega} A_i \cdot \mathbf{1}_{\text{wetland}}(i)}{\sum_{i \in \Omega} A_i} \in [0, 1]\] where: - \(\Omega\) is the set of cells comprising the catchment. - \(A_i\) is the exact WGS84 geodesic area of cell \(i\) (\(\text{m}^2\)). - \(\mathbf{1}_{\text{wetland}}(i) \in \{0, 1\}\) is the multi-sensor wetland indicator function.
In the primary \(Y3\) cohort: * 79 DOC catchments and 45 TOC catchments have \(W01 = 0.0\) (zero mapped wetlands). * In many machine-learning workflows, zero-target records are erroneously discarded or assigned arbitrary non-zero pseudocounts. * Methodological Mandate: In this thesis, all \(W01 = 0.0\) catchments are strictly retained. Dropping them would induce survivorship bias and prevent models from learning the hydrochemical signatures of arid, alpine, or well-drained catchments devoid of wetland carbon sources.
The primary scoring metric for continuous wetland fraction prediction is catchment-weighted Mean Absolute Error (MAE): \[\text{MAE}_{\text{weighted}}(W01) = \frac{\sum_{i=1}^N w_i \cdot |y_i - \hat{y}_i|}{\sum_{i=1}^N w_i}\] (Secondary metric: Root Mean Squared Error, RMSE).
\(W02\) disaggregates mapped wetland area into seven mutually exclusive, collectively exhaustive functional wetland classes adapted from the Ramsar and GLWD classification frameworks:
| Family Code | Wetland Family Name | Dominant Hydrologic / Ecological Character | Fluvial Carbon Signature |
|---|---|---|---|
F1 |
Lacustrine | Permanent open water, lakes, and deep ponds | Carbon retention, photo-bleaching, autochthonous DOC |
F2 |
Riverine | Active river floodplains, oxbows, riparian ribbons | High-frequency pulse flushing during bankfull discharge |
F3 |
Palustrine | Non-tidal marshes, swamps, and wet meadows | High DOC mobilization from emergent macrophyte roots |
F4 |
Ephemeral | Intermittent, seasonal, or temporary floodplains | Sharp seasonal DOC concentration spikes upon rewetting |
F5 |
Peatland | Ombrotrophic bogs, minerotrophic fens, mires | Massive export of aromatic, high-molecular-weight humic acids |
F6 |
Coastal | Tidal salt marshes, mangrove swamps, estuaries | Saline flocculation, tidal exchange dynamics |
F7 |
Saline / Brackish | Inland saline depressions, soda lakes, playas | High ionic strength, alkaline humic dissolution |
Because each family share represents the proportion of total mapped wetland area, the components of \(W02\) must sum exactly to unity: \[W02_k = \frac{A_{\text{family } k}}{A_{\text{wetland}}} = \frac{A_{\text{family } k}}{\sum_{j=1}^7 A_{\text{family } j}}\] \[\mathbf{y}_{W02} = \left[ W02_1, W02_2, \dots, W02_7 \right]^T \in S^6 \iff \sum_{k=1}^7 W02_k = 1.0 \quad \text{and} \quad W02_k \ge 0 \quad \forall k\]
A foundational mathematical principle governs \(W02\): \[\lim_{A_{\text{wetland}} \to 0}
\frac{A_{\text{family } k}}{A_{\text{wetland}}} = \frac{0}{0} \implies
\text{Undefined}\] * If a catchment contains zero wetland area
(\(W01 = 0\)), its wetland composition
does not exist (\(\mathbf{0}
\notin S^6\)). * Imputing a zero vector (\([0,0,0,0,0,0,0]\)) or a uniform vector
(\([1/7, \dots, 1/7]\)) violates
compositional geometry and induces severe model bias. *
Methodological Mandate: In all \(W01 = 0\) catchments (\(n=79\) in DOC; \(n=45\) in TOC), \(W02\) is explicitly preserved as
NA (structurally undefined). These records
are evaluated in \(W01\) models but
automatically excluded from \(W02\)
compositional evaluation.
During global raster integration, floating-point summation across
millions of pixels occasionally produces tiny rounding artifacts (e.g.,
a single riverine share was recorded as \(1.0000000000000002\), which is \(2.22 \times 10^{-16}\) above \(1.0\)). Under Stage
WT006/AM001, these values are
preserved exactly within a frozen \(10^{-12}\) numerical tolerance without
artificial clipping or distortion.
Because \(W02\) resides on a simplex, standard Mean Squared Error (MSE) is geometric nonsense. The primary evaluation metric is catchment-weighted Total Variation Distance (TVD): \[\text{TVD}_{\text{weighted}}(W02) = \frac{\sum_{i=1}^N w_i \cdot \left( \frac{1}{2} \sum_{k=1}^7 |y_{i,k} - \hat{y}_{i,k}| \right)}{\sum_{i=1}^N w_i}\] * Physical Interpretation: TVD represents the exact percentage of catchment wetland area that would need to be reallocated among the 7 families to achieve perfect compositional agreement. * Properties: \(0 \le \text{TVD} \le 1\). * (Secondary metric: family-specific weighted MAE).
While \(W01\) and \(W02\) define wetland abundance and typology, they do not account for where wetlands are located along the stream network. A wetland situated \(50\text{ km}\) upstream in an alpine headwater undergoes substantial in-stream mineralization before reaching the outlet, whereas a riparian wetland \(500\text{ m}\) upstream of the sampling station exports fresh, un-degraded carbon directly into the sample bottle.
Under W03-000 through W03-003, structural
connectivity was operationalized: 1. Downstream Flowpath
Distance (\(D_{\text{down}}\),
km): The flow-direction stream distance from each wetland pixel
to the catchment monitoring outlet. 2. Topological In-Stream
Index (\(I_{\text{topo}}\)):
Flow-weighted river network travel time proxy.
Governance Ruling: \(W03\) is cataloged as an authoritative secondary structural descriptor outside the core prediction targets. It is not added as a predictor of \(W01\) or \(W02\) to prevent circular cross-target contamination, but is preserved for downstream process interpretation.
| Analyte Branch | Total Monitored Records | Valid \(W01\) Records | \(W01 = 0\) True Zeros | Defined \(W02\) Records | Undefined \(W02\) Records | Primary Evaluation Metric (\(W01\)) | Primary Evaluation Metric (\(W02\)) |
|---|---|---|---|---|---|---|---|
| DOC | 4,523 | 4,523 (\(100\%\)) | 79 | 4,444 | 79 | Catchment-weighted MAE | Catchment-weighted TVD |
| TOC | 2,715 | 2,715 (\(100\%\)) | 45 | 2,670 | 45 | Catchment-weighted MAE | Catchment-weighted TVD |
Rivers and streams are not passive conduits transporting carbon from land to sea; they act as active, highly sensitive integrators of upstream terrestrial ecosystem processes. Wetlands—specifically peatlands, riparian ribbons, and marshes—are the dominant global sources of dissolved organic matter (DOM) in lotic systems: 1. Humic and Fulvic Acid Leaching: Anaerobic, saturated wetland soils impede complete microbial respiration, leading to the accumulation of organic acids that leach into surface runoff. 2. Spectroscopic and Color Imprints: Water draining peatlands and forested wetlands exhibits high specific UV absorbance at 254 nm (\(\text{SUVA}_{254}\)) and rich dissolved organic carbon concentrations. 3. Hydrological Flushing Dynamics: During storm events and snowmelt, rising water tables intersect organic-rich upper soil horizons in wetlands, generating intense concentration pulses in downstream channels.
Block 04_Hydrochemistry_Predictors formulates the
chemical feature matrix \(\mathbf{X}_{\text{chem}}\) used to test how
accurately these in-stream signatures can recover upstream wetland area
(\(W01\)) and composition (\(W02\)).
In environmental literature, researchers occasionally combine DOC and TOC measurements into a single “organic carbon” variable when sample sizes are small. In macroscopic fluvial modeling, this introduces substantial systematic error: * Analytical Disconnect: DOC is operationally defined by membrane filtration (\(0.45\,\mu\text{m}\)), removing all suspended mineral grains, cellular debris, and macro-particulates. TOC is unfiltered. * Geomorphic Variance: In high-relief, mountainous, or agricultural basins, particulate organic carbon (\(\text{POC} = \text{TOC} - \text{DOC}\)) can fluctuate by orders of magnitude due to soil erosion, bank collapse, and suspended sediment transport, completely decoupling TOC from wetland peat leaching. * Chemical Reactivity: DOC represents the mobile, chemically reactive fraction that governs downstream lake carbon budgets, trihalomethane formation in drinking water, and microbial respiration.
Methodological Mandate: Under Stage
HP007, DOC and TOC are maintained in strictly independent analytical pipelines. Models are trained and evaluated separately on DOC (\(N = 4,523\)) and TOC (\(N = 2,715\)). Cross-analyte pooling is explicitly prohibited.
In water quality monitoring, a significant proportion of samples fall below analytical detection limits (\(< \text{DL}\), left-censored) or occasionally exceed maximum spectrophotometric ranges (\(> \text{UL}\), right-censored).
Common heuristics such as replacing non-detects with \(0\) or \(\text{DL}/2\): * Artificially compress empirical variance. * Create false non-linearities and threshold artifacts in regression models. * Induce artificial spatial clustering in pristine headwaters where true concentrations are low.
Every observation \(i\) is represented as an identification interval \([L_i, U_i]\): \[C_i \in [L_i, U_i] \quad \text{where} \quad \begin{cases} L_i = U_i = C_i, & \text{if directly measured} \\ L_i = 0, \; U_i = \text{DL}, & \text{if left-censored } (< \text{DL}) \\ L_i = \text{UL}, \; U_i = +\infty, & \text{if right-censored } (> \text{UL}) \end{cases}\]
From these intervals, two parallel primary predictor scenarios are extracted for each station: 1. Lower-Endpoint Scenario (\(C_{\text{lower}}\)): \[C_{\text{lower}} = \text{Station Median of } L_i\] Represents the most conservative baseline of organic carbon export. 2. Upper-Endpoint Scenario (\(C_{\text{upper}}\)): \[C_{\text{upper}} = \text{Station Median of } U_i\] Represents the maximum potential carbon concentration under analytical uncertainty.
Governance Constraint: \(C_{\text{lower}}\) and \(C_{\text{upper}}\) represent alternative data regimes, evaluated in parallel model runs to test whether detection limits alter scientific conclusions. They are never entered simultaneously into a regression model, as their high collinearity would destabilize parameter estimation.
To ensure that machine learning models do not mistake temperature-driven biological processing or pH-driven solubility for wetland extent, two critical in-situ physico-chemical parameters were extracted:
pH_canonical_point_value)TEMP_canonical_point_value, °C)Methodological Mandate: In Stage
HP007, missing in-situ pH (\(n=153\)) and water temperature (\(n=344\)) are strictly preserved as rawNA. Global pre-imputation (such as inserting global medians, mean substitution, or whole-matrix SVD imputation) is formally forbidden. Any imputation must be learned strictly within the training folds of cross-validation during downstream model fitting to prevent data leakage.
In wetland-dominated catchments, the mobility of organic carbon is intimately coupled with iron biogeochemistry: * Under reducing, waterlogged conditions in peatlands and riparian soils, insoluble ferric iron (\(\text{Fe}^{3+}\)) is microbially reduced to soluble ferrous iron (\(\text{Fe}^{2+}\)). * Soluble iron complexes with humic acids, forming mobile organo-metallic colloids that export vast quantities of carbon into headwaters. Upon entering oxygenated stream reaches, iron oxidation can cause co-precipitation of dissolved organic carbon.
To facilitate specialized process sensitivity analyses, lower- and upper-endpoint scenarios were derived for: * Total Iron (\(\text{Fe}_{\text{Tot}}\)): Lower and upper endpoint scenarios (\(\text{mg/L}\)). * Dissolved Iron (\(\text{Fe}_{\text{Dis}}\)): Lower and upper endpoint scenarios (\(\text{mg/L}\)).
Governance Constraint: Iron features are designated as secondary process sensitivity inputs. Because iron is measured at only a subset of global stations, it is excluded from the core primary matrix to maintain maximum global station retention (\(N = 5,003\)).
| Analyte Branch | Retained Records (\(Y3\)) | Unique Catchments | Point-Identified Carbon Records | Non-Point Carbon Records | Retained Missing In-Situ pH | Retained Missing In-Situ Temp | Primary Analytical Role |
|---|---|---|---|---|---|---|---|
| DOC | 4,523 | 4,477 | 4,499 (\(99.47\%\)) | 24 (\(0.53\%\)) | 153 (\(3.38\%\)) | 344 (\(7.61\%\)) | Core Primary Predictor Matrix |
| TOC | 2,715 | 2,674 | 2,713 (\(99.93\%\)) | 2 (\(0.07\%\)) | 47 (\(1.73\%\)) | 98 (\(3.61\%\)) | Core Primary Predictor Matrix |
In physical hydrology, topography is the primary boundary condition dictating the gravitational movement of water, the distribution of saturated soil zones, and the mechanical energy of stream networks: 1. Slope and Water Table Saturation: In steep, high-relief mountainous catchments, gravitational hydraulic gradients drive rapid lateral subsurface and overland flow, shedding precipitation rapidly and preventing prolonged soil waterlogging. In contrast, low-gradient, flat landscapes (slopes \(< 1.5^\circ\)) retard surface drainage, sustaining shallow water tables, extensive anoxic soil horizons, and deep peat accumulation. 2. Topographic Relief and Soil Exposure: High elevation relief (\(\Delta E\)) reflects steep headwaters with exposed bedrock, thin alpine soils, and high physical weathering, whereas low-relief plains are dominated by deep alluvial and organic deposits. 3. Catchment Scale (\(A\)): Upstream drainage area governs the volumetric discharge, residence time, in-stream channel storage, and benthic surface-area-to-volume ratio of the river network.
Block 01_B01_Terrain_Structure provides the foundational
physical landscape controls necessary to prevent machine-learning models
from confusing flat terrain for wetland presence.
On the native MERIT Hydro 3-arcsecond grid, local terrain slope was calculated using a \(3 \times 3\) moving window centered on cell \((r, c)\). To account for spherical convergence toward the poles, grid cell dimensions in the east–west direction (\(\Delta x\)) were scaled by latitude \(\phi\): \[\Delta x(\phi) = R_{\text{Earth}} \cdot \cos(\phi) \cdot \Delta \lambda, \quad \Delta y = R_{\text{Earth}} \cdot \Delta \phi\] where \(\Delta \lambda = \Delta \phi = 3\text{ arcseconds} = \frac{3}{3600}^\circ = \frac{\pi}{2.16 \times 10^6}\text{ radians}\).
Using Horn’s formulation, partial elevation derivatives were computed: \[\frac{\partial z}{\partial x} = \frac{(z_{NW} + 2 z_W + z_{SW}) - (z_{NE} + 2 z_E + z_{SE})}{8 \Delta x(\phi)}\] \[\frac{\partial z}{\partial y} = \frac{(z_{SW} + 2 z_S + z_{SE}) - (z_{NW} + 2 z_N + z_{NE})}{8 \Delta y}\] Local terrain slope \(s_i\) (in degrees) is given by: \[s_i = \arctan \left( \sqrt{\left(\frac{\partial z}{\partial x}\right)^2 + \left(\frac{\partial z}{\partial y}\right)^2} \right) \cdot \frac{180^\circ}{\pi}\]
Because pixel area decreases significantly from the tropics to the sub-Arctic, a simple unweighted arithmetic average of pixel slopes induces severe latitudinal bias. Catchment-level terrain metrics are formulated with exact WGS84 geodesic cell-area weights:
A critical methodological standard enforced in OP001 was
the complete elimination of cross-dataset DEM substitution: *
The Error of Mixed Topography: In many global studies,
researchers delineate drainage basins using one hydrographic network
(such as HydroSHEDS or MERIT Hydro) but extract slopes from alternative
digital elevation models (such as SRTM 30m, ASTER GDEM, or Copernicus
GLO-30). * Boundary Clipping Artifacts: Raster
reprojecting and resampling between conflicting DEM grids introduces
artificial ridge shears, mismatched stream channel elevations, and
severe boundary pixel clipping. * Strict Alignment:
Under OP001, all slope, area, and elevation metrics were
derived directly from the identical MERIT Hydro raster
arrays used to delineate the catchment boundaries, guaranteeing
100% spatial and topological consistency.
Cross-domain correlation analyses of the primary \(Y3\) modeling cohort (\(N = 3,558\) complete cases; op002_feature_correlation_matrix.csv)
revealed profound empirical relationships: * The Dominant
Slope–DOC Correlation: Catchment mean slope exhibits a
strong negative Spearman correlation with stream DOC
concentration (\(\rho =
-0.5006\)). - Flat, low-gradient catchments have high
DOC concentrations (\(15\text{--}40\,\text{mg/L}\)). - Steep,
alpine catchments have low DOC concentrations (\(< 2\,\text{mg/L}\)). *
Geomorphic Coherence: - Catchment slope correlates
positively with elevation range (\(\rho =
+0.7778\)). - Catchment area correlates with elevation range
(\(\rho = +0.6640\)).
TOPOGRAPHIC REGIMES & CARBON EXPORT
┌─────────────────────────────────┐ ┌─────────────────────────────────┐
│ High-Relief / Mountainous │ │ Low-Relief / Flatland │
│ - Slopes: > 8.0 degrees │ │ - Slopes: < 1.5 degrees │
│ - Rapid Overland Flushing │ │ - Stagnant Hydraulic Drainage │
│ - Thin Organic Soil Mantle │ │ - Deep Peat & Saturated Mires │
│ - Low Dissolved Organic Carbon │ │ - Very High Stream DOC (>15mg) │
│ - Fast Hydraulic Travel Time │ │ - Prolonged Biogeochemical Lag │
└─────────────────────────────────┘ └─────────────────────────────────┘Defense Argument: Because flat terrain is physically required for both wetland peat formation and high DOC leaching, a statistical model that omits terrain slope would erroneously attribute all carbon variation to wetland abundance. Including \(S\) and \(\Delta E\) in the core context matrix \(\mathbf{X}_{\text{core}}\) shields the thesis against terrain-induced omitted variable bias.
| Feature Identifier | Physical Construct | Unit | Global Completeness | Primary Role in Core Matrix \(\mathbf{X}\) |
|---|---|---|---|---|
full_catchment_area_km2 |
Topographic drainage basin area | \(\text{km}^2\) | 100.0% (5,556/5,556) | Core Context: Hydrological scaling |
mean_full_catchment_slope_degrees |
Geodesic-area weighted mean terrain slope | degrees | 100.0% (5,556/5,556) | Core Context: Runoff velocity & saturation control |
full_catchment_elevation_range_m |
Difference between maximum & minimum elevation | m | 100.0% (5,556/5,556) | Core Context: Macroscopic geomorphic relief |
Catchment hydrochemistry is governed by the atmospheric flux of water and energy: 1. Precipitation (\(P\)) as the Solute Flusher: Rain and snowmelt provide the fluid mass necessary to saturate peat layers, mobilize organic acids from upper soil horizons, and flush dissolved organic matter into active stream networks. 2. Evapotranspiration (\(PET\)) as the Solute Concentrator: Atmospheric evaporative demand concentrates solutes in surface waters, accelerates evapotranspirative drawdown in riparian fens, and dictates whether wetlands remain permanently saturated or desiccate seasonally. 3. Thermal Regime (\(T\)) as the Kinetic Driver: Soil temperature controls soil microbial respiration, vegetative net primary productivity, plant litter decomposition, and the enzymatic breakdown of phenolic compounds.
Block 02_B02_Hydroclimate operationalizes
high-resolution climatological boundary conditions to control for global
bioclimatic gradients across the Northern Hemisphere.
Macro-scale climate datasets (such as WorldClim or coarse ERA5 reanalysis) frequently fail in mountainous and coastal terrain due to over-smoothed topography. Block B02 relies on CHELSA V2.1 (Karger et al., 2017, 2021): * Resolution: 30-arcsecond grid cells (\(\approx 1\text{ km} \times 1\text{ km}\)). * Downscaling Physics: Downscales ERA5 atmospheric reanalysis using specialized mechanistic models: - Orographic windward/leeward precipitation enhancement. - Valley cold-air pooling and temperature inversions. - Penman-Monteith potential evapotranspiration driven by high-resolution solar radiation, vapor pressure deficit, temperature, and boundary layer wind speed.
A common flaw in macroscopic water quality literature is the application of a static 30-year climatological normal (e.g., 1970–2000) to water quality grabs collected in 2018 or 2022. If a region experienced severe multi-year drought or historic pluvial flooding during its monitoring window, static climatologies distort the empirical relationship between climate and stream chemistry.
Under B02-001 through B02-005: 1.
Station-Specific Temporal Query: For every monitoring
station history, the exact list of qualifying sampling years was
identified (B02_qualifying_years). 2. Annual Layer
Slicing: CHELSA annual precipitation, PET, and temperature
rasters were sliced for those specific calendar years. 3.
Climatological Mean Aggregation: \[\bar{P}_{\text{catchment}} =
\frac{1}{|Y_{\text{qual}}|} \sum_{y \in Y_{\text{qual}}} \left(
\frac{\sum_{i \in \Omega} A_i \cdot P_{i, y}}{\sum_{i \in \Omega} A_i}
\right)\] This guaranteed that the hydroclimatic covariates
reflect the exact meteorological conditions present during the
multi-year carbon sampling period.
Across the native CHELSA grid, five fundamental hydroclimatic descriptors were aggregated:
To prevent boundary coastal distortion and alpine snow/ice masking errors: * Cell-Area Weighting: Cell values were weighted by exact WGS84 geodesic area \(A_i\). * The 95% Common Support Rule: A catchment is deemed valid if and only if valid, non-null CHELSA data is available across at least \(95\%\) of the catchment’s physical area: \[\Phi_{\text{support}} = \frac{\sum_{i \in \Omega_{\text{valid}}} A_i}{\sum_{i \in \Omega} A_i} \ge 0.95\] * Empirical Result: Across all 5,556 global catchments, the observed common valid support fraction was \(\Phi_{\text{support}} = 1.000\) (100% complete) with zero missing or rejected catchments.
As established in methodological audits, in-situ streamflow (\(Q\), \(\text{m}^3/\text{s}\)) is unavailable for \(>99.6\%\) of GEMStat carbon grabs. Incorporating gridded modeled runoff (such as GloFAS or ERA5-Land): - Introduces unquantifiable model-on-model structural error (LISFLOOD routing assumptions). - Collapses resolution in headwater catchments smaller than the \(10\text{ km}\) GloFAS grid. - Risks mediator conditioning bias, because wetlands naturally attenuate discharge (\(W01 \to Q \to C\)).
Methodological Defense: The atmospheric water balance (\(P, PET, AI, CMD\)) captures the primary climatic driver of catchment water yield at the physical landscape boundary. It provides complete, high-resolution (\(1\text{ km}\)) global coverage, preserves small headwater basin integrity, and avoids the causal and spatial routing errors inherent in global streamflow models.
| Feature Identifier | Physical Construct | Unit | Temporal Semantics | Completeness |
|---|---|---|---|---|
mean_annual_ppt_mm |
Mean Annual Precipitation (\(P\)) | mm/yr | Exact Qualifying Years | 100.0% |
mean_annual_pet_mm |
Potential Evapotranspiration (\(PET\)) | mm/yr | Exact Qualifying Years | 100.0% |
mean_annual_temperature_midpoint_degC |
Mean Annual Air Temperature (\(T\)) | °C | Exact Qualifying Years | 100.0% |
aridity_index |
Atmospheric Water Balance (\(P / PET\)) | dimensionless | Exact Qualifying Years | 100.0% |
climate_moisture_deficit_mm |
Evaporative Deficit (\(\max(0, PET - P)\)) | mm/yr | Exact Qualifying Years | 100.0% |
Catchment land cover exerts extensive, well-documented controls on fluvial biogeochemistry: 1. Forest Canopies and Organic Litter: Deep-rooted forest stands generate massive autumnal leaf and needle litter, enriching upper soil horizons with organic compounds and sustaining high baseflow DOC export. 2. Agricultural Transformation (Cropland): Intensive tilling, tile drainage, and nitrogen fertilization enhance organic matter mineralization, reduce soil residence times, and shift stream chemistry toward inorganic nitrogen and lower molecular weight, microbial-like carbon. 3. Urbanization and Impervious Surfaces: Paved catchments produce flash hydrology, dilute baseflow carbon, and introduce petroleum-derived hydrocarbons or wastewater signals. 4. Alpine and High-Latitude Bare Cover: Bare rock, alpine scree, and permanent snow/ice yield dilute, ultra-oligotrophic surface waters with near-zero organic matter.
To test whether hydrochemistry reflects wetlands specifically, rather than general landscape vegetation or human modification, terrestrial land cover must be comprehensively controlled.
A fatal methodological flaw in many macro-scale ecological studies is the inclusion of land-cover “wetland” or “water” classes as independent variables when predicting wetland targets. * The Circularity Trap: If Copernicus land cover class 90 (“Herbaceous Wetland”) were included as a predictor of \(W01\) (Total Wetland Fraction), the statistical model would achieve artificially inflated predictive skill simply by cross-checking one remote-sensing product against another, masking the hydrochemical signal entirely. * The Terrestrial Normalization Protocol: All Copernicus wetland, marsh, mangrove, and open water pixels were completely removed prior to feature extraction. * The Non-Wetland Simplex Denominator: The remaining terrestrial classes were normalized strictly over the non-wetland terrestrial area: \[B03Fk = \frac{A_{\text{terrestrial family } k}}{A_{\text{total terrestrial non-wetland}}} = \frac{A_{\text{terrestrial family } k}}{\sum_{j=1}^7 A_{\text{terrestrial family } j}}\]
The raw Copernicus land cover classes were aggregated into 7 mutually exclusive, collectively exhaustive functional terrestrial classes:
| Class Code | Terrestrial Class Name | Constituent Copernicus Classes | Primary Biogeochemical Role |
|---|---|---|---|
B03F1 |
Forest & Woodland | Closed and open needleleaf, broadleaf, and mixed forests | Dominant natural source of terrestrial organic litterfall and humic soils |
B03F2 |
Shrubland | Woody shrubs, heathlands, arctic dwarf birch/willow | High-latitude tundra soil protection, moderate carbon export |
B03F3 |
Grassland | Natural grasslands, prairies, steppe, savannah | Mineral soil stabilization, root exudates, low aromatic carbon |
B03F4 |
Cropland | Cultivated arable fields, orchards, irrigated agriculture | Soil aeration, tile-drain leaching, accelerated mineralization |
B03F5 |
Urban / Built-Up | Residential, industrial, commercial, transport surfaces | Impervious flash runoff, dilution, anthropogenic contamination |
B03F6 |
Bare / Sparse | Bare rock, gravel bars, sand dunes, sparse alpine moss | Dilute, ultra-low carbon export, rapid mechanical erosion |
B03F7 |
Snow & Ice | Glaciers, ice caps, permanent firn snowfields | Glacial meltwater, ancient sub-ice carbon, high dilution |
Because these 7 features represent relative fractions of the terrestrial catchment, they satisfy the closed simplex constraint: \[\sum_{k=1}^7 B03Fk = 1.0 \quad \text{and} \quad B03Fk \ge 0 \quad \forall k\] > Mathematical Constraint: The 7 features are linearly dependent (the “constant sum constraint”). They cannot be entered simultaneously into an unpenalized ordinary least squares (OLS) linear model with an intercept without inducing singular matrix inversion. In linear models, one category must be omitted as a reference, or Isometric Log-Ratio (ILR) coordinates must be used. Tree-based nonlinear ensembles (such as Extra Trees) handle the raw simplex coordinates natively without singularity.
The Copernicus Global Land Cover time series spans calendar years 1992 through 2022. However, GEMStat water quality monitoring records extend through 2023.
To prevent temporal mismatch errors while maximizing sample
retention, Stage OP000G formulated a
dual-realization framework:
TEMPORAL REALIZATION FRAMEWORK
Carbon Monitoring: 1990 ... 1992 ══════════════════════════ 2022 2023
Copernicus Series: 1992 ══════════════════════════ 2022 [ None ]
▲ ▲ ▲
│ │ │
1. EXACT_YEAR Realization: [ Missing ] └──────── Exact Synchrony ───────┘ [ Missing ]
(3,679 Complete in DOC) (Pre-1992) (1,179 Records)
2. 2023_FROM_2022 View: [ Missing ] └──────── Exact Synchrony ───────┘ ── Proxied ──┘
(4,476 Complete in DOC) (Pre-1992) (from 2022)EXACT_YEAR (Primary Conservative
View)SENSITIVITY_2023_FROM_2022
(Secondary Sensitivity View)| Monitoring Tier | Analyte | Realization | Total Rows | Complete B03 Context | Incomplete B03 Context | Completeness Rate (%) |
|---|---|---|---|---|---|---|
| \(Y2\) | DOC | EXACT_YEAR |
4,948 | 3,961 | 987 | 80.05% |
| \(Y2\) | DOC | 2023_FROM_2022 |
4,948 | 4,900 | 48 | 99.03% |
| \(Y3\) (Primary) | DOC | EXACT_YEAR |
4,523 | 3,679 | 844 | 81.34% |
| \(Y3\) (Primary) | DOC | 2023_FROM_2022 |
4,523 | 4,476 | 47 | 98.96% |
| \(Y3\) (Primary) | TOC | EXACT_YEAR |
2,715 | 2,270 | 445 | 83.61% |
| \(Y3\) (Primary) | TOC | 2023_FROM_2022 |
2,715 | 2,652 | 63 | 97.68% |
| \(Y4\) | DOC | EXACT_YEAR |
4,134 | 3,450 | 684 | 83.45% |
| \(Y4\) | DOC | 2023_FROM_2022 |
4,134 | 4,088 | 46 | 98.89% |
B04-000)During exploratory stages (RP004 / B07),
global gridded Soil Organic Carbon (SOC) stock maps were evaluated and
formally excluded from the primary predictor set due to three
insurmountable methodological liabilities: 1. Severe Depth
Uncertainty: Gridded global SOC maps rely heavily on
pedotransfer functions and modeled bulk density estimates that exhibit
extreme error margins in waterlogged or histic horizons. 2.
Physical Denominator Conflation: Total carbon stocks
integrate across the entire terrestrial profile (often down to 1 or 2
meters), whereas fluvial organic carbon mobilization is governed by
shallow, active surface runoff and near-surface saturated soil layers.
3. Collinearity and Circularity with Wetland Targets:
Mapped SOC hotspots almost perfectly coincide with histosols, bogs, and
fens, creating direct circular dependencies with the wetland target
variables (\(W01, W02\)).
A total omission of all soil properties was challenged: Does the
valid rejection of SOC stocks justify omitting mineral soil context
altogether? Under authorized reassessment in B04-000,
candidate soil properties from ISRIC SoilGrids 250m
v2.0 were re-evaluated:
| Candidate Property | Physical Construct | Prospective Evaluation | Final Disposition in B04 |
|---|---|---|---|
clay |
Mineral soil texture fraction (\(\text{g/kg}\)) | Controls hydraulic conductivity, infiltration, and mineral sorption of DOC | Advanced to Prospective Pilot |
phh2o |
Soil reaction in water suspension (\(\text{pH} \times 10\)) | Governs humic acid dissociation, microbial mineralization, and flocculation | Advanced to Prospective Pilot |
cec |
Cation exchange capacity (\(\text{mmol(c)/kg}\)) | Geochemical buffer capacity and cation bridging | Placed in reserve (secondary priority) |
soc |
Soil organic carbon concentration (\(\text{dg/kg}\)) | Terrestrial organic carbon pool | Excluded (retains prior RP004 rejection) |
ocs |
Organic carbon stock (\(\text{t/ha}\)) | Integrated areal carbon stock | Excluded (retains prior RP004 rejection) |
B04-001)SoilGrids 250m v2.0 provides continuous predictions across 6 standard depth layers: \(0\text{--}5\), \(5\text{--}15\), \(15\text{--}30\), \(30\text{--}60\), \(60\text{--}100\), and \(100\text{--}200\text{ cm}\).
To avoid overfitting while capturing vertical differentiation, two fixed aggregation intervals were prospectively locked: 1. Topsoil Primary Context (\(0\text{--}30\text{ cm}\)): \[\Delta z_1 = 5\text{ cm},\quad \Delta z_2 = 10\text{ cm},\quad \Delta z_3 = 15\text{ cm} \quad (\text{Total } H_1 = 30\text{ cm})\] 2. Subsoil Sensitivity Context (\(30\text{--}100\text{ cm}\)): \[\Delta z_4 = 30\text{ cm},\quad \Delta z_5 = 40\text{ cm} \quad (\text{Total } H_2 = 70\text{ cm})\]
For a catchment composed of valid spatial cells \(\Omega_{\text{common}}\), the catchment-aggregated soil property \(\bar{S}\) across depth interval \(H\) is defined as: \[\bar{S}_{\text{catchment}} = \frac{\sum_{i \in \Omega_{\text{common}}} A_i \sum_{k \in H} \Delta z_k \, s_{i,k}}{\sum_{i \in \Omega_{\text{common}}} A_i \sum_{k \in H} \Delta z_k} = \frac{\sum_{i \in \Omega_{\text{common}}} A_i \, \bar{s}_i}{\sum_{i \in \Omega_{\text{common}}} A_i}\] where: - \(s_{i,k}\) is the SoilGrids mean prediction at cell \(i\) for depth layer \(k\). - \(\Delta z_k\) is the vertical thickness of layer \(k\). - \(A_i\) is the exact WGS84 geodesic area of cell \(i\) (\(\text{m}^2\)). - \(\Omega_{\text{common}}\) is the set of cells satisfying the common valid horizontal support rule.
A critical methodological safeguard of B04 was the prohibition of
arbitrary imputation: * Rule: A cell \(i\) belongs to \(\Omega_{\text{common}}\) if and only if
every constituent layer \(k
\in H\) contains a valid, non-null, unmasked raster value. *
No Missing-Depth Fill: If a pixel has valid data at
\(0\text{--}5\text{ cm}\) but is null
at \(15\text{--}30\text{ cm}\) (e.g.,
shallow bedrock or water mask), that pixel is excluded entirely from the
\(0\text{--}30\text{ cm}\) aggregation.
* No Renormalization: The aggregated denominator is
strictly the area of \(\Omega_{\text{common}}\), not the total
catchment envelope. * Explicit Support Diagnostics: The
common support fraction is explicitly recorded: \[\Phi_{\text{support}} = \frac{\sum_{i \in
\Omega_{\text{common}}} A_i}{A_{\text{catchment}}}\] If \(\Phi_{\text{support}} = 0\), the descriptor
is assigned explicit NA (no zero imputation).
SoilGrids provides 5th (\(Q_{0.05}\)) and 95th (\(Q_{0.95}\)) quantile layers representing the ISRIC model’s prediction distribution. B04 prospectively aggregated this diagnostic spread: \[\Delta Q_{\text{catchment}} = \frac{\sum_{i \in \Omega_{\text{common}}} A_i \sum_{k \in H} \Delta z_k \, (Q_{0.95, i, k} - Q_{0.05, i, k})}{\sum_{i \in \Omega_{\text{common}}} A_i \sum_{k \in H} \Delta z_k}\] > Authoritative Constraint: \(\Delta Q_{\text{catchment}}\) was formally cataloged as a spatial mapping diagnostic width, explicitly forbidden from being interpreted as a statistical confidence interval for the catchment mean.
B04-002 / B04-003A)B04-002A &
B04-002B)A deterministic, metadata-only cohort of 10 catchments comprising 34
incremental MERIT Hydro components was frozen prior to accessing raster
arrays: * Data Lock (B04-002A): 30 global
SoilGrids VRTs were verified against published ISRIC SHA256 checksums.
360 intersecting native GeoTIFFs (250m) were downloaded and
cryptographically hashed. * Pilot Execution
(B04-002B): 10/10 catchments, 34/34 components,
and 40/40 property-band combinations executed successfully with zero
runtime failures. * Empirical Results: - Direct
hierarchy rollups matched component direct sums to \(< 10^{-12}\) relative difference. -
Observed common support fractions \(\Phi_{\text{support}}\) ranged from
\(0.643026\) to \(1.000000\) (median \(0.943313\)), demonstrating robust
horizontal coverage. * Identified Bottleneck: The pilot
required \(7,464\text{
seconds}\) (~2.07 hours) for only 10 catchments, with
\(>95\%\) of runtime consumed by
boundary polygon geometric rasterization.
B04-003A)To render population processing feasible, an optimized vector-raster intersection engine was designed and benchmarked directly against the pilot reference: * Algorithmic Enhancement: Streamlined boundary clipping and vectorized spatial masking within local affine windows. * Equivalence Verification: Tested across all 34 incremental components: - Exact reproduction of component geometries: 34/34 PASS (area difference \(< 10^{-7}\)). - Exact reproduction of final descriptors: 40/40 PASS within frozen numerical tolerances (\(\Delta_{\text{clay}} < 10^{-6}\text{ g/kg}\), \(\Delta_{\text{pH}} < 10^{-6}\)). * Observed Performance Gain: Runtime dropped from \(7,464\text{ s}\) to \(54.08\text{ s}\), achieving a \(138.04\times\) speedup without compromising mathematical fidelity.
B04-003B–003D)B04-003B)Extending the fast engine to all 5,556 catchments revealed
fundamental spatial edge cases in the native SoilGrids projection
(Interrupted Goode Homolosine, EPSG:152160 / ESRI:54052): 1.
Projection Discontinuity & Boundary Shearing:
Catchments crossing Goode Homolosine projection cut lines produced
topologically invalid multi-polygons when projected as a monolithic
WGS84 shape. 2. The Piecewise Formulation: The protocol
was amended to project each authoritative MERIT scientific-mask piece
independently into SoilGrids Homolosine space before forming their
polygonal union. This resolved all 5,556 geometry footprints with zero
topological errors. 3. Footprint Census Output: -
clay requirement: 1,418 native GeoTIFF tiles per depth
layer. - phh2o requirement: 875 native GeoTIFF tiles per
depth layer. - Total global payload: 34,395 native GeoTIFF
tiles across 30 layers.
B04-003C & B04-003D)B04_003D_POPULATION_SOURCE_LOCK_MANIFEST.csv (34,395
rows):SHA256: f1c819768dae8524aba4cb924daba4167432a9d6ef98bec2be55e18f2741fb8dB04_003D_POPULATION_BOUNDED_VRT_MANIFEST.csv (30
rows):SHA256: 0b6343f333bf55e5776316cac7ac83de42a596f774a662a57a9262132168817fB04-004)Prior to launching population extraction, the production pipeline was gated against the 34 pilot components across 4 property bands (\(34 \times 4 = 136\) comparisons): * Result: 136/136 PASS (Zero divergence in cell counts, weighted means, or diagnostic widths).
When executed on the global population queue, the exact-overlap algorithm hit a severe computational scaling barrier on high-order drainage basins:
| Metric | Order-24 Benchmark Component
(MERITC_n15e080_r02793_c01054) |
|---|---|
| Drainage Basin Region | Lower Ganges–Brahmaputra / Deltaic System |
| Incremental Drainage Area | \(\approx 269,894.4\text{ km}^2\) |
| Native MERIT Hydro Grid Cells | \(33,496,762\text{ cells}\) |
| SoilGrids 250m Bounding Grid Cells | \(\approx 8,770,000\text{ cells}\) |
| Boundary Polygon Vertices | \(> 180,000\text{ vertices}\) |
| Observed Processing Time | \(> 8.5\text{ hours}\) for a single component (projected weeks for global queue) |
To overcome this wall, several engineering approximations were evaluated and rejected: 1. Rejection of Constant Projected Cell Area (62,500 m²): Approximating all cells as \(250\text{ m} \times 250\text{ m}\) was firmly rejected because projection distortions in Homolosine space introduced systematic latitude-dependent area errors that violated frozen conservation tolerances. 2. Rejection of Boundary-Raster Shortcuts: Faster pixel approximations missed cells straddling the true vector perimeter, violating the zero-tolerance geometric rule. 3. The Disproportionate Frontier: Maintaining the exact-overlap scientific standard for giant multi-million-cell catchments would require weeks of specialized high-performance parallel computing, disproportionate to an auxiliary context block within a master’s thesis.
The integration pipeline strictly decouples general catchment environmental context registries from analyte-specific chemistry matrices. This architecture ensures that landscape context is evaluated across the entire monitoring network without forcing premature drops due to missing water quality grabs.
These tables integrate Terrain (B01), Hydroclimate (B02), and Land Cover (B03) across all temporal tiers (\(Y2, Y3, Y4\)) and both land-cover realizations:
| Table File Name | Tier | Realization | Retained Rows | \(B03\) Complete | \(B03\) Incomplete | Unique Catchments |
|---|---|---|---|---|---|---|
OP002_CONTEXT_Y2_EXACT_YEAR.csv |
Y2 | EXACT_YEAR | 8,031 | 6,567 | 1,464 | 4,895 (DOC) / 3,034 (TOC) |
OP002_CONTEXT_Y2_SENSITIVITY_2023_FROM_2022.csv |
Y2 | 2023_FROM_2022 | 8,031 | 7,911 | 120 | 4,895 (DOC) / 3,034 (TOC) |
OP002_CONTEXT_Y3_EXACT_YEAR.csv |
Y3 | EXACT_YEAR | 7,238 | 5,949 | 1,289 | 4,477 (DOC) / 2,674 (TOC) |
OP002_CONTEXT_Y3_SENSITIVITY_2023_FROM_2022.csv |
Y3 | 2023_FROM_2022 | 7,238 | 7,128 | 110 | 4,477 (DOC) / 2,674 (TOC) |
OP002_CONTEXT_Y4_EXACT_YEAR.csv |
Y4 | EXACT_YEAR | 6,487 | 5,464 | 1,023 | 4,097 (DOC) / 2,318 (TOC) |
OP002_CONTEXT_Y4_SENSITIVITY_2023_FROM_2022.csv |
Y4 | 2023_FROM_2022 | 6,487 | 6,380 | 107 | 4,097 (DOC) / 2,318 (TOC) |
For the primary 3-year support tier (\(Y3\)), the frozen hydrochemistry branches from HP007 are merged directly with the matching catchment context:
| Table File Name | Analyte | Realization | Retained Rows | Complete Context | Non-Point Carbon | Missing In-Situ pH | Missing In-Situ Temp | Confirmed Spatial Mismatch |
|---|---|---|---|---|---|---|---|---|
OP002_DOC_Y3_CHEMISTRY_CONTEXT_EXACT_YEAR.csv |
DOC | EXACT_YEAR | 4,523 | 3,679 | 24 | 153 | 344 | 2 |
OP002_DOC_Y3_CHEMISTRY_CONTEXT_SENSITIVITY_2023_FROM_2022.csv |
DOC | 2023_FROM_2022 | 4,523 | 4,476 | 24 | 153 | 344 | 2 |
OP002_TOC_Y3_CHEMISTRY_CONTEXT_EXACT_YEAR.csv |
TOC | EXACT_YEAR | 2,715 | 2,270 | 2 | 47 | 98 | 2 |
OP002_TOC_Y3_CHEMISTRY_CONTEXT_SENSITIVITY_2023_FROM_2022.csv |
TOC | 2023_FROM_2022 | 2,715 | 2,652 | 2 | 47 | 98 | 2 |
INTEGRATED_FIELD_ROLES.csv)The integrated tables contain 152 distinct columns.
To prevent information leakage and invalid model training, every column
is assigned an immutable functional role in INTEGRATED_FIELD_ROLES.csv:
152 SCHEMA COLUMNS TAXONOMY
┌─────────────────────────────────────────────────────────────────────────────────────────────────┐
│ 1. Identifiers & Grouping (Not Features) │
│ - station_id, catchment_id, parameter, country │
├─────────────────────────────────────────────────────────────────────────────────────────────────┤
│ 2. Core Context Predictors (Candidate Features X_core) │
│ - Terrain: full_catchment_area_km2, mean_full_catchment_slope_degrees, │
│ full_catchment_elevation_range_m │
│ - Hydroclimate: mean_annual_ppt_mm, mean_annual_pet_mm, │
│ mean_annual_temperature_midpoint_degC │
│ - Land Cover: B03F1 to B03F7 (Raw compositional fractions; simplex sum = 1.0) │
├─────────────────────────────────────────────────────────────────────────────────────────────────┤
│ 3. Core Hydrochemistry Predictors (Candidate Features X_chem) │
│ - Carbon Scenarios: DOC/TOC lower & upper endpoint scenarios (mg/L) │
│ - In-Situ Physico-Chemical: pH_canonical_point_value, TEMP_canonical_point_value │
│ - Secondary Sensitivity: Fe_Tot & Fe_Dis lower/upper endpoints │
├─────────────────────────────────────────────────────────────────────────────────────────────────┤
│ 4. Provenance & QC Metadata (STRICTLY FORBIDDEN AS MODEL PREDICTORS) │
│ - Temporal Support: B02_qualifying_years, B03_target_years, DOC_numeric_years │
│ - Reliability Flags: DOC_censor_affected, DOC_absolute_identification_interval_width │
│ - Spatial QC Flags: spatial_qc_confirmed_catchment_mismatch, spatial_qc_v023w_reviewed │
│ - Completeness Indicators: B01_complete, B02_complete, B03_complete │
└─────────────────────────────────────────────────────────────────────────────────────────────────┘target_derived = False for all 152 columns. No predictor
contains or approximates \(W01\), \(W02\), or \(W03\).global_pre_imputation_allowed = False for every single
feature. Missing in-situ pH (\(n=153\)
in DOC) and temperature (\(n=344\) in
DOC) remain as raw NA. Any imputation must take place
strictly inside cross-validation training folds during modelling to
prevent leakage.DOC_lower_endpoint_scenario_mg_l and
DOC_upper_endpoint_scenario_mg_l) represent alternative
data scenarios, never simultaneous independent
variables.OP003)Stage OP003 completed the definitive synthesis of all 12
candidate environmental and anthropic domains considered throughout the
thesis lifecycle (CURRENT_PREDICTOR_FAMILY_DISPOSITIONS.csv):
| Family Code | Construct / Domain | Final Status | Methodological Basis & Boundary |
|---|---|---|---|
HP007 |
Hydrochemistry | ADOPTED (Core) | DOC/TOC kept separate; stream pH & temperature primary; Fe secondary; endpoints evaluated as alternative bounding scenarios. |
B01 |
Terrain Structure | ADOPTED (Core) | Catchment area, mean slope, elevation range from MERIT Hydro. |
B02 |
Hydroclimate | ADOPTED (Core) | CHELSA precipitation, PET, temperature aligned to exact analyte-specific sampling years. |
B03 |
Non-Wetland Land Cover | ADOPTED (Core) | Raw 7-family terrestrial composition; exact-year primary view with 2023-from-2022 sensitivity. |
B04_CURRENT |
Soil Context (Clay & pH) | NOT ADOPTED | Closed on computational scaling limits on mega-basins; 34,395 GeoTIFFs preserved as negative evidence. |
B05_LEGACY |
Mapped Wetland Composition | TRANSFERRED TO TARGET | Lineage fulfilled by \(W02\) (7-family simplex target)
under WT003/WT007. Not a predictor of
itself! |
B04_LEGACY |
Mapped Wetland Extent | TRANSFERRED TO TARGET | Lineage fulfilled by \(W01\) (total wetland fraction target). Independent target variable. |
W03 |
Structural Connectivity | SECONDARY (Outside Core) | Downstream river distance & topological index; authoritative secondary descriptor, not an automatic \(W01/W02\) predictor. |
B07_LEGACY |
Soil Organic Carbon Stocks | NOT ADOPTED | Prohibitive bulk-density uncertainty, deep-profile extrapolation errors, and circularity with peatland extent. |
B08_LEGACY |
Wastewater / HydroWASTE | DEFERRED / UNADOPTED | Requires rigorous point-source routing and temporal matching; zero effluent cannot be proven from urban proxies. |
B09_W04 |
Drainage & Rewetting | NO GENERAL PRODUCT | Lack of globally consistent historical drainage/rewetting inventories; proxies rejected to avoid bias. |
OTHER |
Lakes & Human Footprint | DECLARED LIMITATIONS | Upstream impoundments and fine-scale human infrastructure cataloged as explicit thesis boundary limitations. |
Because Copernicus Global Land Cover terminates in 2022 while GEMStat water quality monitoring extends through 2023, two parallel land-cover realizations were engineered:
TEMPORAL REALIZATION DESIGN
Carbon Monitoring Years: 1990 ... 1992 ══════════════════════════ 2022 2023
Copernicus Land Cover: 1992 ══════════════════════════ 2022 [None]
▲ ▲ ▲
│ │ │
1. EXACT_YEAR Realization: [ Missing ] └──────── Exact Synchrony ───────┘ [ Missing ]
(3,679 DOC Complete) (Pre-1992) (1,179 Records)
2. 2023_FROM_2022 Realization: [ Missing ] └──────── Exact Synchrony ───────┘ ── Proxied ──┘
(4,476 DOC Complete) (Pre-1992) (from 2022)EXACT_YEAR (Primary Conservative
View):
SENSITIVITY_2023_FROM_2022 (Secondary
Sensitivity View):
Two catchments in the primary cohort have confirmed
coordinate/catchment mismatches in GEMStat metadata: - Identified by
spatial_qc_confirmed_catchment_mismatch = True. - Rather
than silently deleting them, they are tagged to allow seamless
sensitivity testing between the full 4,523-row population and the
4,521-row high-stringency spatial cohort.
AM001)Stage AM001 merged the frozen OP002
predictor tables with independent wetland targets from
WT006/WT007 using verified spatial catchment
identifiers.
The linkage preserved every original predictor string, carbon censor scenario, and target response:
| Analyte Branch | Retained Records | Unique Catchments | Valid \(W01\) Targets | \(W01 = 0\) Catchments | Defined \(W02\) Targets | Undefined \(W02\) Records | Monitored Hierarchy Groups | Largest Group |
|---|---|---|---|---|---|---|---|---|
| DOC | 4,523 | 4,477 | 4,523 (\(100\%\)) | 79 | 4,444 | 79 | 672 | 311 catchments |
| TOC | 2,715 | 2,674 | 2,715 (\(100\%\)) | 45 | 2,670 | 45 | 484 | 273 catchments |
A foundational mathematical safeguard in AM001 governs
wetland composition (\(W02\)): * \(W02\) represents the 7-family simplex
shares of total wetland area: \[W02_k =
\frac{\text{Area of Wetland Family } k}{\text{Total Mapped Wetland Area
} (W01)}\] * In catchments where total wetland extent is zero
(\(W01 = 0\)), the compositional
denominator is zero. * Methodological Mandate: In these
catchments (\(n=79\) in DOC; \(n=45\) in TOC), \(W02\) is strictly
undefined, not a vector of seven zeros (\(\mathbf{0} \notin S^6\)). These records are
retained for \(W01\) modeling but
excluded from \(W02\) compositional
evaluation.
During target linkage, a single frozen riverine wetland share had an
exact value of \(1.0000000000000002\)
(\(2.22 \times 10^{-16}\) above unity
due to floating-point summation). Rather than artificially clipping or
renormalizing the target vector, AM001 preserved this exact
value under the preregistered \(10^{-12}\) QA numerical tolerance (AM001_SOURCE_FLOATING_POINT_BOUNDARY_ROUNDOFF.csv),
maintaining bit-for-bit audit integrity.
AM002A)The central scientific question of the thesis is: Does surface water hydrochemistry provide distinct, incremental predictive power for upstream wetland characteristics beyond static environmental context?
To test this rigorously without confounding population size with
predictive skill, AM002A preregistered a matched, three-way
paired comparison protocol.
THE THREE PAIRED FEATURE VIEWS
┌────────────────────────────────────────────────────────────────────────────────────────┐
│ 1. Chemistry-Only View (X_chem, 3 Core Features): │
│ - Carbon Scenario (DOC or TOC lower/upper endpoint, mg/L) │
│ - In-Situ Stream pH (canonical point value) │
│ - In-Situ Stream Water Temperature (°C) │
├────────────────────────────────────────────────────────────────────────────────────────┤
│ 2. Context-Only View (X_context, 13 Core Features): │
│ - Terrain (B01): Catchment Area, Mean Slope, Elevation Range │
│ - Hydroclimate (B02): Precipitation, PET, Air Temperature │
│ - Land Cover (B03): 7 Terrestrial Simplex Shares (B03F1 to B03F7) │
├────────────────────────────────────────────────────────────────────────────────────────┤
│ 3. Combined View (X_comb, 16 Core Features): │
│ - [ X_chem + X_context ] (Full Feature Union) │
└────────────────────────────────────────────────────────────────────────────────────────┘All three models are fitted and evaluated on identical, matched sample records: \[\Delta \text{Loss} = \text{Loss}_{\text{Context}} - \text{Loss}_{\text{Combined}}\] * If \(\Delta \text{Loss} > 0\): Hydrochemistry provides true incremental information that cannot be explained away by topography, climate, or upland land cover. * If \(\Delta \text{Loss} \le 0\): Hydrochemistry is redundant once landscape context is known.
| Analyte Branch | Population Scope | Target | Paired Analysis Records | Unique Catchments | Retained Unimputed pH | Retained Unimputed Temp |
|---|---|---|---|---|---|---|
| DOC | Primary Exact-Year | \(W01\) | 3,679 | 3,637 | 101 missing | 120 missing |
| DOC | Primary Exact-Year | \(W02\) | 3,611 | 3,574 | 99 missing | 118 missing |
| DOC | Expanded 2023 Sensitivity | \(W01\) | 4,476 | 4,430 | 138 missing | 302 missing |
| DOC | Expanded 2023 Sensitivity | \(W02\) | 4,397 | 4,356 | 136 missing | 298 missing |
| TOC | Primary Exact-Year | \(W01\) | 2,270 | 2,231 | 23 missing | 37 missing |
| TOC | Primary Exact-Year | \(W02\) | 2,225 | 2,191 | 23 missing | 37 missing |
| TOC | Expanded 2023 Sensitivity | \(W01\) | 2,652 | 2,611 | 23 missing | 48 missing |
| TOC | Expanded 2023 Sensitivity | \(W02\) | 2,607 | 2,571 | 23 missing | 48 missing |
In global water quality monitoring, multiple monitoring stations frequently sample the same catchment outlet or share nested drainage segments. If uncorrected, heavily monitored catchments would dominate model fitting and evaluation scores. * Weighting Rule: Every retained catchment receives an exact total weight of \(1.0\): \[w_i = \frac{1}{N_{\text{stations}}(c(i))}\] where \(N_{\text{stations}}(c(i))\) is the number of stations sharing catchment \(c(i)\). * These weights are applied consistently during model fitting and out-of-fold evaluation scoring.
AM002B)In catchment science, standard random K-fold cross-validation is methodologically flawed: 1. Spatial Autocorrelation: Stations close to one another share climatic and geomorphic conditions, leading to severe information leakage and artificially optimistic test scores (Roberts et al. 2017). 2. Nested Hydrological Topologies: Upstream headwater stations drain directly into downstream monitoring stations. Random splitting places the headwater in training and the outlet in testing, leaking direct mass-balance transport.
To ensure genuine spatial extrapolation, AM002B
preregistered a 5-fold geographic holdout design
derived from spherical K-means clustering on the 937 monitored hierarchy
groups: * Indivisible Graph Units: Sibling tributaries
and downstream mainstems belonging to the same drainage hierarchy are
never split across folds.
THE 100 KM OUTLET BUFFER GUARD
┌─────────────────────────────────────────────────────────────────────────────────┐
│ │
│ TEST FOLD REGION TRAINING REGION │
│ (Held-Out Geometry) (Candidate Training Catchments)│
│ │
│ [Test Group] [Training Group] │
│ (•) ─── 100 km Spatial Buffer ─── (•) (Valid Train) │
│ \ / │
│ \ [PURGE ZONE] / │
│ \ (•) / │
│ ─── [PURGED] ────── │
│ (Training Group within │
│ 100 km of Test Group) │
│ │
└─────────────────────────────────────────────────────────────────────────────────┘For every held-out test region, an outlet-to-outlet geodesic buffer distance of \(100\text{ km}\) is applied across all 5,556 global catchments: * Any training group whose outlet lies within \(100\text{ km}\) of any test group outlet in that fold is completely purged from the training set. * This eliminates boundary leakage while preserving independent geographic extrapolation.
| Outer Fold | Geographic Region | Test Records | Test Groups | Train Records (0 km Buffer) | Train Records (100 km Buffer) | Purged Training Records | Min Outlet Distance (km) |
|---|---|---|---|---|---|---|---|
| F1 | Northern Europe / Baltic | 139 | 49 | 3,540 | 3,482 | 58 | 208.9 km |
| F2 | Western Europe (France Core) | 1,740 | 169 | 1,939 | 1,923 | 16 | 192.2 km |
| F3 | Eastern Europe / Central Asia | 87 | 38 | 3,592 | 3,592 | 0 | 268.9 km |
| F4 | North America (Mexico Core) | 1,695 | 250 | 1,984 | 1,984 | 0 | 368.9 km |
| F5 | East Asia / Pacific Margin | 18 | 11 | 3,661 | 3,657 | 4 | 471.5 km |
Critical Methodological Transparency: The fold sample sizes are strongly uneven (\(F2\) and \(F4\) contain large national networks; \(F5\) has 18 records).
AM002Bexplicitly notes that this reflects real-world global monitoring infrastructure. Results are evaluated across pooled out-of-fold predictions and reported by region, avoiding claims of uniform Northern Hemisphere representation.
To eliminate the danger of \(p\)-hacking, hyperparameter overfitting, or
post-hoc model tuning on sparse geographic folds (where some inner folds
have \(N = 86\)), AM002B
preregistered three fixed model families with zero empirical
hyperparameter search:
DecisionTreeRegressor(max_depth=3, min_samples_leaf=5).ExtraTreesRegressor(n_estimators=256, max_depth=12, min_samples_leaf=5, bootstrap=False, max_features=1.0).bootstrap=False ensures
that every training observation participates with its exact analytical
catchment weight.A major technical innovation in AM002B is the rejection
of separate 1-dimensional regressions for each wetland family. *
Native Multi-Output Regression: A single Extra Trees
model is fitted simultaneously on the 7-dimensional simplex response
\(\mathbf{y} \in \mathbb{R}^7\). *
Convex Combination Preservation: Because tree leaf
predictions are positive weighted averages of training response vectors,
and all training vectors lie on the simplex (\(\sum y_k = 1.0, y_k \ge 0\)), their convex
combination mathematically guarantees: \[\hat{\mathbf{y}}_{\text{leaf}} = \sum_{j \in
\text{leaf}} \alpha_j \mathbf{y}_j \implies \sum_{k=1}^7 \hat{y}_k = 1.0
\quad \text{and} \quad \hat{y}_k \ge 0\] * Predictions satisfy
simplex constraints natively to within \(10^{-10}\) numerical precision without
artificial post-hoc normalization or clipping!
AM003) & External
SealingPrior to launching full primary fitting across all 20 outer splits,
AM003 defines a two-cell operational pilot: 1.
DOC / W02 / F5: Tests large training (\(N=3,589\)) with sparse test (\(N=18\)). 2. TOC / W02 / F2:
Tests small training (\(N=520\)) with
large test (\(N=1,693\)). *
Bounds: Capped at 20 model fits and 10 minutes runtime.
* Full primary execution is capped at 200 model fits and a 1-hour
wall-clock budget.
Throughout all stages of AM001, AM002A, and
AM002B, the high-density independent validation dataset in
Lower Saxony (Germany) remains 100% sealed and
untouched under 02_Methodology/07_Validation/. No
Lower Saxony coordinates, station data, or wetland targets were accessed
or used in model formulation.
| Symbol | Mathematical Construct | Physical Definition & Units |
|---|---|---|
| \(W01\) | Total Catchment Wetland Fraction | Areal proportion of catchment covered by mapped wetlands (\([0, 1]\)) |
| \(W02\) | Wetland Compositional Vector | 7-family compositional simplex vector (\(\mathbf{y} \in S^6 \subset \mathbb{R}^7, \sum_{k=1}^7 y_k = 1.0\)) |
| \(W03\) | Structural Wetland Connectivity | Secondary downstream flowpath distance (\(D_{\text{down}}\), km) and topological travel index |
| \(S^6\) | 6-Dimensional Simplex | The closed geometric manifold \(\left\{ \mathbf{y} \in \mathbb{R}^7 \;\middle|\; \sum_{k=1}^7 y_k = 1.0, \; y_k \ge 0 \right\}\) |
| \(\text{DOC}\) | Dissolved Organic Carbon | Membrane-filtered organic carbon concentration (\(< 0.45\,\mu\text{m}\), \(\text{mg C/L}\)) |
| \(\text{TOC}\) | Total Organic Carbon | Unfiltered organic carbon concentration (\(\text{DOC} + \text{POC}\), \(\text{mg C/L}\)) |
| \(C_{\text{lower}}\) | Lower-Endpoint Carbon Scenario | Station median concentration treating left-censored grabs as \(0\,\text{mg/L}\) |
| \(C_{\text{upper}}\) | Upper-Endpoint Carbon Scenario | Station median concentration treating left-censored grabs as \(\text{DL}\,\text{mg/L}\) |
| \(A\) | Drainage Basin Area | Exact WGS84 ellipsoidal geodesic catchment surface area (\(\text{km}^2\)) |
| \(S\) | Catchment Mean Slope | Geodesic-area weighted terrain slope in degrees (\(^\circ\)) from 3-arcsecond DEM |
| \(\Delta E\) | Elevation Range | Macro-geomorphic relief: \(\max_{i \in \Omega} E_i - \min_{i \in \Omega} E_i\) (meters) |
| \(P\) | Mean Annual Precipitation | Catchment-averaged annual precipitation depth from CHELSA V2.1 (mm/yr) |
| \(PET\) | Potential Evapotranspiration | Penman-Monteith atmospheric evaporative demand from CHELSA V2.1 (mm/yr) |
| \(AI\) | Aridity Index | Dimensionless atmospheric water balance ratio (\(P / PET\)) |
| \(CMD\) | Climate Moisture Deficit | Seasonal cumulative evaporative deficit: \(\max(0, PET - P)\) (mm/yr) |
| \(B03F1\text{--}F7\) | Terrestrial Land Cover Shares | Relative fractions of non-wetland terrestrial area summing to \(1.0\) (\(S^6\)) |
| \(\Phi_{\text{support}}\) | Common Valid Support Fraction | Proportion of catchment area with valid, non-null data across all constituent raster layers |
| \(w_i\) | Catchment Analytical Sample Weight | Equal-catchment weight: \(1 / N_{\text{stations}}(c(i))\), ensuring \(\sum_{i \in c} w_i = 1.0\) |
| \(\text{MAE}_{\text{weighted}}\) | Weighted Mean Absolute Error | Primary continuous loss metric for \(W01\): \(\frac{\sum w_i |y_i - \hat{y}_i|}{\sum w_i}\) |
| \(\text{TVD}_{\text{weighted}}\) | Weighted Total Variation Distance | Primary compositional loss metric for \(W02\): \(\frac{\sum w_i \cdot \frac{1}{2} \sum_{k=1}^7 |y_{i,k} - \hat{y}_{i,k}|}{\sum w_i}\) |
| \(\Delta \text{Loss}\) | Incremental Information Contrast | \(\text{Loss}(\mathbf{X}_{\text{context}}) - \text{Loss}(\mathbf{X}_{\text{combined}})\) |
| \(G = (V, E)\) | Catchment Hydrography Graph | Directed Acyclic Graph (DAG) with \(|V| = 5,556\) catchments and \(|E| = 4,619\) flow edges |
| \(\mathbf{X}_{\text{core}}\) | Core Predictor Matrix | Feature block \([\mathbf{X}_{\text{chem}}, \mathbf{X}_{\text{terrain}}, \mathbf{X}_{\text{climate}}, \mathbf{X}_{\text{landcover}}]\) |
This compendium represents the permanent, publication-grade methodological record of the Wetland_Thesis_2026 project.