Water-quality modelling case study · India

Yamuna at Delhi: BOD–DO compliance modelling under CPCB Class C

A screening-level 1D Streeter–Phelps model of the 22 km Wazirabad → Okhla reach, calibrated against CPCB station data 2018–2022, with parameter and forcing uncertainty propagated through a 2000-run Latin Hypercube Monte Carlo and translated into compliance probabilities under five management scenarios.

The question

Which combination of source treatment, drain interception and managed environmental flow can move the dry-season Yamuna at Delhi toward CPCB Class C compliance — and which of the two Class C standards (DO ≥ 4 mg/L, BOD ≤ 3 mg/L) is actually binding?

The 22 km Wazirabad → Okhla reach is one of the most-studied urban-river BOD–DO problems in South Asia. After upstream diversions the headwater flow drops to about 4 m³/s in the dry season, while the Najafgarh, Shahdara and Sahibabad drains collectively inject roughly 52 m³/s of high-BOD wastewater along the reach. CPCB monitors four stations along the reach monthly. The case study answers the question above as a screening-level analysis whose purpose is to inform whether a higher-complexity tool (QUAL2K, WASP) is justified before committing to capital investment.

Headline results

0.78
Pooled NSE (BOD)
0.95
Pooled NSE (DO)
+1.6%
Pooled PBIAS (BOD)
−0.9%
Pooled PBIAS (DO)
2,000
LHS Monte Carlo runs
5
Uncertain parameters

Management insight

  • Binding constraint: BOD, not DO. Joint Class C is effectively unreachable on this reach under the tested scenarios in the dry season.
  • Best near-term lever: drain treatment / STP upgrade. P(DO ≥ 4) rises from 4.8% to 81.5% at ~70% drain BOD removal alone.
  • Weak standalone lever: environmental-flow augmentation. ×3 Wazirabad release alone only moves P(DO ≥ 4) to ~8% — dry-season Qhead is an order of magnitude smaller than the combined drain inflow.

Methodology

A 1D steady-state Streeter–Phelps model of the reach, with explicit drain-mixing at three confluences, calibrated against 2018–2022 monthly medians at four CPCB stations (Palla, Nizamuddin, ITO Bridge, Okhla). Parameter and forcing uncertainty are propagated through a 2000-run Latin Hypercube Monte Carlo, and the outputs are translated into compliance probabilities for the two CPCB Class C standards.

Governing equations

(1) ∂L/∂x = −(kd / u)·L
(2) ∂O/∂x = (ka / u)·(Os − O) − (kd / u)·L
(3) ka,20 = 3.93·u0.5 / H1.5   (O’Connor–Dobbins reaeration)
(4) Os(T) = 14.652 − 0.41022·T + 0.00799·T² − 7.78×10−5·T³   (Benson–Krause)
(5) Cmix = (Qu·Cu + Qt·Ct) / (Qu + Qt)   (tributary mixing)
(6) P(comply) = (1/N) ∑ 𝟙{ DOi ≥ 4 ∩ BODi ≤ 3 },  N = 2000

Temperature corrections: kd(T) = kd,20·1.047(T−20); ka(T) = ka,20·1.024(T−20). Full equation set in the methods appendix.

Calibration

Pre- and post-monsoon BOD/DO are used in calibration; monsoon medians are held back as a validation case. The calibration is “Very Good” under Moriasi et al. (2007) at all four stations. Best-fit values from the 25×25 SSR grid: kd,20 = 0.46 1/d, ka multiplier = 1.10 (× O’Connor–Dobbins). On the four-station monsoon hold-out the model achieves a MAPE of ~9% for DO and ~44% for BOD — the DO hold-out is a genuine validation result; the BOD error is reported honestly because the steady-state model does not represent in-channel BOD storage or barrage-impoundment dynamics.

Uncertainty propagation

Five uncertain inputs are sampled by Latin Hypercube (2000 runs):

ParameterDistributionRange / parametersSource
Headwater Q (multiplier)Lognormalσ = 0.35CWC vs. CPCB Wazirabad release variance
kd,20Uniform0.20–0.55 1/dChapra 1997 urban-stream range, widened to bracket the calibrated optimum
ka (multiplier)Uniform0.7–1.4Wraps O’Connor–Dobbins, Owens–Gibbs, Churchill alternatives
Drain BOD (multiplier)Lognormalσ = 0.25CPCB drain-grab variability around reach medians
Drain Q (multiplier)Triangularmin 0.6, mode 1.0, max 1.3Diurnal + operational variability

Spearman rank correlations identify the drain BOD multiplier as the dominant uncertainty driver (ρ = +0.93 vs Okhla BOD): source-strength uncertainty dominates over kinetic uncertainty in the dry-season regime. Headwater Q sensitivity is essentially decoupled (|ρ| < 0.1).

Scenarios at Okhla (pre-monsoon)

Scenario Description Median BOD
(mg/L)
Median DO
(mg/L)
P(DO≥4) P(BOD≤3) P(joint)
S0Baseline (current operations)27.41.824.8%0%0%
S1Drain interception + STP retrofit (η ≈ 50%)13.83.9146.4%0%0%
S2Aggressive STP upgrade (η ≈ 70%)8.34.7781.5%0%0%
S3E-flow release at Wazirabad (×3)24.32.297.8%0%0%
S4S2 + S3 combined7.74.9186.9%0%0%

Median values are run-medians of the 2000-run Latin Hypercube Monte Carlo. P(DO ≥ 4) and P(BOD ≤ 3) are the marginal compliance probabilities; P(joint) is the probability of meeting both standards simultaneously. The marginals are shown separately so the binding standard (BOD) is visible scenario by scenario.

Key findings

Finding 1 — BOD compliance is effectively unreachable in the dry season

Even the combined scenario (S4: ~70% drain treatment plus a tripled Wazirabad release) leaves median Okhla BOD at about 7.7 mg/L, and the BOD-marginal compliance probability is below 1% across all five scenarios. Reaching 3 mg/L would likely require above 90% drain BOD removal, which is not credible at the combined loading scale of Najafgarh, Shahdara and Sahibabad without effectively diverting the entire dry-season municipal load.

Finding 2 — DO compliance is reachable, and the route is drain treatment

P(DO ≥ 4) at Okhla rises from 4.8% under the baseline to 81.5% under S2 (aggressive STP upgrade alone) and to 86.9% under S4 (S2 plus a tripled Wazirabad release). The flow-augmentation scenario alone (S3) only moves the probability to 7.8%. The reason BOD remains binding while DO improves is mechanical: DO has a second recovery route through reaeration, whereas BOD is purely load-driven and only responds to source removal.

Finding 3 — Drain BOD is the dominant uncertainty driver

Spearman rank correlations identify the drain BOD multiplier as the dominant driver of Okhla BOD (ρ = +0.93) and a major driver of Okhla DO (ρ = −0.56). Headwater Q is decoupled from the output under current dry-season operations (|ρ| < 0.1). Investment that reduces drain BOD will move Okhla BOD almost one-for-one in this regime; investment in any other lever will not.

Figures

Longitudinal BOD and DO profiles along the reach with CPCB observations overlaid
Fig. 1. Modelled longitudinal BOD (left) and DO (right) profiles along the 22 km Wazirabad → Okhla reach, with CPCB observed station medians overlaid. The DO sag below Najafgarh and the failure of natural recovery within the reach are both visible.
Source-term contributions: headwater versus combined drain inflow
Fig. 2. Source-term breakdown. The dry-season headwater Q (~4 m³/s) is an order of magnitude smaller than the combined drain inflow (~52 m³/s through Najafgarh, Shahdara, Sahibabad). This ratio is the structural reason headwater-Q sensitivity is decoupled from the receptor.
Modelled vs observed BOD and DO at the four CPCB stations
Fig. 3. Calibration scatter at the four CPCB stations (Palla, Nizamuddin, ITO Bridge, Okhla). Pooled NSE = 0.78 (BOD) and 0.95 (DO); pooled PBIAS = +1.6% (BOD) and −0.9% (DO).
Sum-of-squared-residuals contour over the kd-ka calibration grid
Fig. 4. SSR contour over the 25×25 kinetic-parameter grid. The calibrated optimum sits at kd,20 = 0.46 1/d and ka multiplier = 1.10. The valley is well-defined in the kd direction and shallower in ka, consistent with the Spearman ranking.
Monte Carlo scatter of Okhla BOD and DO with Spearman rank correlations
Fig. 5. 2000-run Latin Hypercube Monte Carlo: Okhla BOD and DO scatter against the five uncertain inputs, with Spearman rank correlations. Drain BOD multiplier (ρ = +0.93) is the dominant Okhla-BOD driver; ka (ρ = +0.53) and kd (ρ = −0.54) are the leading kinetic drivers of DO.
Compliance probability and BOD/DO spread by scenario
Fig. 6. Compliance probability (left) and BOD/DO ensemble spread (right) for the five scenarios. The asymmetry between the DO and BOD compliance lifts is the main quantitative result of the case study.

A seventh figure (illustrative un-ionised NH3 screening) is in the notebook only and is not part of the calibrated model.

Scope and limitations

This is a screening-level, public-data case study built on a steady-state 1D representation. It does not resolve diurnal DO swings, sediment oxygen demand, nitrification kinetics, or the slack-water reservoirs above each barrage where eutrophic algal cycles dominate the DO budget. Drain BOD and Q are treated as time-invariant within each season; in reality both have a diurnal and a stormwater signature. Headwater Q is the most contestable input — CWC and CPCB report different dry-season Wazirabad release figures — but not a high-leverage input on this reach: the Spearman ranking shows |ρ| < 0.1 for headwater Q against Okhla BOD, because dry-season Qhead is an order of magnitude smaller than the combined drain inflow. The model is intended for dry-season planning and should not be used to infer monsoon BOD compliance quantitatively without a storage-aware dynamic model.

Reproducibility

Everything here is built from public data (CPCB Yamuna Action Plan reports, CWC Old Railway Bridge gauge records, CPCB station medians 2018–2022). End-to-end runtime on a laptop is ~60 seconds. Full source on GitHub.

git clone https://github.com/venkatnsn/yamuna-delhi-bod-do-case-study.git
cd yamuna-delhi-bod-do-case-study
pip install numpy pandas scipy matplotlib jupyter nbformat
jupyter notebook notebook/Yamuna_BODDO_Analysis.ipynb

To regenerate the case study and methods appendix, the build chain (Node-based DOCX builders + docx2pdf) is documented in the repository README.md.

Key references

  1. Chapra, S.C. (1997). Surface Water-Quality Modeling. McGraw-Hill, New York.
  2. CPCB (2021). Yamuna Water Quality Status Report 2018–2020. Central Pollution Control Board, New Delhi.
  3. Emerson, K., Russo, R.C., Lund, R.E., Thurston, R.V. (1975). Aqueous ammonia equilibrium calculations: effect of pH and temperature. J. Fish. Res. Bd. Canada 32: 2379–2383.
  4. McKay, M.D., Beckman, R.J., Conover, W.J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2): 239–245.
  5. Moriasi, D.N., Arnold, J.G., Van Liew, M.W., et al. (2007). Model evaluation guidelines for systematic quantification of accuracy in watershed simulations. Trans. ASABE 50(3): 885–900.
  6. O’Connor, D.J., Dobbins, W.E. (1958). Mechanism of reaeration in natural streams. Trans. ASCE 123: 641–684.
  7. Streeter, H.W., Phelps, E.B. (1925). A Study of the Pollution and Natural Purification of the Ohio River. US Public Health Service Bulletin 146.