Economic Value Of Water Eval

---
name: economic-value-of-water-eval
description: Evaluates the economic value of hydropower reservoir operations based on sub-seasonal to seasonal precipitation forecasts under varying energy price differentials. It probes how forecast horizon and reservoir storage capacity interact with market prices to determine operational profitability. Use when the user wants to benchmark on 10-year reservoir timeseries, or asks about evaluating this task. Reports overall value of water.
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2108.06269
  bibtex_key: graham2021s2shydropower
  confidence: medium
---

# economic-value-of-water-eval

> The application of sub-seasonal to seasonal (S2S) predictions for hydropower forecasting — Robert M. Graham et al. (2021) (arXiv:2108.06269, 2021)

## What this evaluates

Evaluates the economic value of hydropower reservoir operations based on sub-seasonal to seasonal precipitation forecasts under varying energy price differentials. It probes how forecast horizon and reservoir storage capacity interact with market prices to determine operational profitability.

## Datasets

- **10-year reservoir timeseries** — total ?; splits: full (-1)

## Metrics

- `overall value of water` **(primary)** — range: other
  - Economic value derived from a cost model that accounts for peak and off-peak energy prices and reservoir stage costs. Calculated across a range of price differentials (£5/MWh to £100/MWh) with peak price fixed at £50/MWh.

## Input / output format

**Input**: 10-year timeseries of observed and forecasted inflows, paired with peak (£50/MWh) and variable off-peak energy prices.

**Output**: Average overall value of water for different forecast durations (1 to 6 weeks), with uncertainty bounds.

## Scoring recipe

```python
import numpy as np
def compute_economic_value(forecasts, observed_inflows, peak_price, off_peak_price):
    # Run cost model framework
    # Calculate revenue from water sold at peak vs off-peak prices
    # Subtract stage 1/stage 2 costs for deviations from target water level
    return total_economic_value

# Bootstrap resample 1000 times to get 90% CI
bootstrap_values = [compute_economic_value(resample(forecasts), resample(observed)) for _ in range(1000)]
mean_value = np.mean(bootstrap_values)
ci_90 = mean_value + 2 * np.std(bootstrap_values) / np.sqrt(1000)
```

## Common pitfalls

- Absolute water value depends heavily on the chosen price differential; relative change is more robust.
- Short-term forecasts are not universally better; smaller reservoirs need detailed intra-period distribution, while large reservoirs benefit from longer averaging periods.

## Evidence (verbatim from paper)

> To test the significance of the results, we apply a bootstrap method to resample the 10-year timeseries 1000 times (Messner et al., 2020). All results shown indicate the spread of 2 standard errors based on this bootstrap resampling, which approximately represents the 90% confidence interval. Here we describe the performance of climatological forecasts in this cost model framework. For all forecast periods, the overall value of water decreases near linearly as the price differential between peak and off-peak energy prices increases (Figure S15).

## Citation

```bibtex
@misc{graham2021s2shydropower,
  title={The application of sub-seasonal to seasonal (S2S) predictions for hydropower forecasting},
  author={Robert M. Graham et al. (2021)},
  year={2021},
  note={arXiv:2108.06269}
}
```

- arXiv: 2108.06269