DRV - Deviation of Runoff Volume

The Deviation of Runoff Volume (DRV) is a domain-specific metric primarily utilized in hydrology and environmental engineering.

It evaluates the overall mass balance of a model by calculating the ratio of the total observed (actual) runoff volume to the total simulated (predicted) runoff volume over a specified period.

\[\text{DRV}(y, \hat{y}) = \frac{\sum_{i=1}^{N} y_i}{\sum_{i=1}^{N} \hat{y}_i}\]

Description

Advantages:

  • Mass-balance verification: DRV is exceptionally useful for verifying if a model correctly predicts the total volume of an event (e.g., total rainfall, total flood volume), even if the exact timing of the predictions is slightly off.

  • Highly interpretable: A score of 1.0 means perfect volume matching. A score of 0.5 implies the model over-predicted the total volume by a factor of 2. A score of 2.0 means it under-predicted by half.

Disadvantages:

  • The Cancellation Effect (Crucial Flaw): Like the Coefficient of Residual Mass (CRM), DRV aggregates all values before comparing. Massive under-predictions on day 1 can perfectly cancel out massive over-predictions on day 2, yielding a “perfect” DRV of 1.0 despite terrible daily accuracy. It must be paired with time-step metrics like RMSE or NSE.

  • Zero-Sum Vulnerability: If the sum of the predicted values (\(\sum_{i=1}^{N} \hat{y}_i\)) is exactly zero (e.g., a model predicts absolutely zero runoff for the entire period), the metric will crash due to division by zero.

Properties

  • Best possible score: 1.0 (Indicates perfect agreement between total actual and total predicted volumes. Closer to 1.0 is better).

  • Range: (-inf, +inf) (Practically [0, +inf) since physical volumes are typically non-negative).

  • Mathematical Reference: RStudio Pubs

Example Usage

from numpy import array
from permetrics.regression import RegressionMetric

## 1. For 1-D array (Single-output)
y_true = array([3, -0.5, 2, 7])
y_pred = array([2.5, 0.0, 2, 8])

evaluator = RegressionMetric(y_true, y_pred)
# Calculate Deviation of Runoff Volume
print("DRV: ", evaluator.DRV())

## 2. For > 1-D array (Multi-output)
y_true = array([[0.5, 1], [-1, 1], [7, -6]])
y_pred = array([[0, 2], [-1, 2], [8, -5]])

evaluator = RegressionMetric(y_true, y_pred)
# Return an array of scores for each column
print("DRV (Multi-output): ", evaluator.DRV(multi_output="raw_values"))