Reply to Ogden and Stallard: Phenomenological runoff models in the Panama Canal watershed

Ogden and Stallard (1) argue that our estimates of the effect of reforestation on runoff in the Panama Canal watershed (2) are invalid because we use a particular phenomenological runoff model: the US Department of Agriculture–Natural Resources Conservation Service Curve Number (CN) model. The authors claim that the CN model, originally developed to describe runoff from single storm events in temperate watersheds, does not “work” in humid tropical watersheds and cannot be applied at other temporal or spatial scales. We disagree. The test of any phenomenological model is whether it predicts well at the scale on which data are observed. The CN model does not offer the same insights into hydrological processes as physics-based models, but it has been applied at various temporal (3) and spatial scales (4, 5) with reasonable predictive power. We calibrated our model using precipitation and hydrograph data for the Candelaria subbasin and validated against observed flows for six subbasins in the watershed. At the subbasin scale the model predicted flows within . The predicted margin of error for the whole watershed was found to be 1%. Sensitivity analysis showed that the estimated hydrological flows were relatively stable with respect to CN variations.

Ogden and Stallard (1) are skeptical about the capacity of the CN approach in part because it is a “lumped” parameter model using a single representative value to quantify the behavior of a basin. As they rightly point out, a basin usually possesses a range of land uses and soils. Such spatial variability cannot be captured in a lumped model. This is one reason why we adopted a spatially distributed approach that models each individual pixel within the watershed separately. The authors nevertheless question this approach, because it introduces biases in runoff prediction away from the original lumped runoff estimates. We follow a literature that shows how the CN method can be interpreted to represent a spatial distribution of CNs (4) and varying runoff-producing areas (5). A CN determined by a weighted average of CNs for n pixels is known to bias runoff predictions upwards (6). However, aggregation of the flows from direct estimation of spatially varied runoff using spatially varied CNs leads to essentially the same results as the original, lumped runoff model (assuming the average length of “sheet flow” is below 45 m) (4). This is the procedure we used. Our use of a monthly time step, which required scaling up of the parameter λ, follows an approach tested by Ferguson (3), who reported a 3% margin of error compared with the original approach.

Our report models the impact of reforestation on a range of ecosystem services, including water flows, in the highly variable conditions of the Panama Canal watershed. We found that over much of the watershed, dry-season flows were unlikely to be enhanced by reforestation for any parameter values considered. This is now a hypothesis to be tested empirically and is precisely why it is important to conduct experiments about the impact of vegetation change on wet- and dry-season flows across the watershed.