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# Searching for the Holy Grail of scientific hydrology: Qt=(S, R, Δt)A as closure

## Details

**Authors** Beven, Keith John

**Year** 2006

**Publisher** Hydrology and Earth System Sciences

**Kind of work** article

**Discipline** Hydrology

**Secondary disciplines** Environment & Sustainability

**Applied** false

[Read it at the publisher](https://doi.org/10.5194/hess-10-609-2006) 
10.5194/hess-10-609-2006

## In authors' words

### What they set out to do (purpose)

To examine what is needed to close the balance equations of the Representative Elementary Watershed (REW) concept, which describes a catchment as a unit whose behavior depends on fluxes across its boundary.

### Who or what was studied (sample)

A conceptual and theoretical analysis; no dataset of catchments is analyzed in the portion of the paper that could be read.

### How they did it (methods)

Theoretical argument about the form of boundary flux closure relations in REW balance equations, with reference to hysteretic dynamic responses reported in small experimental catchments.

### What they found (results)

The REW balance equations require closure relations linking internal state variables to boundary fluxes. The author argues these relations are likely to be scale-dependent, nonlinear and hysteretic, and may depend on extremes and heterogeneities within the REW. Simple averaging of local-scale flux relationships is unlikely to describe closure at the REW scale. Hysteresis observed in some small experimental catchments may be partly represented by simple transfer functions. The author ranks finding closure schemes as the second most important problem of 21st-century hydrology, after measuring integrated storages and fluxes at useful scales.

## Commentary

### In short

A hydrologist argues that treating a watershed as a single unit requires rules linking its internal state to what crosses its boundary, and that those rules change with scale and cannot be obtained by simply averaging local measurements.

### Response

The paper bears on the Systems and Relationships patterns. The REW is a whole defined by a boundary and by internal parts, and the closure problem is the problem of relating whole-scale behavior to part-scale relations. The finding that local relations cannot simply be averaged up is a statement that the whole does not behave as an aggregate of its parts. Caveats: this was assessed from the abstract and publisher page only; the argument is theoretical and programmatic rather than an empirical test, and it does not concern distinctions or perspectives in any explicit way.

**Patterns it shows** S, R

Formal proof or model

**Added** 2026-10-21

**How to cite this** Beven, Keith John (2006). Searching for the Holy Grail of scientific hydrology: Qt=(S, R, Δt)A as closure. Hydrology and Earth System Sciences.