Geoscience Reference
In-Depth Information
400
Observed
Simulated
200
0
x 10
4
15
RSS = residual sum of squares in 30−point moving window
10
5
0
0.82
0.8
0.78
0.76
200
100
0
−100
Jun
Jul
Aug
Sep
Oct
Nov
Figure 7.17
Observed and WASMOD simulated discharge (top) for 1984 in the Paso La Ceiba catchment,
Honduras; at the end of October, a period of disinformative data can be seen; the second, third and fourth
plots from the top show the effect of the disinformative data on the residual sum of squares, the Nash-Sutcliffe
efficiency and the magnitude of the residuals (from Beven and Westerberg, 2011, with kind permission of John
Wiley and Sons).
residuals. Classical information measures (Akaike, Bayes, Deviance, Young, etc.) depend critically on
the posterior variance estimates of the model parameter values and the residual variance.
These classical measures effectively assume, however, that the sources of error are essentially stochas-
tic or aleatory in nature, whereas disinformation is a form of knowledge or epistemic error. The classical
measures also assume that every residual is informative in conditioning the model parameters and un-
certainty. The sample of residuals should asymptotically approach the true distribution for the prediction
uncertainty, where generally it is assumed that this true distribution is of simple form and stationary. The
residuals may be correlated, in which case the information content will be smaller and the approach to
the true distribution will be slower. Some sources of uncertainty may induce long-term correlation (an
error in a rainfall input that will also affect the response to later events), but statistical estimation still
requires that the structure of the errors be asymptotically stationary.
The nature of the problem of disinformation resulting from substantial nonstationary epistemic error
is, however, different. Disinformation tends to increase both the posterior parameter and residual variance
(and thereby reduce the apparent information content) but it cannot be represented by some simple form
