Árbók VFÍ/TFÍ - 01.06.2005, Page 211

Mat á rennslislyklum og rennsli
með bayesískri tölfræði
Snorri Ámason er sérfræðingur hjá Vatnamælingum Orkustofnunar. Snorri lauk B.S. prófi í iðnaðarverkfræði vorið 2002
frá Verkfræðideild H( og M.Sc. prófi í verkfræði frá sama skóla vorið 2005.
Dr. Birgir Hrafnkelsson er lektor við véla- og iðnaðarverkfræðiskor Hl. Birgir útskrifaðist sem vélaverkfræðingur frá Hl
1993 og lauk M.Sc. prófi í verkfræði frá sama skóla 1995. Hann lauk doktorsprófi I stærðfræðilegri tölfræði frá Texas
A&M University 1999.
Dr.Ólafur Pétur Pálsson er dósent við véla- og iðnaðarverkfræðiskor H(. Ólafur Pétur útskrifaðist sem vélaverkfræð-
ingur frá H( 1987. Hann lauk civ.ing. prófi frá DTU i Danmörku 1989 og Ph.D. prófi (verkfræði frá sama skóla 1994.
Abstract
Hydrological rating curves are used to convert water level time series to discharge time series.The current method for the
estimation of unknown parameters is based on least squares. Its lack of in-depth uncertainty estimates causes problems
in data processing and it is virtually impossible to incorporate auxiliary information objectively into this method. A work-
ing group undertheChiefsof the Hydrological Institutes of the Nordic countries (CHIN) reported recently [1] that thesub-
jectivity of the methodologies used in the member countries, causes uncertainties in the establishment of rating curves,
resulting in different rating curve estimates between countries.Therefore, long term discharge averages and maximum val-
ues, based on the same data, are surprisingly different.
Here an objective methodology for establishing hydrological rating curves based on Bayesian statistics is presented.The
Bayesian approach naturally combines the statistical model for the data which incorporates the hydrological model, the
data themselves and a priori information which is based on previously collected data and scientific knowledge. Data col-
lected by the Hydrological Service in lceland at the National Energy Authority are analyzed, using scientific and heuristic
methods, establishing a priori knowledge about the required parameters.The combination of data and a priori knowledge
results in a posterior distribution which is used to estimate parameters of the rating curve and to predict discharge for a
given water level. The Bayesian approach provides a more accurate prediction error for discharge than the current
approach based on least squares. Also, credible regions can be estimated for all derived hydrological variables, e.g., annu-
al means, daily means and extreme values.
Series of discharge predictions are the foundation of many important and expensive projects including hydroelectric
power plants, bridges and other transportation structures as well as scientific research such as advanced hydrological
models. All improvement of data processing results in better decision making and planning in these fields.This research
has a strong support from interested parties, both in lceland and abroad, as the goal is a common methodology that will
benefit all of the participating nations as well as other parties interested in increasing the quality of data processing.
Ritrýndar vfsindagreinar i 2 0 9