Processing statistical parameters of concentration along a river network -abstract

Abstract

Water quality models have been under constant development in the last decades. It is a tendency to build robust deterministic models characterized by high data demand in order to get knowledge on non-monitored elements of the stream network. However, based on simple descriptions of the water quality processes many statistical parameters of the concentration time series can be extended to arbitrary point of the stream network. This paper proposes a method for the extension of statistical parameters of concentration along a river network. The proposed method is based on the extension of the idea of linearization. Investigating a single river reach, supposing a simple in-stream process (e.g. 1 st order decay), the downstream mean, standard deviation and correlation values can be calculated via Taylor-series approximation. Also, approximations can be given for values below a confluence of two rivers, if upstream values are known. The proposed method is tested against: 1. Synthetically generated flow and water quality data, where parameters of the data generation are derived based on long-time measurement data. 2. Measured upstream data, and elements of the downstream data series that are calculated one by one based on simple equations describing the in-stream processes. In the 1 st test, upstream daily discharge, BOD concentration and water temperature values were generated synthetically. Statistics of a hypothetical downstream point were calculated (supposing realistic river geometry) in two ways. 1. The downstream concentration was calculated on a daily basis assuming 1 st order decay. Statistical values were calculated from the daily downstream concentration data series for each year ("daily"). 2. With Taylor-series approximation ("approximated"). The approximated statistics showed promising agreement with values calculated on a daily basis. Approximated mean values of the downstream concentration had an error of-10 … 1% relative to the mean calculated on a daily basis. Approximated standard deviation of the downstream concentration had an error of-8 … 9% relative to the standard deviation calculated on a daily basis. The relative error exceeded 5% only in 4% of the cases. As for the correlation between discharge and downstream concentration, the difference between approximated values and values calculated on a daily basis ranged-0.04 … 0.21. It exceeded 0.05 in only 6% of the cases. Concerning the correlation between temperature and downstream concentration, the difference between approximated and calculated values ranged between-0.10 … 0.11. The difference exceeded 0.05 only in 3% of the cases. Investigating a confluence of two rivers with synthetically generated realistic data, the most statistical properties downstream to the confluence could be approximated with very little error relative to the ones calculated on a daily basis.

Full text

Processing statistical parameters of concentration along a river
network – abstract
M. K. Kardos* and L. Koncsos*
* Budapest University of Technology and Economics, Department of Sanitary and Environmental
Engineering, Műegyetem rakpart 3., H-1111 Budapest, Hungary (E-mail: kardos.mate@epito.bme.hu)
Water quality models have been under constant development in the last decades. It is a tendency to
build robust deterministic models characterized by high data demand in order to get knowledge on
non-monitored elements of the stream network. However, based on simple descriptions of the water
quality processes many statistical parameters of the concentration time series can be extended to
arbitrary point of the stream network. This paper proposes a method for the extension of statistical
parameters of concentration along a river network.
The proposed method is based on the extension of the idea of linearization. Investigating a single
river reach, supposing a simple in-stream process (e.g. 1st order decay), the downstream mean,
standard deviation and correlation values can be calculated via Taylor-series approximation. Also,
approximations can be given for values below a confluence of two rivers, if upstream values are
known.
The proposed method is tested against:
1. Synthetically generated flow and water quality data, where parameters of the data generation
are derived based on long-time measurement data.
2. Measured upstream data, and elements of the downstream data series that are calculated one
by one based on simple equations describing the in-stream processes.
In the 1st test, upstream daily discharge, BOD concentration and water temperature values were
generated synthetically. Statistics of a hypothetical downstream point were calculated (supposing
realistic river geometry) in two ways.
1. The downstream concentration was calculated on a daily basis assuming 1st order decay.
Statistical values were calculated from the daily downstream concentration data series for
each year (“daily”).
2. With Taylor-series approximation (“approximated”).
The approximated statistics showed promising agreement with values calculated on a daily basis.
Approximated mean values of the downstream concentration had an error of -10 … 1% relative to
the mean calculated on a daily basis. Approximated standard deviation of the downstream
concentration had an error of -8 … 9% relative to the standard deviation calculated on a daily basis.
The relative error exceeded 5% only in 4% of the cases. As for the correlation between discharge
and downstream concentration, the difference between approximated values and values calculated
on a daily basis ranged -0.04 … 0.21. It exceeded 0.05 in only 6% of the cases. Concerning the
correlation between temperature and downstream concentration, the difference between
approximated and calculated values ranged between -0.10 … 0.11. The difference exceeded 0.05
only in 3% of the cases.
Investigating a confluence of two rivers with synthetically generated realistic data, the most
statistical properties downstream to the confluence could be approximated with very little error
relative to the ones calculated on a daily basis.