By: Hans Jørgen Henriksen, GEUS (October, 2015)

WWW: Anders L Madsen, HUGIN EXPERT A/S

Abstraction of groundwater is a major stressor for terrestrial and aquatic ecosystems especially in countries like Denmark where close to 99% of the water supply is based on groundwater. During the past decades overexploitation in Denmark and many other places has resulted in deterioration of aquifers and poor status of receiving ecosystems. For the second River Basin Management Plans in Denmark, DCE developed a new model for the relationship between flow variables and index scores for three biological quality elements fish (DVFFa/61 sites), macro-phytes (DVPI/91 sites) and macro-invertebrates (DVFI/122 sites), based on an analysis of ecological and measured flow data from 2004 to 2010 (Graeber et al., 2014). GEUS implemented the new indicator for EU WFD RBMP2 for Denmark and even though median minimum flow Qmm was evaluated as having less importance, this variable was used for screening of the most impacted reaches (based on 2700 stations defining ID15 sub-catchments of approximate area of 15 km2), and also for analysing relationships between impacted reaches and 400 groundwater bodies (Henriksen et al. 2014; Henriksen 2015). Based on the calculated values of DVFI, DVPI and DFFVa for the 61-122 stations and the observed values of DVFI, DVPI and DFFVa, and implemented model results with the national water resource model (DK model) for Q90 (dkQ90S), BFI (dkBFI) and Qmm (dkQmm) for the same stations, a dataset was prepared which was further analysed with HUGIN structural and EM learning tools. Hereby a prototype Bayesian network has been constructed as described in details in Henriksen (2015) for evaluating DVFI, DVPI and DFFVa based on either variables estimated based on observed discharge time series (fre1, fre25, fre75, dur3, bfi and q90) including observed sinuosity (sin) or DK modeled variables (Qmm, dkQ90, dkBFI and sin) for 2700 ID15 stations in Denmark.

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

mean: , variance:

It is necessary to press the compute button before interpreting the numbers below

The idea of the network is to enable an exploratory analysis and integrated assessment of the state of ecological flow variables. In the initial situation the network describe the overall results *in average* based on initial distributions of all variables based from the 61-122 sites. So the initial Bayesian network show distributions for all variables, but here the main uncertainty is due to the variability of the 61-122 sites, and to a less degree measurement and model uncertainty, which first are analysed after having entered evidence for either the observed variables (dur3, Fre1, Fre25, Fre75, q90, bfi and sin), or DK modeled data (dkQmm, dkQ90S, dkBFI and sin), or for observed (DVFI, DVPI and/or DFFVa). A traffic light enables a probability distribution for the status intervals (bad, poor, moderate, good and high status).
Inference is the act or process of deriving logical conclusions from premises known or assumed to be true. Let's try to enter the following hydrological regime variables.
Try one of the following examples:

A large downstream catchment in Jutland (220062). Enter the following observed block variables:

- Dur3 = 5 days
- Fre75 = 6.56 (events per year below Q75)
- Fre25 = 8.22 (events per year above Q25)
- Fre1 = 8.22 (events per year above Q50)
- Sin = 3 (slightly meandering)
- q90 = 0.62
- bfi = 0.84

and median minimum flow in the DK model block:

- dkQmm = 9.07 (m3/sek)

As can be seen for example A the BN simulates the mean value for obsDVPI to 0.45 and the variance 0.0004 (observed DVPI is 0.46). BN simulates obsDVFI to 0.98 with variance 0.03 (observed DVFI =0.87) and finally BN simulates obsDFFVa to 0.85 with variance 0.06 (observed DFFVa is 0.95). After this compute traffic light and obtain distribution (be patient!).

For example A the following observed data are available: DVPI = 0.46, DVFI = 0.87 and DFFVa = 0.95. From the DK model (new baseline Henriksen et al. 2015) the following results for 2004-2010: dkQ50 = 15.9 m3/s, dkFre1 = 7.14, dkFre25 = 6.85, dkFre75 = 5.42, dkQ90 = 0.64, dkBFI = 0.87 and dkDur3 = 3.2. DK model has estimated dkQ25 to 22.5 m3/s and dkQ75 to 12.07 m3/s for 2004-2010.

A small catchment on Sjælland (540002): Enter the following in observed block:

- Dur3 = 9 days
- Fre75 = 4.67 (events per year below Q75)
- Fre25 = 7 (events per year above Q25)
- Fre1 = 5.55 (events per year above Q50)
- Sin = 1 (channelized)
- q90 (Q90/Q50) = 0.08
- bfi = 0.50

and in DK model block:

- dkQmm = 0.0012 (m3/sek)

For example B the following observed data are available: obsDVPI = 0.46, obsDVFI = 0.21 and obsDFFVa = 0.01. From the DK model the following results are available: dkQ50 = 0.035 m3/s, dkFre1 = 2.71, dkFre25 = 4, dkFre75 = 1.57, dkQ90 = 0.0385, dkBFI = 0.65 and dkDur3 = 15.1. DK model has estimated dkDVPI = 0.49, dkDVFI = 0.23 and dkDFFVa = 0.35. Compare what is obtained by the BN after having entered evidence as described above. Finally, compute the traffic light to obtain distribution (takes time, be patient!).

Since only a limited number of river stations in Denmark with observed discharge time series the above example of entering results of time series with complete daily discharge show how this information can reduce the uncertainty bound of the estimated DVFI, DFFVa and DVPI, compared to when using model results from DK model. It has been evaluated by GEUS that simulated values of dkFre1, dkFre25, dkFre75 and dkDUR3 should only be used for analyzing differences in simulated EQR values, not for estimate of absolute values. This is the reason behind the Bayesian network where only variables that can be sufficiently accurately determined by the DK model e.g. dkQ90, dkQmm and dkBFI. But since a BN allows evidence to be entered for all variables, we can also enter data for stations where we have calculated estimates of the three variables from the DK model and including observed sin if available. In the following let us demonstrate this for example B. First we initialize the BN, and enter the following three variables as evidence: enter

- sin = 1

- dkQmm = 0.0012 m3/s
- dkBFI = 0.65
- dkQ90S= 0.0385

It has been demonstrated how the BN can be used in different ways to estimate DVPI, DVFI and DFFVa. Where observed data of sin, fre1, fre25, fre75, dur3, bfi and q90 are available this will give the best estimates of DVPI, DVFI and DFFVa. If there is also observed DVPI or DVFI or DFFVa these measurements can also be entered as evidence, in order to update the BN and to reduce variances and uncertainty bounds. Furthermore, if no observed DVPI, DVFI and DFFVa, data from DK model can be entered as evidence for a estimate of DVFI, DVPI and DFFVa. Again, such estimates can be consolidated in cases where observed DVFI should be available, or DVPI or DFFVa, for determining the other two variables.

Read more about the constructed Bayesian network

Henriksen, H. J. (2015) Bayesian network for integrated assessment of ecological flow status in Danish rivers based on observed hydrological regime variables. Available for download here: briefing note

For those interested in BBN include: Kjærulff, U. B. and Madsen, A. L. (2013) Bayesian Networks and Influence Diagrams: A Guide to Construction and Analysis. Springer, Second Edition.

Hans Jørgen Henriksen, GEUS, hjh at geus dot dk

Anders L Madsen, HUGIN EXPERT A/S, anders at hugin dot com