Detecting non-stationary in the unit hydrograph

Barry Croke1,2, Joseph Guillaume2, Mun-Ju Shin1

1Department of Mathematics2Fenner School for Environment and Society

Outline

• Data analysis methods – detecting variability in the shape of the UH without resorting to a model

• Adopting a UH model to explore variability in the UH shape between calibration periods

• Comparison between different models• Testing structures of the non-linear

module, and attempting to capture the variability in the UH shape

Data analysis methods

• Direct estimation for Axe Creek• 49 peaks accepted in total• 13 large peaks (>4cumecs)• 28 small peaks (<3cumecs)

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large peaks

small peaks Croke, 2006. A technique for deriving the average event unit hydrograph from streamflow-only data for quick-flow-dominant catchments, Advances in Water Resources. 29, 493-502, doi:10.1016/j.advwatres.2005.06.005.

Pareto analysis of cross-validation results• Identify one or more models per

calibration period, and calculate performance in each calibration period

• Ignore dominated models - inferior in all periods, retain the rest – no reason to eliminate them

• Consider the range of non-dominated performance (RNDP)• Croke, 2010. Exploring changes in catchment response

characteristics: Application of a generic filter for estimating the effective rainfall and unit hydrograph from an observed streamflow timeseries, BHS2010. http://www.hydrology.org.uk/assets/2010%20papers/077Croke.pdf

Apparent non-stationarity in UH

Catchment max R2 RNDPBani 0.999 0.04

Garonne 0.946 0.07Fernow 0.819 0.13Flinders 0.999 0.16Real 0.911 0.17

Wimmera 0.988 0.18Ferson 0.960 0.20

Catchment max R2 RNDPAllier 0.930 0.26

Kamp-Zwettl 0.823 0.56

Axe creek 0.982 1.16Lissbro 0.961 4.41Gilbert 0.996 4.73

Durance 0.554 4.87

Blackberry 0.942 8.40

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Comparison of different models• IHACRES-CMD (Croke and Jakeman, 2004), 2

stores model used• fixed parameters: e=1 (potential evapotranspiration

data used); d=200• calibrated parameters: f=(0.5-1.3); tau_q=(0-10);

tau_s=(10-1000); v_s=(0-1)• GR4J (Perrin, 2000, 2003), 4 parameters• SIMHYD (Chiew et al., 2002), 9 parameter version

used (Podger, 2004)• Sacramento (Burnash et al., 1973), 13

parameters• Calibration algorithm: Shuffled Complex Evolution

algorithm

Questions1. What is the Range of Non-Dominated

Performance (RNDP) across all periods? 2. What is the RNDP in each period? Is it low even

though total RNDP is high? Why?3. Which rainfall-runoff model has more Pareto-

dominated models?4. Which non-dominated model has the worst

performance in each period? Is it consistently the same dataset (pattern)? Is there reason for that period to be problematic?

Results

• Range of non-dominated performance (RNDP) is >0.1 for all catchments, but highly variable

• 3 catchments (Allier, Ferson and Real) have periods that increase the RNDP with R2 (NSE)

• RNDP reduced when R2log is used

• GR4J has the most non-dominated cases• Worst models are SIMHYD (R2 ) and

Sacremento (R2log )

• Five catchments (Durance, Ferson, Garonne, Kamp-zwettle and Real) have pattern of problematic behaviour (from the viewpoint of the models)

Exploring structure of non-linear module• Performance of stationary UH• Modified structure to permit variation

based on catchment wetness• Compensating for suspected intense

events

CMD module formulations

• Stationary UH• Linear• Bilinear• Sin• Exponential• Power law

• Variable UH• 2 effective rainfall time series• Intense events

Adopted structures

• Most common: sinusoidal (9 catchments)

• Mostly low order Nash cascades (2-3 stores)

Allier Exponential 5Axe Creek Bilinear 2Bani Sinusoidal 4Blackberry Exponential 3Durance Sinusoidal 7Fernow Bilinear 2Ferson Bilinear 1Flinders Exponential 3Garrone Sinusoidal 4Gilbert Sinusoidal 2Kamp-zwettl Sinusoidal 3Lissbro Sinusoidal 3Real Sinusoidal 2Wimmera Bilinear 4

Apparent non-stationarity in UH

Catchment max R2 RNDPBani 0.999 0.04

Garonne 0.946 0.07Fernow 0.819 0.13Flinders 0.999 0.16Real 0.911 0.17

Wimmera 0.988 0.18Ferson 0.960 0.20

Catchment max R2 RNDPAllier 0.930 0.26

Kamp-Zwettl 0.823 0.56

Axe creek 0.982 1.16Lissbro 0.961 4.41Gilbert 0.996 4.73

Durance 0.554 4.87

Blackberry 0.942 8.40

Axe Creek: period 1 (1.16)

Allier: period 1 (0.26)

Bani: period 1 (0.04)

Allier: period 1

Axe Creek: correction for variable UH

Axe Creek: correction for variable UH

Axe Creek: period 1

Conclusion

• A key source of non-stationarity in many catchments is variability in the shape of the UH

• Seen as a trend in model residual against observed flow – not present in when plotted against modelled flow, so produced by an unknown driver

• Hypothesis: variability is a result of event-to-event variations in rainfall intensity, and is predominantly a problem when using daily data

• Need to overcome this before addressing smaller effects

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