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5th International Symposium on Integrated Water Resources Management, 3rd International Symposium on Methodology in Hydrology, Hohai University, Nanjing, China, 19-21 November, 2010.

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Ian G. Littlewood

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Ian g littlewood

5th International Symposium on Integrated Water Resources Management, 3rd International Symposium on Methodology in Hydrology, Hohai University, Nanjing, China, 19-21 November, 2010

The effect of sub-optimal effective rainfall on the accuracy of unit hydrograph parameters estimated from different n-hourly data for a small humid-region catchment: method and implications

Ian G. Littlewood

IGLEnvironment, Didcot, Oxford, OX11 7XN, United Kingdom


Ian g littlewood

Part 1 –a summary of some published research undertaken with Barry Croke (Australian National University) and Peter Young (Lancaster University, UK) – presented at the Third International Symposium of the British Hydrological Society (Newcastle, UK, July 2010)

PUB

Part 2 –related work since July 2010 – feedback very welcome

Part 1 …

Littlewood, Nanjing, Nov 2010


Ian g littlewood

IHACRES – 6 parameters (DRCs)

Identification of unit Hydrographs And Component flows from Rainfall, Evaporation and Streamflow data

Jakeman, Littlewood and Whitehead (1990) Journ. Hydrol., 117, 275‑300

(ek)

(uk)

rk

Qk

Non-linear 'loss'

Linear UH module

module

(3 parameters)

tk

(3 parameters)

effective rainfall in time step k (uk) is the portion of rainfall (rk) that eventually leaves the catchment as streamflow

uk is un-observable – generated during model calibration

Littlewood, Nanjing, Nov 2010


Ian g littlewood

IHACRES – 6 parameters (DRCs)

 (q) – quick flow response decay time constant [T]

c– depth of a conceptual catchment wetness store [L]

 (s) – slow flow response decay time constant [T]

w – catchment drying time constant [T]

(ek)

(uk)

rk

Qk

Non-linear 'loss'

Linear UH module

module

(3 parameters)

tk

(3 parameters)

 (s)= SFI (analogous to BFI)

 (s) – proportional volumetric contribution of slow flow to streamflow [-]

f– temperature modulation factor (oC-1)

Littlewood, Nanjing, Nov 2010


Ian g littlewood

loss module

s0 = 0

UH module

quick

slow

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Calculating unit hydrograph DRCs from a (.) and b(.) parameters

DRC

Quick flow

Slow flow

Characteristic decay response times

Relative volumetric flow, where ν(q) + ν(s) = 1,

ν(s) = SFI and

Relative magnitudes of unit hydrograph peaks

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Plynlimon – forest and moorland

Severn

8.7 km2

10.6 km2

Wye

Cefn Brwyn

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Wye at Cefn Brwyn model calibration: 6 December 1987 – 2 July 1988

D = 0.89

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Littlewood, (2007), Tech. Doc. Hydr. No. 81, UNESCO, 149-155.

Littlewood & Croke (2008), HSJ, 53(4), 685-695

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Wye at Cefn Brwyn DRCs against data interval: model calibration 6 December 1987 – 2 July 1988

data interval (hours)

data interval (hours)

(SFI)

ν(s) (-)

data interval (hours)

data interval (hours)

data interval (hours)

Littlewood, (2007), Tech. Doc. Hydr. No.81, UNESCO, 149-155.

Littlewood & Croke (2008), HSJ, 53(4), 685-695

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Wye at Cefn Brwyn

IHACRES (q)

r2 = 0.999

 (q) = 0.692t + 3.27

(t)

data interval (hours)

extrapolating to t= 0 gives the Instantaneous Unit Hydrograph (IUH) parameter  (q)= 3.27 hr

Littlewood, Nanjing, Nov 2010


Ian g littlewood

precision ~ +/-11%

accuracy ~ +140%

data interval (hours)

Littlewood, Nanjing, Nov 2010


Ian g littlewood

precision ~ +/-2%

accuracy ~ +425%

data interval (hours)

Littlewood, Nanjing, Nov 2010


Ian g littlewood

the normalised IHACRES discrete-time UH values have been compared with corresponding DBM continuous-time values (previous work by Littlewood, Croke and Young, 2010)

data interval (hours)

data interval (hours)

(SFI)

 (s) (-)

data interval (hours)

data interval (hours)

data interval (hours)

(comparison of the IHACRES normalised loss module values with DBM continuous-time values has yet to be done)

Littlewood, Nanjing, Nov 2010


Ian g littlewood

 (q)

 (s)

SFI

Data time-step (hours)

Data time-step (hours)

Data time-step (hours)

data interval (hours)

data interval (hours)

data interval (hours)

convergence corroborates the IHACRES empirical/graphical method of estimating data interval-invariant (IUH) model parameters proposed by Littlewood (2007) and Littlewood and Croke (2008)

CT/DBM parameters are much less sensitive to t

why are IHACRES parameters so sensitive to t?

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Part 2

Littlewood, Nanjing, Nov 2010


Ian g littlewood

(uk)

rk

Qk

Non-linear 'loss'

Linear UH module

module

(3 parameters)

tk

(3 parameters)

PC-IHACRES (1997) – PCI (v1.03)

rk , tk

Qk

uk

PCI allows by-passing of the loss module, i.e. it can use effective rainfall generated externally

IHACRES Classic Plus (2006) – ICP(v2.1)

rk , tk

Qk

ICP does not allow by-passing of the loss module

IHACRES software packages downloadable (free) …

Littlewood, Nanjing, Nov 2010


Ian g littlewood

ICP (5 DRCs)

(previous work)

Littlewood, Nanjing, Nov 2010


Ian g littlewood

ICP (5 DRCs)

(previous work)

e.g. u*2,Δ4 = u5,Δ1+ u6,Δ1+ u7,Δ1+ u8,Δ1

Littlewood, Nanjing, Nov 2010


Ian g littlewood

ICP (5 DRCs)

(previous work)

Compare UH DRCs and DRC*s

PCI (3 UH DRC*s)

(this paper)

e.g. u*2,Δ4 = u5,Δ1+ u6,Δ1+ u7,Δ1+ u8,Δ1

Littlewood, Nanjing, Nov 2010


Ian g littlewood

sub-optimal effective rainfall (> hourly)

quasi-optimal effective rainfall

 (q)

 (s)

SFI

uk

u*k

~ +425%~ +250%

~ +110%~ +17%

~ -18~ -6 (pp)

Littlewood, Nanjing, Nov 2010


Ian g littlewood

Concluding remarks

a large part of the inaccuracy associated with an IHACRES UH parameter (DRCs –  (q),  (s)or SFI) calibrated using daily Cefn Brwyn data is due to sub-optimal effective rainfall

similar results are likely for other discrete-time conceptual rainfall–streamflow models,and for other catchments with highly dynamic responses to rainfall

  • there appears to be no escaping the fact that to calibrate discrete-time R-S model parameters with good precision and good accuracy (i.e. low uncertainty), the data must be at a sufficiently high frequency (f *)

  • f * = hourly (or more frequent) for Cefn Brwyn

Littlewood, Nanjing, Nov 2010


Ian g littlewood

f * will be different for different catchments

this has been largely ignored/overlooked

e.g. in several published R-S model parameter regionalisation studies towards predicting streamflow from rainfall in ungauged (flow) catchments –it has been common for daily data to be used for all gauged catchments irrespective of their different dynamic responses to rainfall

inaccuracy associated with a given R-S model parameter for gauged catchments (large for some catchments) introduces imprecision in that parameter estimated for ungauged catchments

Littlewood, Nanjing, Nov 2010


Ian g littlewood

by minimising or eliminating inaccuracy in calibrated R-S model parameters for gauged basins (as demonstrated) it should be possible to improve the precision of estimates for ungauged basins via model parameter regionalisation

but this has not been tried yet …


Ian g littlewood

Thank you


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