Uncertainty in hydrological models - IMAGe

Uncertainty in hydrological models 

Rob Wilby, Department of Geography, Loughborough University (r.l.wilby@lboro.ac.uk) 

Loughborough University campus flash flood 28 June 2012 

Uncertainty in Climate Change Research: An Integrated Approach 

6-17 August 2012 Institute for Mathematics Applied to Geosciences, NCAR, Boulder, CO

Certainty (flood risk) 

Lecture theatre 

Source: Environment Agency 



Certainty (flood risk) 

Source: Adaptation Sub Committee (2011) 



Certainty 

(atmospheric rivers) 

The 900 hPa specific humidity fields at 0600 UTC for the top 10 

winter flood events on the River Eden at Temple Sowerby (left) 

and AR location for top 10 winter floods in selected catchments. 

Source: Lavers et al. (2011) 



Uncertainty “hierarchy” (future risks) 

First order forcings 

Climate models 

Regional consequences 

Downscaling 

•Empirical 

•Dynamical 

Feedbacks 

•Land use 

•Adaptations 

Impact model 

•Structure 

•Parameters 



Typical finding of assessments: 

“much greater tendency for increasing flood risk” 

GCMs under two emissions scenarios (A1B and A1B-2016-5-L), at four time horizons. 

The plots show the 25th, 50th, and 75th percentiles (represented by the boxes), and the 

maximum and minimum values (shown by the extent of the whiskers). 

Source: Warren et al. (2010) from AVOID programme 



National CCRA headline threats 



Hydrological model uncertainty in perspective 



Global water balance (Sv) 

BCCR-BCM2.0 

CCSM3 

CGCM3.1 

CNRM-CM3 

CSIRO-MK3.0 

ECHAM5-MPI-OM 

ECHO-G 

FGOALS-g1.0 

GFDL-CM2.0 

GISS-EH 

GISS-ER 

INM-CM3.0 

IPSL-CM4 

MIROC3.2 

MRI-CGCM2.3.2 

PCM-NCAR 

HadCM3 

HadGEM1 

Input uncertainty (GCMs) 

0.1 

0.08 

0.06 

0.04 

0.02 

0 

-0.02 

-0.04 

-0.06 

-0.08 

-0.1 

E > P 

P > E 

„Ghost‟ moisture sources: Global annual mean residual of the atmospheric water balance (E – P – dw/dt) 

for CMIP3 climate models. One Sverdrup (Sv) is 10 6 m 3 s -1 or 31,600 km 3 yr -1 . Note that four climate 

models have residuals > 0.1 Sv. For comparison, observed atmospheric moisture transport from ocean to 

land is estimated to be 1.2 Sv. Data from Liepert and Previdi (2012). 



Evaluating „fitness‟ for hydrological tasks 

Principles for climate model evaluation 

1. Quantify the uncertainty in the observed data used for model 

evaluation (homogeneity, confidence intervals, outliers) 

2. Compare like with like (grid to grid, scale to scale) 

3. Select indicators of performance relevant to the intended 

hydrological applications (extremes, low-frequency variability) 

4. Evaluate climate models relative to other components of 

hydrological uncertainty (impact model, weighting) 

5. Test combined climate, downscaling and hydrological model 

skill using near-term applications (seasonal forecasts) 

Indicators for evaluation of climate model outputs from the perspective 

of hydrological applications. Source: Wilby (2010) 



Z-score 

Trends consistent with GCMs? 

4 

3 

2 

1 

0 

-1 

-2 

-3 

-4 

1861 1871 1881 1891 1901 1911 1921 1931 1941 1951 1961 1971 

Dee 

Derwent 

Eden1 

Eden2 

Exe 

Itchen 

Medway 

Ouse 

Tee 

Teifi 

Thames 

Tyne 

Wensum 

Wharfe 

Wye 

Average 

Mann-Kendall test for significant trends (Z s ) in area-average winter rainfall 

for 15 river basins in England and Wales. Source: Wilby (2006) 



Time of day 

Time of day 

1988 

1989 

1990 

1991 

1992 

1993 

1994 

1995 

1996 

1997 

1998 

1999 

2000 

2001 

2002 

2003 

2004 

2005 

2006 

2007 

2008 

2009 

2010 

Confounding factors Glutton (observer practices) 

1800 

1600 

1400 

1200 

1000 

800 

Environment Agency water temperature measurement times at Glutton on the River Dove. 

The black line shows the moving average of 12 samples. A shift in sampling time of 2 hours 

between 1990s and 2000s equates to a warming of ~0.7°C. Source: Toone et al. (2011) 



Confounding factors (river regulation) 



Cumulative discharge (km3) 

Cumulative discharge (km3) 

Confounding factors (known unknowns) 

Q = (A.P.k) + (G.ΔT) – (A.E) ± S ± D 

Observed 

Modelled 

Q is the discharge (km 3 ), 

A is the basin area (km 2 ), 

P is the annual precipitation (km), 

k is a scaling factor, 

G is the total snow and glacier melt per year 

ΔT degree temperature change (km 3 /yr/°C), 

E is the annual evaporation total (km), 

S is upstream storage change (km 3 ), 

D is diversions for irrigation or effluent (km 3 ). 

1200 

1000 

800 

600 

400 

200 

0 

1200 

1000 

800 

600 

400 

200 

0 

Syr Darya to Aqjar 

1960 1970 1980 1990 2000 2010 

Observed Modelled 

Vakhsh to Darband 

1960 1970 1980 1990 2000 2010 



Confounding factors (known unknowns) 



Hydrological models 

Input uncertainty 

Structure uncertainty 

1. Empirical/statistical 

2. Water balance 

3. Conceptual 

4. Physically based 

Parameter uncertainty 



Input uncertainty 



Mean daily discharge (m3/s) 

Snowmelt Runoff Model (SRM) 

Q n+1 = [C Sn · α n (T n + ΔT n ) S n + C R · P n ] A · v (1 – k n-1 ) + [Q n · r n+1 ] 

LapseRate 

Tcrit 

0.8 

3 

0.6 

0.4 

0.2 

0 

01 02 03 04 05 06 07 08 09 10 11 12 

2 

1 

0 

01 02 03 04 05 06 07 08 09 10 11 12 

1200 

1000 

800 

Observed 

SRM 

DDF 

0.8 

0.6 

0.4 

0.2 

0 

01 02 03 04 05 06 07 08 09 10 11 12 

Cr 

0.6 

0.4 

0.2 

0 

01 02 03 04 05 06 07 08 09 10 11 12 

Cs 

1 

0.8 

0.6 

0.4 

0.2 

0 

01 02 03 04 05 06 07 08 09 10 11 12 

RCA 

1.5 

1 

0.5 

0 

01 02 03 04 05 06 07 08 09 10 11 12 

600 

400 

200 

0 

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 

Daily mean composite of observed 

and SRM discharges at Darband 

2001-2010 



Fraction of zone that is snow covered 

Input uncertainty (snow cover) 

1.0 

Zone 1 

0.8 

0.6 

0.4 

0.2 

Zone 2 

Zone 3 

Zone 4 

Zone 5 

Zone 6 

Zone 7 

Zone 8 

0.0 

16-Mar 16-Apr 16-May 16-Jun 16-Jul 16-Aug 16-Sep 

Snow-cover duration curves (CDCs) for the upper Vakhsh basin in 2010 



Daily Q (m3/s) 

Jan 

Feb 

Mar 

Apr 

May 

Jun 

Daily Q (m3/s) 

Jul 

Jan 

Aug 

Feb 

Sep 

Mar 

Oct 

Apr 

Nov 

May 

Dec 

Jun 

Jul 

Aug 

Sep 

Oct 

Nov 

Dec 

Input uncertainty (outcome) 

3500 

3000 

2500 

2000 

1500 

Nasty (2001) 

Observed 

SRM 

Hot-dry 

Central 

Warm-wet 

1000 

500 

0 

3500 

Nicer (2003) 

3000 

Observed 

Observed and SRM 

estimates of daily discharge 

in the Naryn under present 

and changed climate for the 

2050s (hot-dry, central, and 

warm-wet). 

2500 

2000 

1500 

1000 

500 

0 

SRM 

Hot-dry 

Central 

Warm-wet 

Source: EBRD (2011) 



Source: Clark et l. (2008) 

Source: Freer et al. (2012) 

Framework for Understanding 

Structural Errors (FUSE) 



PE (mm/day 

PE (mm/day 

PE (mm/day 

PE (mm/day 

Structural uncertainty (PE) 

14 

(A) Potential Evaporation 1961-1990 

14 

(B) Potential Evaporation 2020s 

12 

10 

8 

6 

Thornthwaite 

Blarney-Criddle 

Hamon 

Mass balance 

12 

10 

8 

6 

min 

q1 

median 

q3 

max 

4 

4 

2 

2 

0 

0 



Month 

Month 

14 

(C) Potential Evaporation 2050s 

14 

(D) Potential Evaporation 2080s 

12 

12 

10 

10 

8 

6 

4 

2 

8 

6 

4 

2 

0 


Month 

0 


Estimated PE for 1961-1990 based on the Thornthwaite, Blaney-Criddle and Hamon 

methods and observed temperatures. Mass balance estimates were calculated from 

reservoir (Kairakkum) inflows and outflows. Source: EBRD (2012) 

Month 



Cumulative likelihood 

Structural uncertainty (PE, GCM, emissions) 

1 

2020s 2050s 2080s 

0.8 

0.6 

0.4 

0.2 

0 

0 10 20 30 40 50 60 70 

Annual PE change (%) 

Cumulative likelihood distributions of annual PE increases (% change with respect to the 

1961-1990 baseline) projected by ensembles of PE estimation method, emission scenario, 

and GCM output (for the closest grid-points to the Kairakkum reservoir). 



surface 

evaporation 

soil moisture 

precipitation evaporation 

Parameter uncertainty 

soil moisture store 

reduced 

evaporation rate 

direct 

percolation 

total 

percolation 

saturation 

percolation 

abstraction 

effluent 

return 

unsaturated 

zone 

abstraction 

recharge 

saturated zone 

outflow 

channel flow 


6-17 August 2012 Institute for Mathematics Applied to Geosciences, NCAR, Boulder, CO 

CATCHMOD lumped conceptual model

Parameter uncertainty (high identifiability) 

All data (1961-1990) 

Wettest year (1967/68) 

Driest year (1975/76) 

CATCHMOD direct percolation (DP) parameter 

for Thames basin. Source: Wilby (2005) 



Parameter uncertainty (low identifiability) 

All data (1961-1990) 

Wettest year (1967/68) 

Driest year (1975/76) 

CATCHMOD potential drying constant (PDC) 

parameter for Thames basin. Source: Wilby (2005) 



Parameter uncertainty (outcome) 

Observed and simulated runoff in the Lech basin, Austria for the year 1975. Blue shading 

indicates the range obtained from 20 different parameter sets. Source: Dobler et al. (submitted). 



Overview: Hydrological uncertainties 

in perspective (hydropower) 

Climate change 

scenarios 

Hydrological models 

(REG WBM SRM) 

Upstream river 

regulation 

Hazards 

analysis 

Monthly/annual 

evaporation 

Monthly/annual 

flow factors 

Sedimentation 

data 

Reservoir 

safety 

Reservoir 

water balance 

Operating 

rule scenario 

Energy 

production 

model 

Refurbishment and 

upgrade scenarios 

Source: EBRD (2012) 



Hydrological hazard forecasting 

(scientifically tractable risk reduction measure) 

Panjakent 

Fayzabad 

Somoniyon 

Rushan 

Locations of mudflows and reported flooding 5 to 11 May 2011 compared with TRMM rainfall 



Where the need is greatest

Uncertainty in hydrological models - IMAGe

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?