The influence of Runoff on Recharge

Keith BevenLancaster University, UK

The problem of recharge estimation• Overall water balance constraint

recharge = rainfall – evapotranspiration – runoff (+ runoff recharge)

• But….Not easy to estimate surface and near-surface runoff

• Not easy to estimate evapotranspiration where non-homogeneous surfaces

• Not easy to estimate recharge from soil moisture characteristics (gradients may be near unity at depth but predicted recharge will depend heavily on estimate of hydraulic conductivity)

• May be significant short term dynamic recharge events due to preferential flows associated with a small number of storms in a year at same time as runoff

Horton: Macropores and infiltration

Infiltration into real soils (after Flury et al., WRR, 1994)

The problem of recharge estimation• Traditional split between surface and groundwater

hydrologists

• Surface water hydrologists calibrate on stream discharges as the flow constraint (and have tended not to worry too much about spatial patterns)

• Groundwater hydrologists calibrate on patterns of water table measurements (often averaged to “steady” conditions) with (uncertain) estimates of recharge as a flow constraint

• Distributed catchment models have integrated both – but effects are not easily separated out, there are multiple sources of uncertainty, constraints are limited, and calibration is difficult.

A paradox ………

• Generally, the more physical understanding that is built into a model, the more parameter values must be specified to run the model

• The more parameter values that cannot be estimated precisely, the more degrees of freedom that will be available in fitting the observations (we cannot measure effective parameter values everywhere).

• Therefore the more physical understanding that is built into a model, the greater the problem of equifinality is likely to be.

• A “perfect” model with unknown parameters is no protection against equifinality

Binley and Beven, Groundwater, 2003Application of GLUE based on SSQ criterion

Dotty plot for parameter r in layer 4

0.00088

0.00090

0.00092

0.00094

0.00096

0.00098

0.00100

0.00102

0.00104

0.025 0.03 0.035 0.04 0.045 0.05 0.055

Parameter

L

Equifinality and the Modelling Process

• Take a (thoughtful) sample of all possible models (structures + parameter sets)

• Evaluate those models in terms of both understanding and observations in a particular application

• Reject those models that are non-behavioural (but note that there may be a scale problem in comparing model predictions and observations)

• Devise testable hypotheses to allow further models to be rejected

• [If all models rejected, revise model structures……]

This is the essence of the GLUE methodology

Deconstructing total model error

• Extended GLUE methodology– insist on model providing predictions within

range of “effective observation error” of evaluation variables

– specify an effective observation error to take account of scale dependencies and incommensurability

– models providing predictions outside range are rejected as non-behavioural (all models may be rejected)

– success may depend on allowing realisations of error in input and boundary condition data

Example Application: Modelling Recharge to the Sherwood Sandstone (with Andrew Binley)

• Large scale estimates of change in water contents over time using cross-borehole electrical resistance and radar tomographic imaging

• What are the scale dependent effective parameters if recharge is to be predicted by a 1-D Richards equation model when potential gradients vary due to heterogeneity?

• Conditioning on observations based on GLUE Monte Carlo methodology and model rejection when outside the range of effective observational error

Hatfield

Field site location

TransmitterAntenna

TransmitterAntenna

ReceiverAntenna

Cross Borehole Radar Profiling - Zero Offset Profile (ZOP)

Time of first arrival measured (t ) – allows calculation of effective relative dielectric constant between wells separated distance x

txr

3.0

50,000 Simulations carried out using HYDRUS v6.0(Šimunek et al, 1998)

1-D Richards Equation solutionwith following parameters treated as uncertain for

4 layers in the UZ zone (to 15m) :

r - residual moisture contents - saturated moisture content

and n - van Genuchten curve parametersKs - saturated hydraulic conductivity

Monte Carlo Simulations

maxmin

Likelihood

Weighting realisations in GLUE using effective observation error

Output from each realisation compared with observedmoisture content profile, taking into accountuncertainty in measurement

max

max

Emin

min

E

Goodness of fit Goodness of fit

2

3

4

5

6

7

8

9

10

0 0.1 0.2 0.3

(m3 m-3)

Dep

th (

m)

5% & 95% uncertainty limits

Best estimate of

Upper and lower limits of

Weighting realisations in GLUE using effective observation error

Dotty plots show behavioural parameter sets

0.0

0.2

0.4

0.6

0.8

1.0

0 0.02 0.04 0.06 0.08 0.10.0

0.2

0.4

0.6

0.8

1.0

0.27 0.28 0.29 0.3 0.31 0.32 0.33

0.0

0.2

0.4

0.6

0.8

1.0

0 0.02 0.04 0.06 0.08 0.1 0.12 0.140.0

0.2

0.4

0.6

0.8

1.0

0.1 1 10 100 1000

parameter range

r s

s

Good

ness

of

fit

Good

ness

of

fit

Good

ness

of

fit

Good

ness

of

fit

0.00

0.25

0.50

0.75

1.00

2.5 3.0 3.5 4.0 4.5 5.0

Travel time (years)

Cum

ula

tive L

ikelihood

Estimate of travel times through sandstone usinguncertainty in model predictions

Weighted behavioural simulations consistent with effective observational error…… but remember assumptions of the analysis

The Importance of Spatial Patterns

Surface hydrologists have recognized the importance of spatial patterns of runoff generation, particularly as driven by topography (e.g. TOPMODEL, SHE, InHM, POWER, ……)

But numerical experiments suggest that even small rates of recharge to deeper layers can dramatically influence patterns of wetness

5

7

9

11

13

15

ln(a / tanB)

The Importance of Spatial Patterns

Spatial patterns of evapotranspiration will also influence net recharge

• Use of remote sensing & energy balance closure to estimate patterns of land surface to atmosphere fluxes

• Greater ET fluxes in valley bottoms……

• But is there also greater recharge in valley bottoms?

The Importance of Spatial Patterns

Recharge by river bed infiltration

• LOCAR catchments: pattern of gaining and losing reaches

• Flood plains as subsurface recharge as well as surface water storage areas during periods of overbank flow where floods generated by upstream rainfall

Summary• Spatial patterns are important:

– In infiltration, surface and subsurface runoff generation, and reinfiltration

– In evapotranspiration

– In river bed recharge

• Data are not adequate to properly calibrate models: there are too many sources of uncertainty, including inputs and representation of processes

• Complex models may not necessarily give more robust predictions than simple models

• Thus, prediction of change under future conditions will be even more uncertain, and it might be dangerous to rely on deterministic predictions

and if you might possibly still want to read more…...

• Binley, A and Beven, K J, 2003, Vadose zone model uncertainty as conditioned on geophysical data, Ground Water, 41(2), 119-127.

• Schulz, K., and Beven, K., 2003. Data-supported robust parameterisations in land surface - atmosphere flux predictions: towards a top-down approach, Hydrol. Process., 17, 2259-2277.

• Beven, K. J., 2002, Towards a coherent philosophy for environmental modelling, Proc. Roy. Soc. Lond., A458, 2465-2484 (comment by Philippe Baveye and reply still to appear)

• Beven, K J, 2004, A manifesto for the equifinality thesis, J. Hydrology , in press