1. The influence of Runoff on Recharge
Keith Beven
Lancaster University, UK

2. 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

3. Horton: Macropores and infiltration

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

5. 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.

6. 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

7. Binley and Beven, Groundwater, 2003
Application of GLUE based on SSQ criterion
Dotty plot for parameter qr in layer 4

8. 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

9. 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

10. 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

11. Field site location
Hatfield

12. - Zero Offset Profile (ZOP)
Cross Borehole Radar Profiling
- Zero Offset Profile (ZOP)
Transmitter
Antenna
Transmitter
Antenna
Receiver
Antenna
Time of first arrival measured (t ) –
allows calculation of effective relative
dielectric constant between wells
separated distance x

13. Monte Carlo Simulations
50,000 Simulations carried out using HYDRUS v6.0
(Šimunek et al, 1998)
1-D Richards Equation solution
with following parameters treated as uncertain for
4 layers in the UZ zone (to 15m) :
qr - residual moisture content
qs - saturated moisture content
a and n - van Genuchten curve parameters
Ks - saturated hydraulic conductivity

14. Weighting realisations in GLUE using effective observation error
Output from each realisation compared with observed
moisture content profile, taking into account
uncertainty in measurement
Goodness of fit
Goodness of fit
Likelihood q
qmin q
qmax

15. Weighting realisations in GLUE using effective observation error
5% & 95% uncertainty limits
Best estimate of q
Upper and lower limits of q

16. Dotty plots show behavioural parameter sets
parameter range
Goodness of fit
Goodness of fit qr qs
Goodness of fit
Goodness of fit Ks a

17. Estimate of travel times through sandstone using
uncertainty in model predictions
Weighted behavioural simulations consistent with effective observational error…… but remember assumptions of the analysis

18. 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

19. 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?

20. 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

21. 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

22. 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),
Schulz, K., and Beven, K., Data-supported robust parameterisations in land surface - atmosphere flux predictions: towards a top-down approach, Hydrol. Process., 17,
Beven, K. J., 2002, Towards a coherent philosophy for environmental modelling, Proc. Roy. Soc. Lond., A458, (comment by Philippe Baveye and reply still to appear)
Beven, K J, 2004, A manifesto for the equifinality thesis, J. Hydrology , in press