1. A hierarchical model for Hydrologically Effective Rainfall and Soil Moisture Deficit Jenny Lannon Statistician, WRc Based on PhD work at the University of Reading Supervised by: Dr. A J Wade, Dr. F M Underwood, Dr. E Black

2. The Nitrate Problem Excessive nitrate in freshwater ecosystems can lead to Eutrophication and thus a decline in water quality and biodiversity. The Nitrates Directive (91/676/EC) : Concentration level of nitrate in freshwaters should not exceed 11.3 mg NO 3 -N L -1 This may become an increasing problem under climate change Drinking water standard : 50 mg/l Ranunculus declining as a result of Eutrophication and falling flow

3. Modelling Nitrate Why? Catchment management planning To determine how the factors and processes controlling catchment freshwater quality integrate across spatial and temporal scales. Predicting future levels To predict future streamwater chemistry given projected changes in the environment, in particular the climate. INCA-N Semi-distributed conceptual hydrochemical model Requires; o Rainfall o Temperature o Hydrologically Effective Rainfall (HER) o Soil Moisture Deficit (SMD)

4. The Modelling Process Define/choose emissions scenario to run through climate model Run chosen Climate Model Run chosen ‘Downscaling’ model Temperature (coarse-scale) Rainfall (coarse-scale) Rainfall (catchment-scale) Temperature (catchment-scale) Run Hydrological Model HER SMD INCA-N Nitrate projection Run chosen ‘Downscaling’ model Sources of uncertainty

5. The Modelling Process Research currently performed by climate scientists. See IPCC Reports Established field of statistical research Uncertainty and sensitivity analysis methods researched by hydrological and hydrochemical modellers Define/choose emissions scenario to run through climate model Run chosen Climate Model Run chosen ‘Downscaling’ model Temperature (coarse-scale) Rainfall (coarse-scale) Rainfall (catchment-scale) Temperature (catchment-scale) Run Hydrological Model HER SMD INCA-N Nitrate projection Run chosen ‘Downscaling’ model

6. The Modelling Process Model structures available vary substantially for which none can be deemed ‘best’; HER and SMD are latent variables Define/choose emissions scenario to run through climate model Run chosen Climate Model Run chosen ‘Downscaling’ model Temperature (coarse-scale) Rainfall (coarse-scale) Rainfall (catchment-scale) Temperature (catchment-scale) Run Hydrological Model HER SMD INCA-N Nitrate projection Run chosen ‘Downscaling’ model No general consensus over how to model water transportation

7. Hydrological Models for HER and SMD SMD: The amount of water required for the catchment to reach field capacity HER: The amount of rain which enters the river system (the catchment) after losses from evaporation and transpiration and replenishment of SMD have been taken into account.

8. Hydrological Models for HER and SMD SMD: The amount of water required for the catchment to reach field capacity HER: The amount of rain which enters the river system (the catchment) after losses from evaporation and transpiration and replenishment of SMD have been taken into account. Existing Models MORECS – Complex model for soil and evaporation run and exclusively owned by Met Office. HBV – Complex Rainfall-Runoff model developed for Nordic regions. IHACRES – Simple Rainfall-Runoff model created by the Centre of Ecology and Hydrology. All involve pre-defined process relationships Do estimates of HER and SMD vary between these models?

9. Hydrologically Effective Rainfall (HER)

10. Soil Moisture Deficit (SMD) Do these differences affect nitrate projections?

11. INCA-N projections of Nitrate YES!

12. AIM To construct a hydrological model for HER and SMD specifically to use in conjunction with hydrochemical models including INCA-N. The model should be able to replace all existing models by possessing a reliable model structure derived through statistical relationships.

13. Model formulation Daily data available from a single farm in the Lambourn catchment, South-East England. Rainfall Temperature Soil Moisture Actual Evapotranspiration (AET). Very rare data. SMD and HER are latent variables to be estimated from these data.

14. Daily data available from a single farm in the Lambourn catchment, South-East England. Rainfall Temperature Soil Moisture Actual Evapotranspiration (AET). Very rare data. SMD and HER are latent variables to be estimated from these data. Standard equations; FC = Field Capacity Model formulation

15. Physical relationships between fundamental variables Day t+1 SMD =FC - SM HER AET Temp Rain Day t SMD =FC – SM HER AET Temp Rain Blue nodes: Input. Yellow: Response Variables Hierarchical Statistical Model

16. Model Specification Be constructed as a hierarchical statistical model with response variables of AET and soil moisture. Model fit should be assessed using observations on these two variables. Use rainfall and temperature as input. Estimate HER and SMD through the standard equations which relate to their exact definitions. Posses a model structure which is physically interpretable but developed using only statistically significant relationships. Be parsimonious; sufficient detail and complexity should be incorporated in order to model system behaviour accurately whilst ensuring that the model structure is simple to interpret and utilise. Be constructed in a Bayesian framework using MCMC methods thus being able to supply output information on uncertainty in model estimates. Operate on a daily time-step.

17. AET Negative values do not make sense physically Highly cyclic Consistent between years

18. AET General linear model (Normal) with the following covariates: Daily temperature ‘Wet’ indicator (yes or no on a daily basis) First order Fourier series harmonics Model predictions/fitted values restricted to be >= 0 Vague priors assigned to all parameters

19. Soil Moisture Cyclic Positive values only

20. Soil Moisture Cyclic Positive values only A possible upper and lower plateau? Upper: Field Capacity, Lower: Wilting Point?

21. Soil Moisture Gamma Generalised Linear Model with 2 hierarchical levels; Level One covariates: Wilting Point (WP) Field Capacity (FC) Total rainfall over previous 7 days Average rainfall over pervious 90 days Level Two covariates: Daily rainfall AET First order Fourier series harmonics Vague priors assigned to all parameters except WP and FC

22. Final Model Generalised Linear model with 3 hierarchical levels; AET is first hierarchical level Soil moisture is second and third hierarchical levels Fitted values from AET model feed into linear predictor of soil moisture model Soil moisture AET Temp Rain Model run in WinBUGS Parameter posterior distributions obtained from 100,000 values

23. Model Output: Fitted Means

24. Model Output: Predicted Values

25. Model Output: SMD

26. Model Output: HER

27. Comparison with Existing Models: Nitrate concentration

28. Comparison with Existing Models: Nitrate Load

29. Conclusions Parameter uncertainty in the BHM caused greatest uncertainty in modelled streamwater nitrate concentrations during autumn, although this was never greater than 1 mg N l -1 INCA-N is sensitive to the choice in hydrological model used Hydrological model should represent HER, SMD and AET as accurately as possible to reduce uncertainty in nitrate projections In most cases, the constructed hierarchical statistical model provides the most suitable choice in model through its well-appointed model structure and construction to observed data. Model structure not logical for chalk soils but this has little effect on the resulting nitrate predictions.