Laboratory of Hydrology & Water Resources Management - NTUA

1. THE “ABCD” Regional Model in the X-basin of Pikermi, Attica, Greece FLOODMED RR Workshop, 10th July 2007, Sofia, Bulgaria MAGGIE KOSSIDA Laboratory of Hydrology & Water Resources Management - NTUA

2. Purpose: use the “ABCD model” in an experimental basin in Eastern Attica Region, Greece in order to calculate the streamflow, with the overall goal of evaluating the adequacy, suitability and robustness of this proposed rainfall-runoff model The model was applied on a daily time step, calibrated for the year 2005 and validated for the year 2006 The optimum goal, to apply a regional calibration methodology to numerous Greek catchments of similar characteristics, which estimates model parameters at all sites concurrently in an effort to obtain a good fit tostreamflows at all sites while simultaneously obtaining a good fit to the relationshipbetween model parameters and watershed characteristics. Laboratory of Hydrology & Water Resources Management - NTUA

3. ABCD Basic The “ABCD” Model: • Physically based • Determinative • Lumped • Continuous • Non-linear Input data: P, T (min, max), PET Output data: Q (compared to the Qobs to evaluate the goodness of fit) Intermediate calcs: soil moisture storage, groundwater storage, direct runoff, groundwater outflow to the stream channel, actual ET Laboratory of Hydrology & Water Resources Management - NTUA

4. ABCD Scheme The model runs a series of calculations trying to simulate the different components of the hydrologic cycle using parameters a,b,c and d as fundamental Internal Model Processes along w/the controlling parameter of the ‘ABCD’ Model Model Parameters A= propensity of runoff to occur before soil is saturated B = max(ET + Soil moisture) C = baseflow index D = reciprocal of Grwater Residence time Laboratory of Hydrology & Water Resources Management - NTUA

5. ABCD Equations The model defines two state variables, Wt, termed “available water” and Yt, “evapo-transpiration opportunity” “Available water” is defined as: Pt = precipitation St-1 = soil moisture storage @ begin of t “Evapotranspiration opportunity” is water which will eventually leave the basin in the form of ET and is defined as: “Evapotranspiration opportunity” Yt is postulated as a nonlinear function of "available water" Wt using: Et = evapotr, St = soil moisture Upper limit of Wt is parameter b This function simply assures that: Laboratory of Hydrology & Water Resources Management - NTUA

6. ABCD Equations Allocation of available water between Et and St is accomplished by assuming that the rate of loss of soil moisture to evapotranspiration is proportional to the soil moisture storage, so that: Solving this differential equation and assuming St-1= Yt leads to: The difference between Wt -Yt, is also the sum of groundwater recharge and direct runoff. The parameter c allocates the quantity Wt -Yt between groundwater recharge c(Wt- Yt) and direct runoff (1- c)( Wt- Yt) Groundwater discharge to the stream channel is modeled as dGt . Groundwater storage Gt is modeled using the continuity equation. Gt at the end of period t is equal to previous storage, plus grwater recharge, less grwater outflow: Finally, streamflow Qt is the sum of direct runoff and groundwater discharge: Laboratory of Hydrology & Water Resources Management - NTUA

7. ABCD Parameters Parameter α(0≤α≤1) reflects the "propensity of runoff to occur before the soil is fully saturated" close to 1: flat topography w/low drainage density ≠ In topography with greater relief and drainage density, the value of parameter α is reduced. Urbanization and deforestation tend to decrease parameter α Parameter b reflects the maximum storage in the unsaturated zone above the ground water.The higher the value of b, the higher the resulting soil moisture storage (b is an upper limit on the sum of actual ET and St). This parameter quantifies the ability of the catchment to hold water within the upper soil horizon Laboratory of Hydrology & Water Resources Management - NTUA

8. ABCD Parameters Parameter c controls the allocation of the available water in the unsaturated zone. An amount if water will percolate into the groundwater and the remaining will flow out as direct runoff. Parameter c is reported as the Baseflow Index and is the ratio of the groundwater outflow over the streamflow. In order to estimate c a hydrograph separation method was adopted: IF (Pt-1 + Pt-2 + Pt-3) = 0, THEN Bt= MIN(Qt , Bt-1) OR ELSE Bt = Bt-1 The parameter c is then: annual baseflow/annual streamflow Laboratory of Hydrology & Water Resources Management - NTUA

9. ABCD Parameters Parameter d thereciprocal of the parameter d is equal to the average groundwater residence time. During baseflow conditions, when direct runoff is negligible and when groundwater outflow is linearly proportional to groundwater storage (Qt = dGt), streamflow follows the simple recursion Qt = Kbt . Qo , where Kb is termed the baseflow recession constant. To estimate d the longest available rainless period was selected and the logarithm of the streamflow was plotted vs the time. A best fit line was matched to the data, the slope of which represents the ln of Kb and thus the parameter d Other Parameters The last two parameters that were introduced to the model are the initial Soil Moisture Storage So and the initial Groundwater Storage Go Laboratory of Hydrology & Water Resources Management - NTUA

10. ABCD Snow Module A simple Snowmelt Model is incorporated in order to adjust the Precipitation and convert it to “Effective” Precipitation Principle: during the cold winter days Peff = 0 since the snow accumulated prevents the infiltration, while on the spring warmer days Peff accounts for the precipitation as well as the water that comes from the melting of the snow Snow Accumulation At and Snow Melt Mt are introduced to the model with IF statements Two different base temperatures are incorporated as model parameters ( Tb_melt, Tb_acc) and the following statements are valid: IF Tmean > Tb_accthen At = MAX[At-1 – Mt-1 , 0 ] else At = MAX[At-1 – Mt-1 + Pt , 0 ] IF Tmean > Tb_meltthen Mt = MIN[At , et(Tmean – Tb_melt )] else Mt = 0 The et is a new model parameter, termed the melt factor, and is a sinusoidal function of the Julian day of the year: Laboratory of Hydrology & Water Resources Management - NTUA

11. The X-Basin Study area Experimental basin of Pikermi Location: Attica prefecture, Greece Area: 15.18km2 Mean altitude: 430m (146 – 950 m) Mean slope: 21.2% (0 – 79.4%) Land use: 29.05% semi-urban (Pikermicommunity) 69.43% lowland vegetation (bushes) 0.745%forested land 0.718% earth-roads 0.047% greenhouses Geology: tectonic cracked slate, marls, limestone and conglomerates Monitoring network: 3 rain gauges (200-600m), 2 hydrometric stations (spillway, 10mins flow meter) Laboratory of Hydrology & Water Resources Management - NTUA

12. The X-Basin Study area

13. Objective Functions The “ABCD” model was calibrated for 2005and validated for 2006. The calibration was done both manually and with Excel solver tool, taken into consideration the parameters constraints mentioned. The following 7 objective functions were evaluated: • Nash-Sutcliffe Efficiency Ε • Correlation coefficientr • Model’s Bias • Z1=square real residuals • Z2=square log residuals • Z3=real space residuals • Z4=quartic real residuals Laboratory of Hydrology & Water Resources Management - NTUA

14. Calibration 2005

15. Calibration 2005 Laboratory of Hydrology & Water Resources Management - NTUA

16. Validation 2006

17. Snow Period isolated

18. Sensitivity Analysis ± 25% change in the value of each parameter Parameter α: E, r changes 1-2%. When a1, E decreases about 13% while r only 5% (not repr. O.F. due to increased bias) Parameter b: very stable, 3-5% change in E, r. Z1-Z4 not affected

19. Sensitivity Analysis ± 25% change in the value of each parameter Parameter c: r changes only 1%, while E changes 100% when c reaches boundary values (e.g. c≈1)! Proof that r is not repr. O.F., not to be examined alone!! Ideal c values are 0.72-0.88. Z1 also reaches optimum around this range. Parameter c highly influneces the model since it is related to the baseflow (allocation btw runoff/groundwater) Parameter d: not sensitive

20. Conclusions • Satisfactory calibration & validation • Robust results • Snow plays an important role in the basin, the mechanism is well captured (especially w/the isolated snow model) • ±25% changes in the parameters were shown not to alter significantly the objective functions and the model’s behaviour • Thus, it is concluded that the model’s calibration, although based on numerical optimisation, accurately represents that physical properties of the parameters and the basin characteristics Laboratory of Hydrology & Water Resources Management - NTUA

21. Further Research Regionalization of the parameters of the “ABCD” model There exists a very large number of watershed parameter sets which can produce realistic simulations. Regional calibr. provides a method for reducing the feasible subspace So far, most commonly bivariate and multivariate regression. These methods are unable to uncover basic physical laws Two-step approach: (a) estimation of watershed model parameters at each site (b) attempts to relate model parameters to drainage basin charact. Improvements in regional models can be obtained by formulating spatial theoretical relationships among watershed model parameters and landscape attributes Laboratory of Hydrology & Water Resources Management - NTUA

22. Further Research Traditional At-Site approach: treats each site independently in an effort to obtain the best possible calibration at each site. Regional Calibration approach: attempts to get the best possible calibration at each site while simultaneously obtaining the best possible regional relationships between model parameters and basin characteristics Laboratory of Hydrology & Water Resources Management - NTUA

23. Further Research Regional Regression model parameters α"propensity of runoff to occur before the soil is fully saturated“ b depends on the ability of the catchment to hold water within the upper soil horizon Runoff is expected to decrease as soil permeability increases (relation to soil characteristics) and also depend on land use pattern α = αα – βαP ± …. b = αb + βbP ± …. αα ,βα, αb, βb regional regression model parameters P permeability c fraction of streamflow which arises from groundwater discharge in a given time period c = αc + βcBFI algorithms for estimation of BFI are available (digital filtering algorithm by Nathan & McMahoq (1990) to the more theoretically based algorithm introduced by Rutledge & Daniel (1994) 1/d equals to the average groundwater residence time d = αd - βdln(Kb) Kb baseflow recession constant Laboratory of Hydrology & Water Resources Management - NTUA

24. Further Research In this case the objective is to MAXIMIZE: (Eq. I) m = # sites in the region Ri2 represents the coefficient of determination for site i which measures the goodness of fit of the logarithms of the modeled streamflows at site i Ra2, Rb2, Rc2, Rd2 represent the coefficient of determination associated w/each of the regression models for the parameters a, b, c and d given in the previous equations The idea of the objective function in Eq.I is to maximize the average goodness of fit of the "abcd" model across all sites as well as to maximize the average goodness of fit of the four regional regression models Laboratory of Hydrology & Water Resources Management - NTUA

25. Further Research • Challenges: • Find representative regional regression equation to adequately relate the model parameters to the watershed characteristics • Deal with multicolinearity among model parameters, as well as among the dependant variables in the regional regression relationships. Account for the covariance structure and spurious correlation of the watershed model parameters Laboratory of Hydrology & Water Resources Management - NTUA

26. Thank you for your attention! Laboratory of Hydrology & Water Resources Management - NTUA