WATER USES and AVAILABLE RESOURCES DEMAND Estimating the demand (domestic and industrial) implies generally to determine a daily equivalent discharge that includes all the uses, cumulated and averaged over the population amount. Q= Q* [liter per day per person] One should additionally account for: Variability of the demand in a given period (e.g., day, season) Changes over the long-term Quality and quantity constraints (e.g., preservation of riparian ecosystems) SURFACE WATER and GROUNDWATER The demand can be satisfied by exclusive of joint use of surface and ground water resources. Constraints Q < Q W The correct partitioning should take into account: Minimisation of the risk of excessive abstraction Fluctuation of the surface resource Quality/conservation constraints (e.g., salt intrusion)
WATER DEMAND SWITZERLAND Source: http://www.naturalsciences.ch/topics/water/water_exploitation
WATER DEMAND (individuals) SWITZERLAND USA 280 lcd
WATER DEMAND (communities) SWITZERLAND Developed countries 500-800 liters per day per person Developing countries 60-150 liters per day per person Large Cities 300-600 liters per day per person Small cities 100-150 liters per day per person In regions with insufficient water resources 20-60 liters per day per person Source: UNESCO, 2000
WATER DEMAND (World comparison) [m 3 per year per person] *2.73 à [liter per day per person] Domestic Industrial Source: Eurostat data
SOURCES OF WATER SUPPLY Type of resource and water derivation Continuous SURFACE WATER GROUNDWATER Without river regulation With river regulation Artesian aquifers Phreatic aquifers Selective Lakes (regulated) Reservoirs
WATER USES and AVAILABLE RESOURCES Example: MULTIPURPOSE RESERVOIR DESIGN
QUANTITATIVE EVALUATION OF WATER DEMAND REFERENCE TIME SCALES: Annual Seasonal Monthly DEMAND for WATER SUPPLY Method based on the analysis of population growth Ø Equivalent daily discharge Q* [liters per day per person] Ø Population size [persons] WD = Q* x P DEMAND for IRRIGATION Method based on PET/AET Method based on PET/AET and the regulating function of agricultural soils
POPULATION GROWTH MODEL Based on growth curves that accounts for population development 1.2 K, Saturation, Carrying capacity P, Population 1 0.8 0.6 0.4 0.2 a b P c P dp/dt dp dt 0 0 20 40 60 80 100 120 t, Time a à b P = P exp( r t) b à d d à e 0 P P + r t d = 0 = K - ( K - P ) exp( - r t) P 0 e a à b b à d dp = dt dp = dt dp dt dp dt rp d à e = r( K - P) r K r = Geometric progression Arithmetic progression Geometric saturation GENERAL EXPRESSION rp ( K - P) Growth rate Carrying capacity These approximate models are typically adopted for relatively short term predictions ( 10 years)
POPULATION GROWTH MODEL For time horizons longer than 10 years the complete solution of logistic curve is used: P, Population 1.2 1 0.8 0.6 0.4 0.2 P 0 0 20 40 60 80 100 120 t, Time Maximum growth rate at: Saturation level: t = 100P S p K - ln ( s) q P K = 1+ exp(ln s q = = K - P P rk 0 æ100 - S ç è S p ( s) 0 - qt) 1 at: P = K / 2 0 50 100 Time = p ln = ln ( s ) - qt ö ø Saturation level 100 80 50 10 P (*) Equivalent: KP e rkt = 0 K + P ( rkt 0 e -1) Estimation of K and q by means of least squares, for known P(t 1 ) à S p1 =100 P(t 1 )/K à (*) with t=t 1
MONTHLY WATER BALANCE (THORNTHWAITE) ( S( t + Dt) S( t) ) P = R + ET + - Thornthwaite Potential Evapotranspiration a æ10ta, i ö E P, i = 16bi ç a è I ø ( I ) = 0.016I + 0. 5 ( I ) I = 12 å i= 1 æ ç è T a, i 5 ö ø 1.514 Rough assumption R= 0 if PET > P D= PET- AET Hydrologic deficit depends on the evapotranspiration law only
MONTHLY WATER BALANCE Runoff ( S( t + Dt) S( t) ) P R + ET + - = Water Balance equation Rainfall Storage Evapotranspiration o o o Actual evapotranspiration AET (E a ) can be less than potential evaporation PET (E p ) Storage variation depends on the characteristic of the soil especially on its capability to release water to satisfy the evapotranspiration Actual evapotranspiration and water balance are strongly influenced by the soil regulating function Sensitivity of water balance (water availability) to soil controls on water fluxes
SOIL REGULATING FUNCTION General behaviour Actual Evaporation b R E b = a E p R = f b ( q) R 1 0 0 θ r Residual Water Content θ soil Threshold water content q θ sat Saturated Water Content
MONTHLY WATER BALANCE (modified Thornthwaite method) 1/3 ( S( t + Dt) S( t) ) P = R + ET + - Computation of Hydrologic Deficit The time origin is considered to be the beginning of the dry season when P < E P L( t) P( t) - E ( t) = Water volume potentially released by the soil during the P dry season (L<0). Negative number. B( t) = Sinit - S( t) B( t) E( t) - P( t) Water volume effectively released by the soil during the dry season from its origin (B>0). Positive number. Sinit Initial storage at the beginning of dry season =!! Remember dry season when P < E P - db dt dl dt = æ ç è S S max ö ø m!! Hypothesis water is released (evaporation occurs) proportionally to the degree of saturation of the soil
MONTHLY WATER BALANCE (modified Thornthwaite method) 2/3 Governing equation for soil water storage and evapotranspiration processes - db dt dl dt = æ ç è S S max ö ø m a = æ ç è S( t) S max ö ø l = æ ç è L( t) S max ö ø da = dl a m Initial conditions S init = S max a init = 1 Integrating: Case 1 m = 0 d a = dl d( E ( t) - P( t) ) = d( E ( t) P( t) ) E a = E p a p - Unconditional release
MONTHLY WATER BALANCE (modified Thornthwaite method) 3/3 Case 2 m = 1 a = a init e l Case 3 m ¹ 1 a 1 = init m 1- [ ] 1-m a + ( 1- ) l m m = 3 m = 1.5 m = 0 m = 1 λ Increasing (negatively) means progressing of the drying season and therefore less storage is available and less water can be used for evapotranspiration.
PARAMETER m vs SOIL CHARACTERISTICS (mod. Thornthwaite) 2.50 2.5 2.00 2.0 1.50 1.5 m [-] 1.00 m [-] 1.0 0.50 0.5 0.00 0.0-0.50 170.00 220.00 270.00 320.00 370.00 420.00 Field capacity [mm] -0.5 10 12 14 16 18 20 22 24 Wassergehalt [% Vol] 7.00 6.00 5.00 m [-] 4.00 3.00 2.00 1.00 0.00 0.00 50.00 100.00 150.00 200.00 250.00 Field capacity [mm]
HYDROLOGIC DEFICIT FROM ET (FAO method) 1/5 Reference (ET O ) crop evapotranspiration under standard (ET C ) and non-standard conditions (ET C,adj ) FAO suggest the use of Penman-Monteith equation to compute Epot (ET O ) potential evapotranspiration. Deficit = ET 0 (1 - K s K c,adj ) FAO CROP EVAPOTRANSPIRATION BOOK: http://www.fao.org/docrep/x0490e/x0490e00.htm
HYDROLOGIC DEFICIT FROM ET (FAO method) 2/5
HYDROLOGIC DEFICIT FROM ET (FAO method) 3/5
HYDROLOGIC DEFICIT FROM ET (FAO method) 4/5
HYDROLOGIC DEFICIT FROM ET (FAO method) 5/5
QUANTITATIVE EVALUATION OF WATER AVAILABILITY o Reference Time Scales (for planning): Annual Seasonal /Monthly o Annual streamflow modelling (simple conceptual watershed model) o Monthly streamflow modelling (simple conceptual watershed model, time series analysis and stochastic modelling)
A SIMPLE WATERSHED MODEL FOR ANNUAL STREAMFLOW SIMULATION
THE abc MODEL - ANNUAL STREAMFLOW SIMULATION Input: (P t ) State Variable: (GS t ) Output: (E t, Q t ) o Estimation of parameters by trial and error or by optimization of some objective function. o It requires joint observation of precipitation and streamflow.
THE abc MODEL SIMPLIFIED Input: (P t ) State Variable: (S t ) Output: (E t, Q t )
PHYSICAL PLAUSIBILITY of the abc MODEL By manipulating Q t one can obtain:
A SIMPLE WATERSHED MODEL FOR SEASONAL STREAMFLOW SIMULATION
THE abc MODEL - SEASONAL STREAMFLOW SIMULATION Input: P t PET t State Variable: SM t GS t Output: (AET t, Q t ) Parameters: a,c,d, SM*, FC (Field capacity) 0< a < 1 0< c < 1 0< c+d <1 Estimation of parameters by trial and error or by optimization of some objective function.
THE abc MODEL - SEASONAL STREAMFLOW SIMULATION Snow accounting Input: P t PET t State Variable: SM t GS t Output: (AET t, Q t ) Parameters: a,c,d, SM*, FC (Field capacity) 0< a 1 +a 2 < 1, a 2 = 0 in summer 0< b < b* 0< c < 1 0< c+d <1 Estimation of parameters by trial and error or by optimization of some objective function.