1. Example of conceptual land-atmosphere model Land atmosphere interaction – conceptual model exercise Bart van den Hurk (KNMI/IMAU)

2. Example of conceptual land-atmosphere model Last week Explore the thermal coupling For instance: Look for a relationship between u and skin conductivity that has roughly the same  T a /  t using –  air = 1 (switching off radiation response) –T a -T soil = 10K (initial gradient)

3. Example of conceptual land-atmosphere model L F in E R P ds/dt Layout of a conceptual land-atmosphere hydrology model F out

4. Example of conceptual land-atmosphere model uw / L +  E = E pot s c R =  Ps r P = 0.5  (s) (uw/L + E) ds/dt = (P-E-R)/D Layout of a conceptual land-atmosphere hydrology model Stochastic forcing residual  = evaporative fraction Q* = net radiation  = precip.efficiency  = runoff efficiency D = soil depth L = horizontal length scale uw = wind speed  atm.moisture r, c = coefficients

5. Example of conceptual land-atmosphere model Stochastic Differential Eq (SDE) G = drift term (gains and losses by P, E, R) gr = random term r = Gaussian number with variance 1 and mean 0 stochastic (forcing) term Discretization and rewriting leads to

6. Example of conceptual land-atmosphere model Column structure … F in +  E R P ds/dt E R P F out = F in E R P ds/dt F out = F in i=1 i=2 i=n

7. Example of conceptual land-atmosphere model Parameterization of , E, R Precipitation efficiency  (s) = a s + b Evaporation E(s) = E pot s c E pot (i) = linear interpolation between E pot (1) and E pot (n) i = column number, n = nr of columns Runoff R =  P s r

8. Example of conceptual land-atmosphere model Code list REALRAEFF0.0 / 0.2! coefficient A in PrecEff = A s + B REALRBEFF0.3 / 0.2! coefficient B in PrecEff = A s + B REALRUW200.! advection U x W (m/s kg/m2 = kg/m s) REALRLEN1000000! horizontal length scale (m) REALRSDEV0.1! Standard deviation of stochastic term ! on UW/L (fraction) REALRAEPOT1.! Epot at first column (m/yr) REALRBEPOT2.! Epot at last column (m/yr) REALRECOF0.5! Coefficient c in E = Epot s^c REALRR0.1! Coefficient r in R = e P s^r REALREPSIL0.1! Coefficient e in R = e P s^r (runoff ! efficiency) REALRSDEP0.5! Storage reseroir depth (m) REALRTIME0.0001! Time step length (yr) REAL RZCR0.01! soil saturation below which red noise is ! restricted to postive values REAL RSTMAX1! clipping value of zst REAL RYEAR10! Number of years to simulate INTEGERNCOL10! nr of adjacent columns INTEGER NPPSTEP1000! output interval (nr of steps) weak / strong

9. Example of conceptual land-atmosphere model Weak coupling between s and 

10. Example of conceptual land-atmosphere model Strong coupling between s and 

11. Example of conceptual land-atmosphere model Soil moisture evolution weak strong

12. Example of conceptual land-atmosphere model More information Bart van den Hurk –hurkvd@knmi.nl –www.knmi.nl/~hurkvd