Land atmosphere interaction – introduction and a conceptual model

1. Land atmosphere interaction – introduction and a conceptual model Bart van den Hurk (KNMI/IMAU) Land atmosphere interaction and conceptual model

2. Last time assignment • Identify a new topic that involves land use-climate feedback, and describe the feedback processes using the diagram qualitatively, e.g. • green roofs in cities • irrigation • crop disease • ... Land atmosphere interaction and conceptual model

3. Definition of feedback • According to Oxford Dictionary • 1 information given in response to a product, performance etc., used as a basis for improvement. • 2 the modification or control of a process or system by its results or effects. • 3 the return of a fraction of the output of an amplifier, microphone, or other device to the input, causing distortion or a whistling sound. • Negative/positive feedback • output damps/amplifies the process generating the output Land atmosphere interaction and conceptual model

4. Thermal land-atmosphere coupling Q* H G • Typical nighttime surface energy balance: • The surface temperature takes value closing the energy balance. Determined by: • radiative input • radiative & turbulent cooling to atmosphere • diffusion of heat into soil Land atmosphere interaction and conceptual model

5. Feedback of surface energy balance • In most occasions: • Ts is strongly coupled to atmosphere (high wind speed) and/or soil (efficient conduction of heat) • Special conditions: ‘runaway’ surface temperature • weak winds • low turbulence due to stable stratification • strong radiative cooling (clear sky) • Feedback loop: • low L and H  low Ts  large Ta – Ts  stable stratification  poor turbulent coupling (low H)  low near surface air temperature Land atmosphere interaction and conceptual model

6. A simple surface energy balance Q* H G • See spreadsheet • Ta(t) = aTa(t-t) + (1-a)Ts • Q* = L - Ts4 = H + G • L = a Ta4 • H = cpUCH(z/L) (Ts – Ta) • z/L = f(Ts-Ta, u) (stability) • G = (Ts – Tsoil) • Tsoil(t) = sTsoil(t-t) + (1-soil)Ts Land atmosphere interaction and conceptual model

7. Hydrological land-atmosphere coupling • In typical mid-latitude climate: soil moisture is resulting from P – E balance, E is mainly energy limited • In dry warm summers, E can become moisture limited • Feedback loop: • low precipitation  low soil moisture  low evaporation  low precipitation • Requires • sensitivity of evaporation to soil moisture • sensitivity of precipitation to evaporation Land atmosphere interaction and conceptual model

8. When strong positive hydrological feedback likely? ET→P W→ET climate transition zones sensitivity Arid Humid wet dry Land atmosphere interaction and conceptual model

9. Areas with strong feedback Koster et al, Science, 2004 Land atmosphere interaction and conceptual model

10. Precipitation efficiency and recycling ratio • Precipitation efficiency • How much of the water passing an area is actually raining out? • Multiple definitions: Land atmosphere interaction and conceptual model

11. Precipitation efficiency and recycling ratio • Recycling ratio • How much of the total precipitation originates from local evaporation? • Budget equation: Land atmosphere interaction and conceptual model

12. Some examples p = 83%  = 17% p = 22%  = 8% p = 28%  = 11% Land atmosphere interaction and conceptual model

13. Global distribution Trenberth, J.Climate, 1999 Land atmosphere interaction and conceptual model

14. A Lagrangian approach P = Pa + Pl  = Pl/P E = Ea + El  = El/E El = Pl • Subdivide into continental and ocean source/sink, P = Pc + Po E = Ec + Eo • and trace water via Lagrangian (trajectory following) buget equation: Pa = advected P Pl = originating from local E Ea = E leaving domain El = E staying within domain R = recycling ratio E = evaporation L = integration length scale x = grid box length t = model time step q = column water content (Dominguez et al, 2006) Land atmosphere interaction and conceptual model

15. Continental sources/sinks mean moisture flux Van der Ent et al, 2010 Land atmosphere interaction and conceptual model

16. Layout of a conceptual land-atmosphere hydrology model Fin Fout P R E ds/dt L Land atmosphere interaction and conceptual model

17. Layout of a conceptual land-atmosphere hydrology model Stochastic forcing P = 0.5 g(s) (uw/L + E) uw / L + s residual R = ePsr E = Epot sc • = evaporative fraction Q* = net radiation • = precip.efficiency • = runoff efficiency D = soil depth L = horizontal length scale uw = wind speed  atm.moisture r, c = coefficients ds/dt = (P-E-R)/D Land atmosphere interaction and conceptual model

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

19. Column structure Fout = Fin Fin +  Fout = Fin Fout = Fin P P P … E E E R R R ds/dt ds/dt ds/dt i=n i=1 i=2 Land atmosphere interaction and conceptual model

20. Parameterization of , E, R • Precipitation efficiency (s) = a s + b • Evaporation E(s) = Epot sc Epot(i) = linear interpolation between Epot(1) and Epot(n) i = column number, n = nr of columns • Runoff R = P sr Land atmosphere interaction and conceptual model

21. Code list weak / strong REAL RAEFF 0.0 / 0.2 ! coefficient A in PrecEff = A s + B REAL RBEFF 0.3 / 0.2 ! coefficient B in PrecEff = A s + B REAL RUW 200. ! advection U x W (m/s kg/m2 = kg/m s) REAL RLEN 1000000 ! horizontal length scale (m) REAL RSDEV 0.1 ! Standard deviation of stochastic term ! on UW/L (fraction) REAL RAEPOT 1. ! Epot at first column (m/yr) REAL RBEPOT 2. ! Epot at last column (m/yr) REAL RECOF 0.5 ! Coefficient c in E = Epot s^c REAL RR 0.1 ! Coefficient r in R = e P s^r REAL REPSIL 0.1 ! Coefficient e in R = e P s^r (runoff ! efficiency) REAL RSDEP 0.5 ! Storage reseroir depth (m) REAL RTIME 0.0001 ! Time step length (yr) REAL RZCR 0.01 ! soil saturation below which red noise is ! restricted to postive values REAL RSTMAX 1 ! clipping value of zst REAL RYEAR 10 ! Number of years to simulate INTEGER NCOL 10 ! nr of adjacent columns INTEGER NPPSTEP 1000 ! output interval (nr of steps) Land atmosphere interaction and conceptual model

22. Weak coupling between s and  Land atmosphere interaction and conceptual model

23. Strong coupling between s and  Land atmosphere interaction and conceptual model

24. Soil moisture evolution weak strong Land atmosphere interaction and conceptual model

25. Summary • Response (one factor affecting another) feedback (closed loop of responses) • Land-atmosphere feedback at multiple time/space scales • Relevant domains: • Carbon-climate feedback • Land use – climate feedback • Thermal coupling • Hydrological coupling • ... • Conceptual model oversimplifies but allows systematic exploration Land atmosphere interaction and conceptual model

26. Next week (mandatory!) • Prepare an experimental set-up using the conceptual model • Write down, hand over to me (will be commented), add student nr • Criteria • Should be inspired by a “true” physical question • Should include at least 2 experiments • Should describe the analysis method and conclusions expected • Example: • Strong/weak coupling affects the gradient of precipitation more than the gradient of soil moisture Land atmosphere interaction and conceptual model

27. More information • Bart van den Hurk • hurkvd@knmi.nl • www.knmi.nl/~hurkvd Land atmosphere interaction and conceptual model