Surface Stress and Mixing in Small Sheltered Boreal

Surface Stress and Mixing in Small, Sheltered Boreal Lakes 6 th Workshop on Parameterization of Lakes in NWP and Climate Modelling Toulouse, 22 -24 October 2019 Murray D. Mac. Kay, Zen Mariani Science and Technology Branch Environment and Climate Change Canada Experimental Lakes Area, Canada

Canadian Small Lake Model L 239, Experimental Lakes Area Standard run BIAS -0. 15 o. C RMSE 0. 59 o. C 25 Ts (o. C) 20 15 10 19 July ? ? 8 Aug 28 Aug 17 Sept 2013 7 Oct 27 Oct

Canadian Small Lake Model L 239, Experimental Lakes Area obs CSLM 17 19 21 July 2013 23 25

• Internal boundary layer (IBL) due to sudden change in roughness at shore • Surface stress varies with fetch Figure 1: Theoretical IBL depths (a) and surface stress (b) as a function of fetch for the rough – to – smooth transition case of Bradley (1968). Solid curves – Panofsky and Townsend (1964) approach; dashed curves – Jensen (1978) approach with A=1 (thick dash) and A=2 (thin dash) as indicated. Error bars in (b) represent the range of observed values from Bradley (1968), and surface stress values are normalized by the upstream value. Mac. Kay, M. D. : Incorporating Wind Sheltering and Sediment Heat Flux into 1 -D Models of Small Boreal Lakes: A Case Study with the Canadian Small Lake Model V 2. 0, Geosci. Model Dev. 12, 3045 -3054, 2019.

L 239 d (m) IBL depth grass τ0/τ- shrub forest L 239 • Forested • Mean fetch: 737 m • Predicted IBL depth: 75 m – 140 m • Mean fetch: 737 m • Mean stress ratio: 0. 1 • Asymptotic stress ratio: 0. 2 Stress reduction factor: 0. 5 Fetch (m) Figure 2: Theoretical IBL depths (a) and surface stress (b) as a function of fetch over water for a rough – to – smooth transition (off shore flow) forested landscapes (black curves, M=6. 9); shrubland (blue curves, M=4. 6), and grassland (red curves, M=2. 3). Solid curves – Panofsky and Townsend (1964) approach; dashed curves – Jensen (1978) approach with A=1 (thin dashed), and A=2 (thick dashed). Surface stress values are normalized by the upstream value. Thin horizontal lines represent equilibrium downstream values proposed by Jensen (1978) for downstream surface Rossby number Ro=108. Mac. Kay, M. D. : Incorporating Wind Sheltering and Sediment Heat Flux into 1 -D Models of Small Boreal Lakes: A Case Study with the Canadian Small Lake Model V 2. 0, Geosci. Model Dev. 12, 3045 -3054, 2019.

Canadian Small Lake Model L 239, Experimental Lakes Area

Canadian Small Lake Model L 239, Experimental Lakes Area Standard run Sheltered run BIAS -0. 15 o. C -0. 13 o. C RMSE 0. 59 o. C 0. 52 o. C 25 Ts (o. C) 20 15 10 19 July better 8 Aug 28 Aug 17 Sept 7 Oct 27 Oct

Canadian Small Lake Model T (o. C) h (cm) L 239, Experimental Lakes Area Ice Thickness 10 0 1 m Temp 5 4 3 2 1 6 Nov 11 Nov 16 Nov 2013 21 Nov

Ice Thickness 0 5 4 3 2 1 T (o. C) h (cm) 10 1 m Temp 12 Nov 25 Nov 8 Nov 6 Nov 12 Nov 11 Nov 25 Nov 16 Nov 2013 21 Nov 8 Nov

• Forested shoreline not simply a change in roughness • Impact of large change in displacement height, canopy dynamics important • Numerous LES, wind tunnel, and (a few) field observations support this

Wind Tunnel Studies Driver and Seegmiller, 1985, AIAA. The solid backward facing step Reattachment XR ≈ 6 h Fig. 6 Flow over solid BFS. Contours of normalized mean streamwise velocity and streamlines resulting from LDV profile measurements. a Full dataset, and b zoomed to details of separation region just downwind of the canopy edge. A grey box illustrates the location of the solid step. Data from Driver and Seegmiller

Wind Tunnel Studies Driver and Seegmiller, 1985, AIAA. The solid backward facing step Fig. 7 Solid BFS turbulent flow fields. Turbulence fields from LDV profile measurements for: a turbulence intensity, b and Reynolds stress distribution. A grey box illustrates the location of the solid step. Data from Driver and Seegmiller

Wind Tunnel Studies Markfort et al. 2014, Environ. Fluid Mech. The canopy backward facing step Fig. 8 Canopy BFS flow fields. Contours of normalized mean streamwise velocity and streamlines resulting of ensemble averaged PIV velocity measurements over and downwind of the canopy edge combined with x-wire profiles. The velocity measurements are normalized by the freestream velocity, U 0. a Full dataset and, b) zoomed to details of separation region just downwind of the canopy edge. A thick black line outlines the edge and top of the canopy

Wind Tunnel Studies Markfort et al. 2014, Environ. Fluid Mech. The canopy backward facing step Fig. 9 Canopy BFS turbulence fields. a Turbulence intensity and b Reynolds shear stress distribution in the x–z plane from combined fields of ensemble averaged PIV and x-wire measurements. A black line outlines the edge and top of the canopy

Surface stress Markfort et al. 2014, Environ. Fluid Mech. Mac. Kay, M. D. , 2019, Geosci. Model Dev. Rough to smooth transition from Bradley (1968) and theoretical models. Fig. 16 Surface shear stress distribution (measured with Preston tube); with an exponential fit following Eq. (12), behind a solid BFS (gray solid line, R 2 = 0. 85), [21] and a canopy BFS (black solid line, R 2 = 0. 95); and power law fit behind a solid BFS (black dashed line, R 2 = 0. 99). The zero-crossing corresponds to the reattachment of the flow at x = XR

Large Eddy Simulations Kanani-Suhring and Raasch, 2017, BLM Fig. 3 Streamwise vertical slices of: mean streamwise and vertical velocity components, a u and b w, respectively, from simulations LAI 2 (left) and LAI 8 (right).

Large Eddy Simulations Schlegel et al. 2015, BLM. Very detailed 3 -d canopy structure Very small clearing: 3 hc = 90 m Fig. 4 Dimensionless mean velocity vector (U, V, W) in the plane Y = 0. Colouring of the vector depicts the lateral velocity component (V), with red indicating positive (northward) and blue negative (southward) motion.

Large Eddy Simulations Schlegel et al. 2015, BLM. Fig. 9 Normalized turbulent kinetic energy K. The coordinates and values are normalized according to Eqs. 10 and 13. Colouring depicts the PAD values. a Vertical slice at Y = 0. b Horizontal slice at Z = 0. 3

Large Eddy Simulations Schlegel et al. 2015, BLM. Fig. 10 Normalized Reynolds stress Rxz. The coordinates and values are normalized according to Eqs. 10 and 12. Colouring depicts the PAD values. a Vertical slice at Y = 0. b Horizontal slice at Z = 0. 3

Glazunov and Stepanenko, 2015, Izvestiya, Atmospheric and Oceanic Physics Fig. 4. (a) Mean flow in the vertical plane passing through the center of the lake in Ecb 16. The longitudinal mean wind velocity is gray. Wind direction is marked by streamlines. (b) TKE in the same cross section normalized to the squared friction velocity in the windstream.

Field Measurements Detto et al. 2008, Ecol. Applic. FIG. 2. (a) Aerial view of the grass-covered forest clearing and the adjacent pine forest. The location of the central grass mast, the pine forest tower, the edge mast, and (inset) a picture of the three sonic anemometer configurations at the edge are shown. (b) The plan and (c) side views of the experimental setup are shown. The approximate 1 -m planar distance shown in the side view is from the center of the sonic anemometer head to the crown of the nearest tree.

Time is ripe for a lidar boundary layer study over lakes • Observe turbulence, wind profiles, K-H eddies, rotors, etc over sheltered lakes • Focus on transition to autumn (stable to convective conditions) • Never been done with lidars ( I think)

Rawson Lake Watershed

EXPERIMENTAL LAKES AREA Overview L 239 470 L 240 979

EXPERIMENTAL LAKES AREA Meteorology Current instrumentation L 239 470 L 240 T-chain Radiation 979

Meteorology L 239 T-chain Radiation lidar L 240

L 240 L 239

Lidar RHIs A (9 o) L 239 lidar L 240 B (31 o) C (57 o)

RHI Elevations 0. 25 o – 3. 0 o @ 0. 25 o = 12 rays 4 o, 6 o, 8 o = 3 rays x 3 scans x 2 lakes x 2 s/ray = 180 s + z = 60 m 1 VAD = 6*10 s = 60 s 1 vertical stare = 30 s Movement = 30 s TOTAL CYCLE: 300 s 8. 0 6. 0 o o 4. 0 o 3. 0 o … Dead zone (60 m) z = 15 m lidar 1. 0 o 0. 75 o 0. 25 o raft L ~ 1000 m shore (trees = 15 m)

CIRCULATION FEATURES e. g. use RHI scans to diagnose: (i) Contours of U, W; streamlines - can we detect: flow separation/reattachment intermittent rotors KH waves, wavelengths shear length scale U/(d. U/Dz)

NEXT YEAR Lidar RHIs L 239 Centre Raft 2 nd lidar Perpendicular scans to produce turbulence and Reynolds stress profiles Compare with sonic anemometer array lidar L 240

Summary • 1 -D lake models frequently neglect impact of wind sheltering on surface stress • This can lead to excessive mixing and cold LST bias in summer during wind events • Early IBL work, but also recent wind tunnel and LES studies suggest surface stress varies with fetch and overall should be reduced for small lakes (50% in our case) • But this leads to weak autumn mixing, early re-stratification and premature ice-on. We hypothesize: In summer: over-lake daytime boundary layer near neutral or stable forest edge acts like canopy BFS significant TKE generated aloft, eventually makes its way to surface stress ramps up slowly to equilibrium value In autumn: over-lake daytime boundary layer more unstable significant TKE generated aloft, transported much more efficiently to surface stress ramps up much more quickly Diagnose this summer – autumn transition with scanning Doppler wind lidars