1. CENTER FOR EMBEDDED NETWORKED SENSING UCLA USC UCR CALTECH UCM Sap Flow – Lots of ways to do it

2. Water diffuses “down-hill” from high to low concentration (  c) over a distance (  x) Everything diffuses like Fick’s First Law: Flow rate  cxcx Some Physics

3. Flow rate   w (psi) = the “concentration” of water  w (pure water) = 0.0 mega-Pascals  w (everything else) = negative MPa   w  x

4.  w (wet soil)  -0.1 MPa  w (atmosphere)  -95 MPa

5.  w (wet soil)  -0.1 MPa  w (root)  -0.5 MPa  w (stem)  -0.6 MPa  w (branch)  -0.8 MPa  w (atmosphere)  -95 MPa

6.  w (wet soil)  -0.1 MPa  w (root)  -0.5 MPa  w (stem)  -0.6 MPa  w (branch)  -0.8 MPa  w (atmosphere)  -95 MPa HIGH WATER FLOW Transpiration (day) stomata open resistance low

7.  w (wet soil)  -0.1 MPa  w (root)  -0.1 MPa  w (stem)  -0.1 MPa  w (branch)  -0.1 MPa  w (atmosphere)  -95 MPa No/little transpiration (night) stomata closed resistance high very low water flow

8.  w (dry soil)  -1.5 MPa  w (root)  -1.9 MPa  w (stem)  -2.0 MPa  w (branch)  -2.2 MPa  w (atmosphere)  -95 MPa Low water flow Low transpiration (stressed) stomata closed? resistance medium

9. Different water sources High soil water content Low soil water Transpiration for 3 hours only Transpiration for 12 hours Equal rates of water transport

10. Buy a pre-built system = $$,$$$ Sap Flow – Lots of ways to do it

11. Do it yourself = less $, but more work Building sap flow probes

12. Heated probe drops in temperature (relative to unheated probe) when sap flows. Heated probe temperature is higher during low or no sap flow. Measurement systems

13. Installation

16. 106,6,925,10.44,43.57,44.87,91.5,2.345,4.839,-.01,4.655,6.493,4.592,4.013,5.108,-.023,3.049,2.273,1.918,24.59,4.092,51.54,4.141,0,19.77,24.01,22.19,-6999,21.73,19.94,22.56 106,6,930,30.75,55,52.52,95.6,2.322,5.046,-.003,5.062,5.862,4.684,4.098,5.371,-.013,4.217,3.602,2.283,24.24,4.365,49.6,4.487,0,20.16,25.47,22.15,-6999,21.92,20.3,23.53 106,6,935,57.45,64.89,46.95,100.9,2.164,5.197,0,5.453,4.434,4.75,3.891,5.296,-.039,11.32,16.46,4.105,23.59,4.184,47.3,4.493,0,21.52,26.61,22.58,-6999,-6999,21.06,24.18 106,6,940,26.73,76.5,35.93,96.9,1.99,5.322,-.013,5.736,5.115,4.802,3.73,4.963,-.161,39.57,48.53,8.5,23.16,4.335,44.8,4.46,0,24.59,27.25,22.95,-6999,-6999,22.51,24.86 106,6,945,-85.9,89.1,26.18,94,1.885,5.43,-.003,5.963,7.21,4.874,3.704,4.799,-.158,38.02,47.56,8.65,23.25,4.993,42.54,4.723,0,25.13,27.07,22.93,-6999,-6999,22.76,24.77 106,6,950,-99.7,102,26.68,92.2,1.848,5.519,-.007,6.16,7.54,4.93,3.68,4.726,-.158,36.3,46.41,8.74,23.46,5.94,40.49,5.394,0,24.8,28.44,23.61,-6999,-6999,23.85,25.56 106,6,955,-95.1,114.3,26.34,89.5,1.858,5.614,.007,6.367,7.59,5.009,3.805,4.887,-.138,34.54,45.22,8.83,23.2,6.469,38.24,5.966,0,24.97,28.53,23.5,-6999,-6999,25.24,25.94 106,6,1000,-97.9,124.8,22.95,79.8,1.838,5.657,-.007,6.429,7.6,5.061,3.973,5.551,-.141,32.69,43.83,8.89,22.63,6.591,35.76,6.166,0,24.71,28.26,24.02,-6999,-6999,25.71,25.55 106,6,1005,-123.3,132,22.72,75.5,1.865,5.725,-.003,6.472,7.63,5.12,4.357,5.646,-.135,31.02,42.57,8.95,22.08,6.695,33.33,6.321,0,24.94,28.87,24.44,-6999,-6999,26.23,25.68 106,6,1010,-159.4,136.4,21.96,75.5,1.884,5.808,-.01,6.873,7.64,5.173,4.272,5.722,-.141,29.39,41.38,9.02,21.42,6.797,30.9,6.452,0,25.4,28.95,24.46,-6999,-6999,26.84,26.24 106,6,1015,-150.6,138.6,20.7,71.9,1.957,5.886,0,7.05,7.66,5.232,4.015,5.498,-.132,27.65,39.95,9.08,20.75,6.886,28.35,6.537,0,25.52,28.82,25.79,-6999,-6999,27.19,26.06 106,6,1020,-163.4,137.4,18.98,64.11,2.124,5.965,-.007,7.22,7.67,5.291,3.943,5.241,-.135,26.01,38.6,9.17,20.01,6.994,25.93,6.616,0,26.19,29.48,25.87,-6999,-6999,27.54,26.19 106,6,1025,-23.47,133.4,20.64,51.28,2.331,6.014,-.007,7.35,7.63,5.337,3.943,5.123,-.132,24.28,37.02,9.21,19.18,7.09,23.51,6.688,0,26.26,29.78,25.06,-6999,-6999,27.66,26.66 106,6,1030,16.93,127.5,20.65,41.65,2.456,6.093,-.007,7.52,7.65,5.419,3.972,5.139,-.122,22.32,35.52,9.25,18.54,7.24,21.11,6.78,0,25.93,29.02,24.6,-6999,-6999,27.26,26.27 106,6,1035,9.46,120.6,20.83,34,2.69,6.142,-.013,7.67,7.62,5.455,3.995,5.172,-.128,20.62,33.9,9.3,17.63,7.42,18.91,6.901,0,25.99,29.6,24.27,-6999,-6999,27.11,26.9 106,6,1040,-26.43,112.8,20.08,30.07,2.975,6.188,-.01,7.82,7.61,5.504,4.241,5.231,-.118,18.97,32.26,9.32,16.85,7.58,16.66,6.993,0,26.07,29.47,24.64,-6999,-6999,26.91,26.58 106,6,1045,-67.36,104.5,18.34,24.78,3.11,6.22,-.013,7.97,7.6,5.55,4.573,5.287,-.112,17.36,30.68,9.34,16.07,7.79,14.42,7.08,0,26.88,29.73,24.82,-6999,-6999,27.15,26.91 106,6,1050,-51.68,96.9,19.24,18.44,3.192,6.256,-.007,8.11,7.61,5.609,4.829,5.378,-.105,15.85,29.08,9.38,15.3,7.97,12.4,7.13,0,26.45,29.31,24.93,-6999,-6999,26.75,26.59 106,6,1055,-23.14,89.5,15.08,15.9,3.241,6.282,-.01,8.22,7.59,5.645,4.573,5.539,-.102,14.38,27.25,9.4,14.59,8.21,10.71,7.22,0,26.83,29.47,25.6,-6999,-6999,26.78,26.95 106,6,1100,-29.76,82.4,14.69,12.53,3.274,6.312,-.003,8.31,7.58,5.704,4.356,5.536,-.099,13.03,25.45,9.42,13.7,8.41,9.26,7.38,0,26.82,30.22,25,-6999,-6999,26.82,27.67 106,6,1105,-31.42,76,9.08,10.51,3.31,6.325,-.01,8.38,7.56,5.743,4.392,5.559,-.095,11.87,23.9,9.43,12.9,8.62,8.03,7.45,0,26.95,29.62,25.47,-6999,-6999,26.79,27.51 106,6,1110,-36.27,69.86,7.71,9.08,3.363,6.335,-.013,8.44,7.55,5.795,4.467,5.598,-.089,10.8,22.13,9.44,12.13,8.77,7.26,7.46,0,27.71,29.85,25.84,-6999,-6999,27.45,27.34 106,6,1115,-19.87,64.26,9.26,7.84,3.435,6.354,-.003,8.51,7.55,5.851,4.539,5.697,-.072,9.83,20.49,9.47,11.46,8.97,7.05,7.54,0,27.6,29.2,25.71,-6999,-6999,27.33,27 106,6,1120,11.6,59.46,11.15,4.8,3.478,6.338,-.013,8.53,7.5,5.874,4.517,5.802,-.079,9.16,18.79,9.51,10.67,9.1,6.982,7.62,0,27.46,29.09,25.21,-6999,-6999,27.05,26.85 106,6,1125,-76.6,55.6,14.5,12.38,3.54,6.347,-.01,8.54,7.48,5.923,4.543,5.867,-.072,8.96,17.18,9.57,10,9.23,7,7.7,0,28.22,30.6,26.06,-6999,-6999,27.85,28 106,6,1130,-117.6,52.03,16.79,14.06,3.573,6.324,-.007,8.48,7.47,5.979,4.648,5.959,-.066,8.85,15.42,9.61,9.33,9.23,7,7.7,0,28.33,29.97,25.96,-6999,-6999,28.15,27.45 106,6,1135,-16.64,49.28,9.6,16.76,3.616,6.324,0,8.5,7.45,6.002,4.618,5.962,-.056,8.85,13.94,9.86,8.9,9.74,7.11,8.03,0,28.17,29.04,25.41,-6999,-6999,28.09,26.34 106,6,1140,-8.2,45.96,-3.807,14.2,3.629,6.327,-.01,8.62,7.46,6.064,4.661,5.906,-.066,8.8,12.6,10.59,8.52,9.66,7.08,7.87,0,27.68,28.79,25.63,-6999,-6999,27.83,26.45 106,6,1145,-94,42.43,-1.952,-45.47,3.655,6.327,-.003,8.71,7.44,6.11,4.703,5.919,-.049,8.83,11.24,11.25,8.08,9.57,7.12,7.84,0,28.24,29.93,25.88,-658.3,-6999,28.65,27.31 106,6,1150,-6999,38.58,-115.4,-6999,3.668,6.343,-.013,8.72,7.39,6.13,4.776,5.965,-.049,8.94,10.11,12.22,8.05,9.67,7.16,7.92,0,29.88,30.79,25.23,-94.4,-6999,29.98,26.43 106,6,1155,-594.8,35.87,-20.01,-66.45,3.619,6.337,-.007,8.71,7.45,6.231,5.173,6.084,-.043,9.01,8.92,13.27,8.05,9.72,7.2,7.97,0,29.04,30.5,26.4,-214.9,-6999,29.71,27.02 106,6,1200,-1372,33.84,-9.71,29.71,3.586,6.327,-.01,8.62,7.44,6.271,5.738,6.261,-.046,9.04,7.99,14.39,8.11,9.8,7.23,7.98,0,27.95,29.08,-6999,-35.77,26.32,29.1,26.5 106,6,1205,-1319,32.65,-6.312,32.21,3.566,6.34,-.007,8.61,7.47,6.34,5.413,6.179,-.039,9.12,7.13,15.98,8.14,9.83,7.31,8.01,0,28.61,29.15,26.56,-300.5,31.98,29.43,26.78 106,6,1210,-1315,33.07,-4.539,33.16,3.592,6.34,-.01,8.58,7.53,6.428,5.383,6.336,-.043,9.1,6.606,16.98,8.17,9.9,7.34,8.01,0,28.53,28.12,25.97,-316.2,26.13,29.52,26.03 106,6,1215,-1326,34.47,-3.026,30.58,3.595,6.323,-.013,8.6,7.5,6.438,5.285,6.399,-.046,9.11,6.412,18.33,8.18,9.96,7.36,7.99,0,28.1,28.96,25.77,-235.9,26.01,29.49,26.69 106,6,1220,-1337,35.38,-1.627,27.72,3.641,6.313,0,8.24,7.51,6.504,5.741,6.556,-.036,9.14,6.431,19.85,8.26,10.01,7.44,8.02,0,27.65,27.9,25.85,-189.7,45.01,28.96,25.65 106,6,1225,-1335,36.21,.016,25.91,3.687,6.244,0,8.34,7.53,6.589,5.826,6.559,-.033,9.16,6.49,21.04,8.3,9.93,7.47,8.03,0,29.18,28.91,25.9,-92.9,26.48,30.23,26.01 106,6,1230,-1330,35.89,.862,19.03,3.726,6.188,-.007,8.07,7.5,6.605,5.862,6.608,-.039,9.18,6.569,22.48,8.35,9.89,7.54,8.06,0,29.21,28.74,-6999,-13.67,-6999,30.28,27.4 106,6,1235,-1335,33.43,3.449,14.79,3.743,6.129,-.003,7.84,7.48,6.605,6.047,6.714,-.039,9.17,6.622,23.99,8.39,9.89,7.52,8.06,0,29.16,27.88,-6999,99.3,30.19,30.26,26.25 106,6,1240,-1490,-6999,5.898,10.47,3.811,6.182,-.01,8.11,7.47,6.645,6.525,7.1,-.043,9.22,6.745,25.69,8.44,9.99,7.37,8.12,0,28.64,28.27,-6999,-6999,31.99,29.82,25.94 106,6,1245,-6999,-13.73,7.93,7.42,3.819,6.194,-.011,8.46,7.44,6.635,6.665,7.23,-.046,9.18,6.778,26.59,8.47,9.96,7.21,8.1,0,29.26,26.98,-6999,-6999,28.07,30.11,26.45 106,6,1250,-6999,-6999,-6999,4.25,4.146,6.408,-.013,8.57,7.44,6.663,6.717,7.26,-.048,9.19,6.841,27.61,8.49,9.89,7.01,8.1,0,29.04,27.24,-6999,-6999,55.12,29.62,26.95 106,6,1255,44.32,22.99,10.58,2.424,4.369,6.43,-.014,8.63,7.48,6.69,6.693,6.929,-.047,9.19,6.913,26.22,8.51,9.86,6.876,8.11,0,28.75,27.8,-6999,-6999,-6999,29.29,25.47 Data!

17. Temperature difference trace

18. zero sap-flow points (night) Temperature difference trace

19. Daily zero sap-flow subtracted Temperature difference trace

21. Sap flow: u = 0.000119 × Z 1.231 where Z = (  T 0 –  T) /  T Units of sap flow: m 3 H 2 O m -2 sap wood area s -1 Empirical transformation

22. Sap flow trace

23. Units of sap flow: m 3 H 2 O m -2 sap wood area s -1 1 m 3 H 2 O = 1000 liters 10 cm sap wood thickness 80 cm diam  r 2 -  r 2 = 0.049 m 2 Multiply results by 4900 Units of sap flow: liters s -1 Units transform

24. Sap flow – nice units

25. Is sap flow decreasing?

26. Interpreting sap flow: micromet

27. $6000 $15 $320 Light (PAR) sensing

28. Interpreting sap flow: micromet dew point = 9.1°C dew point = 15.3 °C

29. Interpreting sap flow: micromet

30. Interpreting sap flow: um? But note: temperature fluctuations even when no power is applied to the heated probe – temperature gradients!