I v~ eFT<~ f'f*f{J - - I UNITED STATES I DEPARTMENT OF THE INTERIOR GEOLOGICAL SURVEY I WATER RESOURCES DIVISION I I I ESTIMATING STEADY-STATE EVAPORATION RATES FROM I BARE SOILS UNDER CONDITIONS OF HIGH WATER TABLE BY I C. D. RIPPLE, J. RUBIN AND T. E. A. VAN HYLCKAMA I I~ I~ .- OPEN-FILE REPORT IcC I I Wa.tvr. RcuoUJtee6 fJ.iv.U.ion I Mualo J'aJtk, Cali6o!UUa. I 1910 I I l.128) I I Contents I 2 Page 3 Symbols----------~---------------------------------------------- iii I 4 Abstract-------------------------------------------------------- 1 5- Introduction------~--------------------------------------------~ 2 I 6 Theory-------------------------.--------------------------------- 4 7 Meteorological equation----------·-------------------------- 5 I Soil equation---------------------------------------------- 8 8 Application-----------------------------------------------------· 14 I 9 Data required--------------------------------------------~- 14 10- Homogeneous soil---------------------------------------•--- 17 Layered soil----------------------------------------------- 30 I 11 Effects of vapor·transfer---------------------------------- 36 I 12 Discussion, experimental test; and conclusions-------------.----- 46 13 Appendix: Flow charts for es.timating steady-state evaporation rates from bare soils-------------------- 58 14 I References------------------~----------------------------------- 60 15- I 16 Illustrations I 17 18 Figure 1. The water-table-soil-atmosphere systems considered: I 19 Case A. A homogeneous soil with water transferred 20- exclusively in liquid form; Case B. A layered soil with I 21 water transferred exclusively in liquid form; Case c. 22 A homogeneous soil with water transferred in liquid and 9 I 23 vapor forms------------------------------------------------ I 24 25-- ll. S. GOVERNMENT PIUNTING OFFICE: 1959 0-511171 I 867-100 i I I I Page 1 n I 2 Figure 2. Dimensionless plots of f·= f(e) = (e+l) (;1) ---- 19 3 yu 4 Figure 3. Dimensionless plots. of I = I(y ) I u = r ...2L. 20 Jo yn+l 5- I 6 Figure 4. Dependence of dimensionless soil water suction, s, I 7 on dimensionless soil height, z: A. Soil parameter n = 2; 8 B. Soil parameter n = 5----------------------------------- 21 I 9 Figure 5. Plots relating dimensionless evaporation, e, to 10- dimensionless depth to water ·table, .(,---------------------- . 23- I u Figure 6. The intercept method for determining evaporation I 12 rates: A. Chino clay; B. Buckeye soil------------•----- 25 13 Figure 7. Dependence of evaporation rates on water table I 14 depths, calculated by intersection method (solid lines).: 15- A. Chino clay; B. Buckeye soil--~--------------------•-- 27 I 16 Figure 8. The dependence of relative evaporation rates, 17 E/E po t' upon the potential evaporation rates, Epo t' for I 18 Chino clay------------------------------------------------- 29 I 19 Figure 9e The influence of layering on the relation between 20- evaporation rate and depth to water table: i. the I 21 homogeneous case(~= 0); ii. a two-layered soil; 22 iii. a three-layered soil.,.·-------------------------------- 37 I 23 Figure 10. Comparison of actual versus estimated evaporation· I 24 rates for a given depth to water table--------------------- 53 25·- II. S. GOVERNMENT PHINTING OFFICE: 1959 0- 511171 I 867 ·100 ii I I~ ·:>r:.·l I I Symbols = a subscript, indicating a variable determined in the air, I ;a H em above the soil surface. a I I I:u = a subscript, indicating a variable determined at the soil I surface. I = a subscript, indicating a variable which involves water .v I vapor transfer. I ..a -1 = sensible heat transfer into the air, cal em day -· I b = -B(Tu - ~) /L~, gm em -4 -3 0 -1 B = (1'\/cr) (C/o.)s', gm em K • -1 I c = E/Dhv' em I D = a coefficient characterizing the molecular diffusion of watert a ! a -1 I vapor in free air, em day Dhv = a coefficient characterizing the molecular diffusion of I. a -1 soil-water vapor caused by humidity gradients, em day • I DTv = a coefficient characterizing the molecular diffusion of a -1 o -1 · soil-water vapor caused by thermal gradients, em day K •· I e E/K t' rate of evaporation from the soil, dimensionless. = sa -1 I E = rate of evaporation from the soil, em day • e rate of potential evaporation, dimensionless. pot = -1 E rate of potential evaporation, em day pot = I soil-limited = ~'-&tias~rate of evaporation from the soil, dimensionless. soil-limited I E 1 co = ·2i,_ j tirg.Arate o f evaporat~on· f rom t h e soi 1 , em day~ I f(e) = a functional relation defined by equation 27. • t.l..l\( ti'"·l ':· •j, , :• ! II' I iii I 1.. : ;•1';7 I I ... -------·-----~------·-·-·-------------·· ..... - .... ·-·- .... -.--.............. , I a function which relates E and S , using meteorological = u I parameters. = a function which relates E and su' using soil parameters. ..a I = acceleration of gravity, = 980 em sec ·· ;G(V a) = a theoretically or empirically derived known function of -1 -1 I wind speed, em day mb I = relative humidity, dimensionless. air relative humidity at height H above the soil surface, = a I dimensionless. 1H height of meteorological measurements above the soil surface, a = I em. ·h = surface soil relative humidity, dimensionless. I u .H roughness parameter, em (usually, for bare soils, .u = 0.01 S H s 0.-03). I. u soil humidity at depth L , dimensionless. = relative u I h* = soil relative humidity at d.epth L *, dimensionless. 1 ~ I(y) = the integral relation defined by the right-hand side of I equation 18. = von Karman constant = 0.41, dimensionless. I -1 K = Kliq = hydraulic conductivity for liquid flow, em day -1 .K hydraulic conductivity of water saturated soil,. em day I sat = -1 hydraulic conductivity ·for vapor flow, em day Kvap = I = L/S%' dimensionless depth to water table. I L = total distance between the water table and soil surface, em. .. ; • ' '. : \ 1·. I'~ •.\. 1·: • • ' •H i.'.. ! 11 .. •• • • ~· l : •. I I .. [.' iv I I . ;·~. 1 I r·--·-··-- .. -------·------...,...----- ---------------·---------------- ------.--. ! I I I i L. in the multilayer case, the thickness of soil layer, em, j J = layers above ~he water table (that is, j = 1 means one layer i I 1 above the water table, etc.). I jL thickness of the uppermost soil layer, em. : u = I iL* = thickness of the uppermost portion of the dry soil surface I I U at which ~ was determined, em. I :L' = thickness of the dry soil layer in which isothermal vapor u I transfer is assumed to predominate, em. -1 :M = molecular weight of water = 18 gm mol • ; I n = an integer soil coefficient which usually ranges from 2 for clays to 5 in sands. I p = saturation vapor pressure of water, mb. p(T) = a known relation between the saturation water. vapor . I pressure and temperature (given in tabular or functional I form), mb. P = ambient pressure, mb (taken asP= 1000mb in this study). -1 I q = flux of water, em day -2 -1 Qg = soil heat flux into the ground, cal em day I = net radiative flux received by the soil surface, cal em ~ -1 I day • 7 0 -1 R = gas constant = 8.32 x 10 erg K • s = S/S~, dimensionless suction. I 2 s = soil water suction, defined as the negative of the soil water I pressure head, em of water. I Sj = in the multilayer case, the soil water suction at the upper interface of layer j, em of water. I 1,1 • .'! ,,·.'·' v I I I I s water suction at the soil surface, em of water. u = = a constant soil coefficient representing S at K = L K I ":! sat' em of water. I T = temperature, °K. 0 T = air temperature at H , K. I a . a T surface soil temperature, °K. u = I :r,. = soil temperature at depth L:, °K. -1 = wind speed at height H , em day a I y = a variable, defined by equation 16. = a variable, defined in conjunction.with the right-ha~d side I of equation 31 of the layered ·Soil case. I z = Z/S~,· dimensionless height above water table. Z = vertical height above the water table, em. I = tortuosity factor, dimensionless. ...:3 0 -1 I d(log p )/dT, gm em K s = e v 0 -1 I y = psychrometric constant, 0.000659 P, mb K I e: = water/air molecular ratio= 0.622 (dimensionless). C = a ratio of the average temperature gradient in the air-filled I soil pores to the overall soil temperature_ gradient, dimensionless. I 11 = soil porosity, dimensionless. -1 = latent heat of vaporization of water at T , cal gm A. a -3 I = air density at T , gm em a ...:3 p = P (T) = density of saturated water vapor, gm ern p is a I v v . v function of temperature. I -·· . - ... vi I ·-··· .. -- -¥·--- .. :... ·-- ...·----· ---------~-- -·-··-...:.--~...,..----··. -'3 = water density at appropriate T, grn em = volumetric air cqntent of the soil, dimensionless. = a dimensionless function defining the effectiveness of the water-fl;'ee ·pore· space for diffusion. ., I l 1 ,. ' , 1 .' ~ I , ', · : '•i. : I J• ' , . • ··~ 1 ~ •l ; , vii ,,126) I I I 2 3 4 I I I 5 .. I I I b I ESTIMATING STEADY-STATE EVAPORATION RATES FROM I I 7 BARE SOILS UNDER CONDITIONS OF HIGH WATER TABLE I I I I H I By C. D. Ripple, J. Rubin and T. E. A. van Hylckama i I I 1.:1 I I i I 10- I I ABSTRACT I. t I 11 I I I A procedure that combines meteorological and soil equations of i !water transfer makes it possible to estimate approximately the I ! I steady-state evaporation from bare soi·ls under conditions of high water; I, . · . .Ii l4 1 I table. Field data required include soil-water retention curves, water 1 1?· • j table depth and a record of air temperature, air humidity and wind I lb ~velocity at one elevation. The procedure takes into acount the I l i ~relevant atmospheric factors and the soil's capability to conduct I~ 'water in liquid and vapor .forms.