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MARCH 1959 MONTHLY WEATHER REVIEW^ 101
A MODULATED SOIL MOISTURE BUDGET
R. M. HOLMES Field Husbandry, Soils and Aqricultural Engineerinq Division, Experimental Farms Service, Canada Department of Agriculture, Ottawa a n d G. W. ROBERTSON
Department of Transport, seconded to Field Husbandry, Soils a n d Agricultural Engineering Division, Experimental Farms Service, Canada Department of Agriculture, Ottawa
[Manuscript received November 25, 1958; revised February 27, 1959
ABSTRACT
Most meteorologicalsoilmoisturebudgets do notaccountforsoilmoisture stress changesin the drying cycle or forchanges in groundcover or expandingrootsystem. A^ simplemodulatedtechnique^ is^ described which considersthesefactors.Soilmoisturestressdetermined by this technique hasa significantlyhigher correlation with wheat yield than does moisture stress determined by R common method.
1. INTRODUCTION
An important phase of research in agricultural meteor- ology and soil physics is concerned wit,h soil moisture and the process of evaporation. The soil, plant,andat- mosphere each play important roles in this process but are only parts of acontinuoussystem of transport of water fromtheearthtotheatmosphere.While much emphasis has been placed on the individual components of this continuum, there has been less at,tention devoted to the system as a whole than it would appear to merit. I t is recognized that moisture use by crops cannot pass a maximum which is determined by the amount of energy available, fromthesunandthehorizontaltransfer of heat, toconvertliquidwater to watervapor. As’ long as water is freely available for evaporation at the earth- atmosphere interface,therate of evaporation ismostly dependent upon meteorological parameters. The amount of evapotranspiration required t o satisfy the atmospheric demand has been calledpotentialevapotranspiration (PE) [eo]. However, asthe soil dries,theavailable moisture decreases, hydraulic tension increases, and trans- portof water to the interface is insufficient to meet the atmospheric demand and actual evapotranspiration ( A E ) falls short of PE [6,7]. The commonest soil moisturebudgetconsists of sub- tracting daily PE fromdailyrainfall.Thisamount is then subtracted (or added when rain exceeds PE) from the moisture present in the soil to give the new soil mois- ture storage, until available stores have been exhausted. For budgeting irrigation water, this process is continued on a daily basis until a certain permissible soil moisture deficit occurs. A t this time an amount of water equal t o the deficit is appliedtoreturn soil moisturestorageto field capacity. This is^ a^ simplified description^ of^ moisture use by cropsunderirrigation.“Dryland”soilspresent
many problems with meteorological moisture budgets be- cause theyarerarelyat field capacityandplantroots explore deep moisturestores. Mostmethodsofdetermining PE are semi-empirical [2, 6,10,14,15,20,21]. Evaporation pans or atmometers have also been used [3,5,8,12,24]. As stated previously, when the soil driesout A E becomes less than PE. Thorntllwaite suggests thatAE is in ratio to thesoil mois- t’ure in storage (SM). That is, when SM is 1/2 the total
storage possible, A E is 1/2 PE. H e proposes that evapo-
transpirationcontinuestonear oven dryness. Thorn- thwaite’s datasupportinghissoilmoisture depletion curve were obtained from vapor pressure and tempera- ture profile measurementstaken at O’Neil, Nebr. [21]. Curves C and D, figure 1, represent Thornthwaite’s con-
cept ; curve D continues to the wilting point andC to oven
dryness. BlaneyandGriddle [2] correlatedactual measure- me,nts of consumptive use (evapotranspiration)with monthly mean temperature and daylength in an attempt to obtain a soil-plant coefficient that, when incorporated intotheirempiricalrelationship,wouldgive it awide application.Theplant coefficients variedfrom 0.85 for alfalfa to 1.2 for rice, and applied to semiarid and arid conditions. Pierce [16] used Thornthwaite’s method of calculating PE andcomparedthesedatatototalwater use by2d year meadow as measuredbyweighing ’ lysimeters. Thornthwaite’s PE was adjusted upward to correct for cropdensity, age, and rooting depth. Pierce’s “dryness” correction curve is represented in curve B figure 1, while his seasonal correction for2dye’ar meadow (state of growth and time of year) is represented in figure 2. This curve is thought to apply to many soils, provided drain- age is not restricted.
102 REVIEWWEATHER MONTHLY MARCH^1959
too
’/a PE 50
0
k
FC Content So11 Moisture PWP O D FIGURE 1.-Variousproposals for adjustment of YE as soil moisture decreases. A ,^ Veihmeyer^ ;^ B,^ Pierre^ ;^ C^ and^ D,^ Thoruthwaite.
Van Bavel’s [22] method of determining PE is a sim- plification of Penman’s equation. Nomograms have been drawn to simplify the estimation of daily PE. No a l l o ~ ance is made for soil dryness and crop density (ground coverage) and only moisture wit,hin the root zone is con- sidered. (Thisamount wouldincrease as the crop de- velops withincreasingdepth of rootzone.) Curve A figure 1 represents Van I3avel’s relationship between soil dryness and PE. This curve is similar to tll:tt, proposed by Veihmeyer [all. I n a recentreview of Rnssian literatl~re, Lemon [Ill presentsseveralsoil moistureevaporation curves. Tl1ey are divided into three port,ions; ( :L) evnpol*ationproceeds in accorclance withtheat~nospl~eric (le111an(1, (b) e \ - : ~ p orationrate declines rapidly as moisture films to t,lre surface become c~isco~lt,i~lnosand transfer of nloist1u.r totheinterface decreases, ( e ) extremely slow nloisture movement isdonlinat,etl by ntlsorpt ive forcw at liquid- solid interfaceswithin the soil. Curves i n figure 3 sng- gest this concept. Except for theinitialplateau,this is characteristic of many “tension-toistl~~,econtent” clwves. Marlatt [13] investigated tlw ch:~npei n AK as tlle soil i n lysimeters and field plotsdried ollt. I3y regular soil sampling at 3-incUh intervalsto 48 inches uuder a, corn cropthroughout,the season, curves similarto t,llose of Lemon [ll] wereobtained. H e found t,llat AI3 pro- ceeded atthepotentialrateupto a pointdepending chiefly on rooting dept,h, then AE fell off’ s h r p l y. These data arerepresented by the curves in figwe 3. The tle- flection pointscorrespond to t,he variouscroproot,ing depths at differentperiodsduringthe season. Philip
[17] obtained the same type of curves by analysis of the
mathematical and physical aspects of soil moisture evap- oration. The horizontalportion of t,he curvesmay roughly correspond to the zone of “bomplete depletion,” described by Hagan [4]. This zone,rrtaybe defined as
10 ‘ 0
% PE
(^0) / ~~~~~ APRIL MAY JUNE JULY AUGUST SEPTEM0ER
**FIGURE2.-Adjustment of PE forstage of growth of meadow. (Pierce)** t’he volume or, in the case of closely spaced plants, the depth from which soil moisture is withdrawn at or near the potential rate until most of the available water **has** been removed. The soil in this zone would be thoroughly permeated with fine roots. The second and third portions of the curves may correspond to the “transitional zone” of Hagan [4]. This area contains a varying concentra- tion of roots,decreasingwithdistancefromtheplant and extending toa considerable depth. hlarlatt [13] compwedthe measured and comput,ed soilmoisturecontent of lysimetersand field plots. Measurement was accomplishedby sampling,and com- putation was achieved by adjusting Thornthwaite’s PE _to_ soil dryness and rootingdepth(accordingto curvw in fig. **3 ).** His correlation was 0.997. Using Van Bavel’s **1:22]** nomograms lle founddepartures of the computed ## and measnretl SM, particularly when t.he soil was dry. ## 2. MOISTURE BUDGETS To he useful, a, scheme for the budgeting or control of soil moisture by the meteorological method should have several characterist.ics. First, the method of characteriz- ing the dryingability of the at,mosphere should **(a)** be convenient **and** simple to use, (b)integrateinto one mensurementall the \-ariotIs meteorologicalfactors affecting the evaporating ability of theatmosphere,(c) (inst>ruments)be free **of** structur:d colnponents that dis- tort evaporation measurements. Second, the manipulation of evaporation data should (a) be realisticinitsdescription of natural processes, (b) haveaccuracy‘compatible with the use to whichit is put, **( c )** besimpleandpractical. Many of the methods presently used to measure evap- or.at,ion do not fill the above requirements as they are not simple or convenient.Those that are, do not accurately integrate meteorological factors affecting evaporation into one nmtsurement. Many instruments are cumbersome and are not free of st,rnctural disadvantages. A case in point ## 104 REVIEWWEATHER MONTHLY MARCH^1959 - I **_-_** **FIGURE** 4.-Soil moisture loss calculatedby modulated budget **( A E )** and by simple budget (PE). **( A** indicates spot Coleman moisture block readings. zone. Recent work by Vasquez and Taylor [24] substan- tiates this view. There may be some criticism of assump- tion (e) since local conditions and individual soils may seriously retard percolation. The individual operationsof this technique are set forth in table 1. For purposes of demonstration, the soil zone **of** complete depletion was assumed to contain 0.25 inch of available water and the transitional zones, 1.0 inch of water, making a total soil storageof 1.25 inches of avail- able moisture. The uppermost 0.25 inch of moisture was evapotranspired at 100 percent of P E ; the remaining 1. inch was withdrawn in a stepwise fashion with 0.25 inch per step, in such manner that the steps were the best fit to the type **of** curves in figure **3.** I n other words, the first 0.25-inch portion of the 1.0 inch in the transitional zone was withdrzlwn at 50 percent, the second at 20 percent, the thirdat 10 percent, and the fourth at 5 percentof PE. Figure 4 compares soil moistureloss by a grass-legume swardcalculatedbytwotechniques: (a) the modulated budget described above, and(b)the co'mmon typedis- cussed briefly atthebeginning of thispaper. PE was estimated with a black Bellani plate atmometer [8]. The differences are clearly discernible particularly as the soil begins to dry out. Spot moisture block readings verified the accuracy **of** the modulated technique. **3.** COMPARISON OF TWO BUDGET TECHNIQUES The two moisture budget techniques partiallydescribed above were programmed for an IBM650 and soil moisture calculations weremade for Lethbridge,Alberta, for 36 years (1921-56 inclusive). I n both techniques, PE was estimated by Thornthwaite's method [191. **_Gomm,on_** _Budget_ ( A ) : The methodemployedinthe simple budget technique has been outlined by Robertson and Holmes [18] and others [2O,221. _Modulated Budget ( B )_ :The basic characteristics of this technique are outlined insection 2 of this paper. The apportionment of the soil zones and the amount of mois- **So11 Moisture Storage** FIGURE **5.-IBhl** **_(is0_** program f o r adjustment of PE **as** soildries and plant roots expand. (Curve **A** for Aug. 1 to May **31** ; curve B J u n e 1 to June **3 0 :** c w r e **C** for July 1 to July **31.)** ture in eachzone is shown in figure 5. The soil drying curve a t Lethbridge for stubble or trash covered plowed ground is approximated in the dashed curve A. The step- wise best fit curve used in programming the IBM 650 is drawn over theidealcurve.Thelength of each step indicates the amount of moisture leaving the soil at the **rate** of PE shown on the ordinate. This curve was used tocalculate soil moisture loss from august 1 (approxi- mateharvestdate)toMay 31 (seedingdate,approxi- mately May 1). The June soil moisture loss curve is rep- resented in curveB, and conditions during July areshown ## graphicallyincurve C. Thesecurves were established by laboratory and field observations. Yield data from a 36-year old "continuous spring wheat" rotation at Leth- bridge were available for correlation comparisons. ## Usingthe common andmodulatedbudgets, PE, AE, and soil moisture deficits (monthlyaverage belowfield capacity)duringthegrowthmonths(May,June, and July) werecalculatedandcompared,throughmultiple and simple linear correlation, with yields of wheat. The resu1t.sare shown in table2. The data indicate that wheat yields at Lethbridgewere not significantly correlated with the evaporating ability of the atmosphere (PE). Soil moisture deficit was more significantly correlated with wheat yieldsthan was actual moisture use (AE). Plant response has been shown to be more closely related to the energy required to taka up water (eg. deficit) ,than to moistureuse per se [4,13,17]. The correlation between yield and average monthly mois- ture deficit below field capacityimprovesasthe season progresses. This indicates that as the crop ages and the rootsaremorefullyramifiedthroughoutthe soil, such factorsasrootinghabit, soil moisturestress, etc., may cause a more pronounced effect on the yield than atmos- phericconditions.Allowance is made for thesefactors in the modified budget ( B ). Army and Ostle **[I]** noted aninverserelationship between theevaporatingability of the atmosphere (e.g., PE) and evapotranspirationfrom **MABCH 1959** REVIEW WEATHERMONTHLY **105** **TARLE** _2.”Simple andmultiple correlationsbetween soil moisture factors_ **_AE,_** _PE, anddejicit(calculated_ by _common_ **_( A )_** _anrlrnodu- lated ( B ) methods) and yield_ of _wheat at Lethbridge, Alberta_ I Correlation coefficient andmethod Soil moisture May **_ryl_** June **ry2** July^ **rY3 ry**^123 _____ PE‘.__............ **-0.27-0.27-0.04-0.04-0.14-0.** ## AE1 ____._........I..-..- 1. 2 0 1 ..-.““1 .29 I”.-..- 1 **.48 i-..o!: 1 **. **0.** Deficit..--- -...... **-.37 *-.38 .32 **-,46 * -. 4 4** **_*“-.63_** **. **68** **1 AE** is not calculated in method **A.** 1 **PE** is calculated the same way in both **A** and R methods. **rrl,2,3** etc., indicates correlation between yield and May, **June,** and July soil moisture * **indicatesignificance at the 1 and **_5_** percent levels respectively. **factors,** respectively. wheat (e.g., AE). An explanation of thisanomaly was found in the complex interrelationship of plant growt,h, available soil moisture, and climate under semi-arid con- ditions. Resultsreportedhereindicate a similartrend. The correlation between August PE and AE is **_T =_** -0. (significant at the 5 percent level). Even thoughtheresultswiththemodulatedbudget indicate considerableversatilityandimprovement over the simpler meteorological methods of estimating soil mois- ture status, one may wonder why correlations with yield of wheat are not higher. Hopkins **[9]** pointed out that inhibitory factorssuch as wind, disease, weeds, insects, etc., are important in many seasons, and that statistical ’ methods may lead to some underestimation of the actual association of yield of wheat and meteorological factors. **4.** SUMMARY The results presented show that a realistic, yet simple ’meteorological soil moisturebudgetis possible. Such a budget readily accounts for soil moisture stress and plant rooting characteristics, etc., and yet has accuracy compat- ible with other methods of determining moisture use by crops. When soil moisture drying curves (such as those in fig. _5 ) ,_ andaccurateestimates of thedryingability of the atmospheresuch as thoseobtainedwith a black Bellani plate atmometer are available, a daily record of soil moisture is possible. Bychangingthe soil drying curves and coefficients, the scheme can _be programmed to_ fit a wide varietg of soils, crops, and crop sequences. REFERENCES 1. T. **J.** Army and B. Ostle, “The Association Between Free-Water Evaporation and Evapotranspiration of Spring Wheat Under thePrevailingClimaticConditions of thePlainsArea **of** Montana,” _Proceedings,_ Soil Science Society of America, vol. **21,1957,** pp. **469-472. 2.** H. **F.** Blaneyand W. D. Criddle, _Consumptive_ **_U s e_** of _W a t e r_ _in theIrrigatedAreas_ of _theUpperColoradoRiverBasin,_ Division **of** IrrigationandWaterConservation,Soil Con- servationService, U.S. Department of Agriculture, **1949. 3.** D. **W.** Bloodgood, R. E. Patterson, and R. L. Smith, Jr., “Water Evaporation Studies in Texas,” _Bulletin_ **_787,_** Texas Agricul- tural Experiment Station, College Station, Tex., **1954. 4. R.** M. Hagan, “Soil-Plant Water Relations,” XIV Netherlands Horticultural Congress, Waganingen,Symposium 11, **1956,** PP. **82-102.** .5. R’. A. Halkias, F. J. Veihmeyer,and A. H. Hendrickson, “De- termination of Water Needs for Crops from Climatic Data,” _Hilgardia,_ vol. **24,** No. **9,** Dee. **1955,** pp. **207-233.** **6. M. H.** Halstead and W. Coney, “SomeMeteorological Aspects of Evapotranspiration,” _Proceedings,_ SoilScience Society of America, **vol. 21, 1957,** pp. **461464. 7.** J. C. 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