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A study of Remote Sensing Information model of soil moisture

Ma Ai Nai and Xue Yong
Institute of Remote Sensing, Peking University
Peking 100871 ,P.R. China


Abstract
Soil moisture is an extremely important problem in monitoring of drought or water logging. Especially, soil moisture map is made with space remote sensing data automatically .In general, soil moisture will be expressed as thermal inertia. This paper discusses theoretical models of thermal inertia and soil moisture of remote sensing information model (RSIM).

Using NOAA satellite AVHRR digital tape data, the ATI and RTI will be made automatically from the thermal inherits model. Finally, using soil moisture model, the Apparent Soil Moisture (ASM) map of large region with no effects of topography and vegetative cover will be automatically finished by computer.

Analysis of soil moisture Remote Sensing Information
There is lots of paper about soil moisture measurement from VIS-Near IR, thermal IR to Microwave (1-4,6,7) (1972,1975,1986,1974,1976). Most scientists discovered that it not only has strong theoretical basis but also has practical values to apply the Remote Sensing Information model (5) (1990) of thermal inertia and soil moisture for timely large area monitoring.

Thermal inertia Remote Sensing Information model (4) (1986)
From above, we know that there are two steps for modeling remote sensing soil moisture. The first is the thermal inertia model and the second is soil moisture model.
  1. Thermal inerita remote sensing information model

    Thermal inerita , P=(Kdc)½ (k is conductivity , d is density , and c is special heat capacity), is a physical variable precluding the variations of temperature of body. Thermal inerita is dorminant factor in week and day variations of temperature of soil. Thermal interia is the characteristic of soil body. It can be obtained from week or day variation of temperature and albedo with thermal physical model .

    From solution of thermal conduction equation with boundary condition expressed by Fourier series of day and night variation of temperature model, we can yield:


    where A is albedo,Td-Tn is day and night difference of temperature, So is solar constant , Ct is the atmospheric transmissivity , A is the function of the solar declination and local latitude . w is the circular frequency of day and night , B is the constant of the ground state and atmosphere's and B may be constant under the condition of relative uniform meteorological condition and smooth terrain. In general,So,Ct,Solar declination and B is constant approximately for one digital image. Ai only have something with local latitude . So, ATI represents relative value of thermal inertia P, i.e., ATI direct proportion to P. ATI = (1-A)(Td-Tn) is apparent thermal inertia model.

  2. Soil moisture remote sensing information model

    Theoretically, soil moisture have something to do with real thermal inertia P=(k d c )½ of ground . Then, we must evaluate real thermal inertia P. From formula (1), we have,


    where a = 2 SoCtAi (ATI)

    There are many factors to affect the soil thermal inertia. In addition to soil moisture, there are topography, vegetal cover, soil texture, organic matter and soil mineral matter , etc. The difference is the quantity of effective level. Topography and vegetal cover is relatively important. In order to elimate the effects of topography and vegetal cover, the plain region was chosen as the experiment ground and the time was in seeding stage. Soil texture, organic matter solid mineral matter etc. were approximately substituted in soil density.

    It is well-known that, according to the definition of temperature conductivity a2 = k/d*c, p= k /(a2)½. The relation among k,d,c a2 and soil moisture has been investigated. But, there is no theoretical formula. Most of them are experimental data (8) (1979). We substitute volume percentage of soil moisture for weight percentage of soil moisture, we have


    where W is weight percentage of soil moisture , the density of water is d= 1(g/cm3) , ds is density of soil.

    From formula (3), it is known that if ds is known, the relation between thermal inertia P and soil moisture W is one by one relation . Then, a lookup table for RTI and W is built.

    Formula (2) and (3) are soil mixture remote sensing information model, where ds is evaluated by false color composition or supervised classification and soil property.
Computer mapping of soil moisture
From the theory of soil moisture remote sensing information model mentioned above, the flowchart of computer mapping is designed (Fig.1)


Fig. Technical flowchart of computer mapping
  1. Calculation of ATI
    ATI is (1-A)/Td-Tn) , where real value of A and Td-Tn are

    A= 0.4230 chl + 0.5770 ch2-----------------------------------(4)

    Td- Tn =ch4 (D) - ch4(N)-----------------------(5)

    Where D represents noon, N represents midnight.

  2. Calculation of RTI (P)

    In formula (2), So=1360 J/m-s; Ct=0.76; B=9.66 J/m.s° C; w= 7.3x101-5 1/s .And,

    Ai= (2/3.14) sin (h) sin(q) sin(t)+(3.14/2)cos(h)cos(q)(sin(2t)+2t)

    where solar declination h= -4°35'24"(1989.3.9), t=arcos(tg(h)tg(q)); Latitute q = N36°-----N41°

    From the parameters above, RTI is ascertained.

  3. The Establishment of Lookup Table

    From formula (3), ds is obtained by false color composition with soil map on the basis of soil texture. The lookup table was built (Fig.2)

    Fig.2 Lookup Table of Apparent Soil Moisture (Wm%), ds(g/cm3) and P(Jm.s.° C)
    (Wm%P)ds 2.71 2.68 2.57 2.50 2.55 2.60 2.65
    5.0 254.46 246.58 218.92 202.36 214.11 226.26 238.84
    10.0 500.84 489.87 450.38 425.73 443.30 461.05 478.99
    15.0 660.86 639.37 567.14 526.33 555.08 585.83 618.66
    20.0 993.23 955.58 827.70 754.14 806.09 861.05 919.15
    25.0 1421.05 1363.07 1167.71 1056.61 1135.04 1218.47 1307.18
    30.0 1951.90 1866.68 1582.06 1421.80 1534.71 1655.55 1784.83

  4. Soil Moisture Mapping
    The composition image of Hebei province plain according to ch4(D),Ch2,ch1, (R, G, B,) circled mountain, sea and cities with visual intepretation , proceeding according to steps mentioned above, we gained soil moisture map (fig. 3)


    Theoretically, this soil moisture represents average soil moisture of the definite depth in soil this depth is unlimited if the soil is homogeneous. In general, this soil moisture is weighted means of real soil moisture of different depth during tilling depth (20cm----40cm) . This soil moisture can be called Apparent Soil Moisture (ASM) and it can be used for monitoring drought better than we think.
  5. To compare with field Measurement of soil moisture

    The remote sensing data is NOAA gigital type of March 9, 1989 . The field measurement data are provided by dydrogist of Hebei pprovince . It is pity there is only one point data . The location was marked roughly in Fig. 1 with a cross "+" . It shows no difference with the result which the computer yielded . The remote sensing data are one pixel information, but, the field measurement data are one point information . Then, the predicted result by the models would be tested to monitor drought with remote sensing soil moisture information model mentioned above. But it is required to be verified by a large amount of work.
References
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  2. Idso, S.B.etal. , J.Geophy Res., 80(1975), 3044-3049 Idso,S.B.et al. , American Scientist,63 (1975, 549-577)

  3. Zhang Xiang Qian, Ma Ai Nai , Remote Sensing Information, 2 (1986), 17-22. (In Chinese)

  4. Ma Ai Nai , Procedingsof ISPRS Commission IV,ID=8 1/6-6/6, the Tsukuba Symmposium (1990)

  5. idso, S.B. and W.L. Ehrler,Geophy, Res.Letters 3(1976), 23-25.

  6. Kahle,A.B.etal., Geophy. Res.Lett. 3(1976), 26-28.

  7. Commitee of soil Physical Properties Mesurement of Japan, Measurement of soil Physics , Science and Technology Literatures Press(1979) . (In Chinese)