5.1.7  Accumulated Potential Water Loss and Soil Moisture Storage


    Accumulated potential water loss and soil moisture storage are computed using the methodology outlined by Thornthwaite and Mather (1955, 1957).  Accumulated potential water loss is the potential deficiency of soil moisture associated with moisture contents below the water-holding capacity of a soil.  Thus, for each soil moisture content there is an associated accumulated potential water loss.  Accumulated potential water loss is 1) increased during dry seasons because of an insufficient supply of water (i.e., maximum percolation) to meet the demands of PET, 2) reduced during wet seasons due to the recharge of soil moisture, and 3) equals zero when soil moisture storage equals the water-holding capacity of the soil.

    Accumulated potential water loss is never equal to the actual water loss, because as the soil moisture declines during a dry season, it becomes increasingly difficult to extract additional water from the soil.  This causes AET to be less than PET during the dry season.  The relationship between accumulated potential water loss and soil moisture is given in Thornthwaite and Mather (1957) as a set of soil moisture retention tables.  These tables are used by the module to compute soil moisture storage for dry months given an accumulated potential water loss, and to compute the accumulated potential water loss for wet months given a moisture content.  An example soil moisture retention table is shown in Table 5.8.

    The accumulated potential water loss for a given month of the dry season is the sum of the absolute value of potential percolation for that month and the accumulated potential water loss of the previous month.  This new accumulated potential water loss is then used to calculate soil moisture for the given month.  For any given month of the wet season, soil moisture is calculated as the sum of the potential percolation for that month and the soil moisture of the previous month.

Table 5.8.  Example Soil Moisture Retention Table for 150-mm Water-Holding Capacity of the
Root Zone (after Thornthwaite and Mather 1957)(a)

 
Soil Moisture Storage (Sm(J))
-Wpj®
¯		 0 1 2 3 4 5 6 7 8 9
10
 140 139 138 137 136 135 134 133 132 131
20
 131 130 129 128 127 127 126 125 124 123
30
 122 122 121 120 119 118 117 116 115 114
40
 114 113 113 112 111 111 110 109 108 107
50
 107 106 106 105 104 103 103 102 101 100
60
 100 99 98 97 97 97 96 95 94 93 
70
 93 92 92 91 90 90 89 89 88 87
80
 87 86 86 85 84 84 84 83 83 82
90
 82 81 81 80 79 79 78 77 77 76
100
 76 76 75 75 74 74 73 73 72 71
110
 71 71 70 70 69 69 68 68 67 67
120
 66 66 66 65 65 64 64 63 63 62
130
 62 62 61 61 60 60 60 59 59 58
140
 58 58 57 57 56 56 55 55 54 54
150
 54 53 53 53 52 52 52 52 51 51
160
 51 51 50 50 50 49 49 48 48 47
170
 47 47 47 46 46 46 45 45 45 44
180
 44 44 44 43 43 43 42 42 42 41
190
 41 41 41 40 40 40 40 39 39 39
200
 39 38 38 38 37 37 37 37 36 36
210
 36 36 35 35 35 35 35 34 34 34
220
 34 34 33 33 33 33 33 32 32 32
230
 32 31 31 31 31 31 30 30 30 30
240
 30 29 29 29 29 29 28 28 28 28



Table 5.8. (contd)

Soil Moisture Storage (Sm(J))
-Wpj®
¯		 0 1 2 3 4 5 6 7 8 9
250
 28 27 27 27 27 27 26 26 26 26
260
 26 26 25 25 25 25 25 24 24 24
270
 24 24 24 23 23 23 23 23 23 23
280
 22 22 22 22 22 22 22 22 21 21
290
 21 21 21 20 20 20 20 20 20 20
300
 20 19 19 19 19 19 19 19 18 18
310
 18 18 18 18 18 18 18 17 17 17
320
 17 17 17 17 17 17 17 16 16 16
330
 16 16 16 16 16 16 16 15 15 15
340
 15 15 15 15 15 15 14 14 14 14
350
 14  14 14 14 14 14 14 13 13 13
360
 13 13 13 13 13 13 13 12 12 12
370
 12 12 12 12 12 12 12 12 11 11
380
 11 11 11 11 11 11 11 11 11 11
390
 11 11 11 10 10 10 10 10 10 10
400
 10 10 10 10 10  10 10 10 9 9
410
 9 9 9 9 9 9 9 9 9 9
420
 9 9 9 8 8 8 8 8 8 8
430
 8 8 8 8 8 8 8 8 8 8
440
 8 8 8 7 7 7 7 7 7 7
(a) Soil moisture retained after different amounts of potential evapotranspiration have occurred. Water-holding capacity of the soil root zone is 150 mm.


 If the soil moisture exceeds the water-holding capacity, the soil moisture is set equal to the water-holding capacity:



where
If the soil moisture remains below the water-holding capacity, a new accumulated potential water loss is computed using the soil moisture retention tables.  The change in the soil moisture storage is the difference between the current and previous month's soil moisture storage:



Thus, the change in soil moisture is positive if the soil moisture has increased, and negative if the soil moisture has decreased.

 Wet seasons are referred to as adequate or inadequate.  An adequate wet season is one with sufficient potential percolation to fully replace the soil moisture depleted during the previous dry season.  When this is the case, the computation of monthly soil moisture and accumulated potential water loss values is simple.  For the last month of an adequate wet season, the soil moisture is equal to the water-holding capacity of the soil and accumulated potential water loss is zero.  Then, starting with the first month of the following dry season, soil moisture and accumulated potential water loss are computed as described in the previous paragraph for all the remaining months of the year.

 An inadequate wet season is one without sufficient potential percolation to fully replace the soil moisture depleted during the previous dry season.  When this is the case, the computation of monthly soil moisture and accumulated potential water loss values is more complicated.  Thornthwaite and Mather (1957) describe a method of successive approximations to determine a starting value of accumulated potential water loss from which to start the monthly computations.  This involves 1) estimating the potential water deficiency at the end of the wet season, 2) estimating the accumulated potential water loss at the end of the dry season by adding on all the negative potential percolation values, 3) determining the associated soil moisture using the soil moisture retention tables, 4) adding on the positive potential percolation values for the wet season to estimate the soil moisture at the end of the wet season, 5) converting that soil moisture back to accumulated potential water loss, and then repeating the process until convergence is achieved.  This process can become quite complicated if a site contains multiple wet and dry seasons.  Details of the aforementioned calculations of accumulated potential water loss and soil moisture storage are given in Whelan et al. (1987).

 A variation on this approach is used in the source term release module.  Soil moisture is initially assumed to be at the water-holding capacity of the soil in January, and the accumulated potential water loss is zero.  Then, soil moisture and accumulated potential water loss are computed for each month in sequence, year after year, until the values in successive years for January converge.  When this occurs, the soil moisture and accumulated potential water loss for each month will have converged.  The benefit of this approach is that it will work for any number of wet and dry seasons, regardless of whether the wet seasons are adequate or inadequate.