2.1. Water balance
Because of the LUC project’s interest in how changes in land use as well as climate are affecting China’s development, any hydrologic model developed to assess the water resources in China must be sensitive to land cover, land use and management practices.
This problem is not a new one and the fact that runoff can vary considerably in time and volume with different land cover, land use, and management practices is well known. As early as 1972, the Soil Conservation Service in the United States had published a method for estimating direct runoff from storm rainfall that addressed this problem for direct runoff. (SCS, 1985) The method was the result of decades of research and has been evolving ever since. In 1986, the Soil Conservation Service developed the TR-55 model, using this ‘curve-number’ method, with the specific goal of assessing the effects of urban development on runoff (SCS, 1986). The ‘curve-number’ method has also been used as the direct runoff component in the HELP (Hydrologic Evaluation of Landfill Performance) model used by the US Environmental Protection Agency (EPA, 1994), the SWAT (Soil Water Assessment Tool) model (USDA, 1994) and many others. Because of its wide acceptance and ability to handle different soil types, land use, and management practices, the ‘curve number’ method is also used as the direct runoff component of CHARM. Once direct runoff is abstracted, the remaining water enters the soil moisture zone where a relatively simple water balance is done, abstracting water for evapotranspiration and sub-surface runoff. The overall structure of the water balance used in the hydrologic model is depicted below in Figure 1:
Precipitation Evapotranspiration
Surface Runoff
Sub-surface runoff Infiltration
Figure 1: Structure of water balance used in CHARM
As shown in Figure 1, the water balance consists of five components: precipitation, surface runoff, infiltration, evapotranspiration, and sub-surface runoff. A water balance equation describing the above figure can be written as:
)
Smax ≡ maximum soil storage capacity
Each of the components of this water balance is discussed in the following sections.
2.2. Precipitation
Precipitation is given as input to the model and is discussed later with the other model inputs.
2.3. Surface Runoff
As discussed above, direct runoff is calculated by CHARM according to the curve number method. The basic premise of the SCS method is that the ratio of direct runoff to total precipitation after an initial abstraction is the same as the ratio of water retained in the soil to the maximum soil retention:
Rmax
Ia ≡the initial water abstraction before any runoff will occur (mm) R ≡water retained in the watershed (mm)
Rmax ≡maximum retention in the watershed (mm) DR ≡direct runoff (mm)
By the continuity principle:
DR I
P
R=( − a)− Equation 3
Substituting equation 3 into equation 2 yields:
a
An empirical relationship was developed for the initial abstraction and is:
2 max
. 0 R
Ia = Equation 5
)
Now, plotting direct runoff over precipitation for many watersheds, the SCS found a family of curves and developed a dimensionless constant, the curve number (CN), to describe these curves. The curve number varies from 0 to 100 and depends on land use, management practices, and soil type. The curve number can be used to calculate the maximum retention (in mm) by the following formula:
) 100 1 (
max =254 −
R CN Equation 7
Tables of curve numbers match land use and management practices and soil types to obtain a curve number for those conditions. A small, sample curve number table is shown in Table 1 below:
Land Use Hydrologic Soil Group
A B C D
Cultivated Land: without conservation treatment 72 81 88 91 Cultivated Land: with conservation treatment 62 71 78 81 Pasture or range land: poor condition 68 79 86 89 Pasture or range land: good condition 39 61 74 80 Wood or forest land: thin stand, poor cover, no mulch 30 58 71 78
Wood or forest land: good cover 25 55 70 77
Commercial and business areas (85% impervious) 89 92 94 95 Industrial districts (72% impervious) 81 88 91 93 Residential: 1 acre lot size (20% impervious) 51 68 79 84 Residential: 1/2 acre lot size (25% impervious) 54 70 80 85 Residential: 1/8 acre lot size (65% impervious) 77 85 90 92 Paved parking lots, roofs, driveways, etc. 98 98 98 98 Table 1: Sample SCS curve number table
The LUC soil types and land use categories were matched with the SCS land use tables to obtain curve numbers for China. Since slope data is available, a slope adjustment is also made by CHARM to the curve number by the following formula (USDA, 1994, p. 13):
2
CN2s ≡curve number for antecedent moisture condition 2 corrected for slope CN2 ≡curve number for antecedent moisture condition 2
CN1 ≡curve number for antecedent moisture condition 1 SL ≡slope (m/m)
The curve number for antecedent moisture condition 1 can be found from the following equation:
The curve numbers, then, allow for the calculation of surface runoff according to equation 6. The remaining rainwater that does not run off directly infiltrates into the soil, where it is influenced by evapotranspiration and sub-surface runoff as described in the following sections.
2.4. Evapotranspiration
To calculate evapotranspiration, CHARM applies a method recommended by FAO (FAO, 1998) and similar to the method used in the Agro-Ecological Zoning Methodology (Fischer et al., 2000). Because the estimation of evapotranspiration itself requires a large number of calculations and is discussed in these other sources, the equations are not included here. However, the development of the equations used for evapotranspiration and their implementation in CHARM is discussed completely in Appendix I.
2.5. Sub-Surface Runoff
The final component of the water balance in CHARM is sub-surface runoff (SSR), which accounts for any water that runs off beneath the soil surface by percolating down through the soil. This process is also accomplished quite simply in CHARM by use of a calibration coefficient (α) multiplied by a function of the relative storage (z). (Kaczmarek, 1991;
David Yates, 1996; Perrin Bowling, 1997):
z2
SSR=α Equation 10
Referring back to Figure 1, we now see that all the components of the water balance are calculated and Equation 1 is complete. With the methods of the individual components established, we can now go on to look at the larger picture of how the model functions.