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            "106": {
                "pageid": 106,
                "ns": 0,
                "title": "Richards Equation:Distributed parameters",
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                        "*": "As with all distributed parameters, the distributed parameters for the Richards\u2019 equation are assigned using index maps and the mapping tables as described in [[Mapping:Assigning Parameter Values to Individual Grid Cells|Chapter 5]].  Assignment of parameters with Richards\u2019 equations differs from the other processes in that for each different soil type in the index map, three soil layers must be defined.  Parameters and discretization must also be assigned for all three layers.  The parameters that must be defined depends on which option is used to define the PCS curves, ''Brooks'' or ''Havercamp''.  The ''Havercamp'' formulation is best if laboratory data are available to fit the needed parameters as detailed below (Figure 22).  Testing by Downer (2002) showed that the Havercamp equations could best define the soil behavior.  If no detailed data exist, as is typical, then the Brooks and Corey (1964) method may be used and the parameters needed for the Brooks and Corey model can either be measured or estimated from soil textures and literature sources such as Rawls, Brakensiek, and Saxton (1982).\n\nParameters for the Richards\u2019 equation are assigned in the ''GSSHA Mapping Table Editor''.  For the Brooks and Corey method, the following parameters are assigned for each of the three layers. \n\n:* ''Hydraulic Conductivity'' \u2013saturated hydraulic conductivity of the soil describes the rate water will enter the soil under unit head and saturated conditions  (cm/hr) .\n:* ''Porosity''  - volume of voids/total volume of soil, fraction between 0.0 to 1.0 (m<sup>3</sup>/m<sup>3</sup>).\n:* ''Residual saturation'' \u2013water content of air dry soil, fraction  between 0.0 to 1.0 (m<sup>3</sup>/m<sup>3</sup>).\n\n[[Image:image041.gif|frame|none|'''Figure 31.''' Water retention curves, water content vs. negative pressure head, for both sand and clay.  The Havercamp, Brooks & Corey and extended Brooks and Corey equations are shown. (BC \u2013 after Brooks & Corey 1964)]]\n\n:* ''Wilting point'' \u2013 fraction between residual saturation and porosity, water content below which plants cannot uptake water from the soil (m<sup>3</sup>/m<sup>3</sup>).\n:* ''Depth'' \u2013 thickness of the soil layer (cm).  Should be rounded up or down to nearest centimeter.\n:* ''Lambda'' \u2013 pore distribution index (cm/cm).  Describes the straight line length to the soil water path length.\n:* ''Bubbling pressure'' \u2013 pressure at which air enters the soil column (cm).  Must be negative.\n:* ''Delta Z'' \u2013 vertical cell size of the layer (cm).  Should be evenly divisible into the depth of the layer.\n\nFor the Havercamp method, the following parameters must be specified for each of the three layers.  Parameters from the Havercamp method must be determined from field or laboratory testing.\n\n:* ''Hydraulic Conductivity'' \u2013saturated hydraulic conductivity of the soil (cm/hr) describes the rate water will enter the soil under unit head and saturated conditions.\n:* ''Porosity''  - volume of voids/total volume of soil, fraction between 0.0 to 1.0 (m<sup>3</sup>/m<sup>3</sup>).\n:* ''Residual saturation'' \u2013water content of air dry soil, fraction  between 0.0 to 1.0 (m<sup>3</sup>/m<sup>3</sup>).\n:* ''Wilting point'' \u2013 fraction between residual saturation and porosity, water content below which plants cannot uptake water from the soil (m<sup>3</sup>/m<sup>3</sup>).\n:* ''Depth'' \u2013 thickness of the soil layer (cm).  Should be rounded up or down to nearest centimeter.\n:* ''Alpha'' \u2013 factor fitted from field or laboratory data.\n:* ''Beta'' \u2013 factor fitted from field for laboratory data.\n:* ''AHAV'' \u2013 factor fitted from field for laboratory data.\n:* ''BHAV'' - factor fitted from field for laboratory data.\n:* ''Delta Z'' \u2013 vertical cell size of the layer (cm).  Should be evenly divisible into the ''depth'' of the layer.\n<noinclude>\n{{PrimNav|PNav11}}\n</noinclude>"
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            "104": {
                "pageid": 104,
                "ns": 0,
                "title": "Richards Equation:Global parameters",
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                        "*": "The global parameters for Richards\u2019 equation are set from the ''GSSHA Job Control Parameters'' dialog under the Infiltration options.  With ''Richard\u2019s infiltration'' toggled on, hit the ''Edit Parameters...'' button to access the global parameter list.  The global parameters are:\n\n:* ''Weight'' \u2013 Fraction  between 0.0 and 1.0 (dimensionless).  This is the weighting factor used to calculate inter-cell hydraulic conductivities when using an ''arithmetic mean'' to calculate the inter-cell hydraulic conductivities.  Use 1.0 for forward weighting, 0.0 for backwards, and 0.5 for central.  The default value is 1.0\n\n[[Image:image039.jpg|frame|none|'''Figure 30.''' GSSHA representation of the unsaturated zone]]\n\n:* ''DTHETA Max'' \u2013 Fraction between 0.0 and the porosity of the soil (m^3/m^3), the maximum allowable water content change in any finite difference cell during a single time-step.  Typical range is between 0.002 and 0.030 (Belmans, Wesseling, and Feddes 1983).  The default value is 0.025.\n:* ''C Option'' \u2013 ''Brooks'' or ''Havercamp'' sets the curves used to define the relationships between water content and soil suction, pressure, and water content and hydraulic conductivity.  An example of the curves for a typical clay and sand are shown in Figure 22. The user is referred to the [[Infiltration:Richards\u2019 Equation#7.1.2 Non-linear Coefficients|''GSSHA User\u2019s Manual'']] for more detailed information on this topic.  The default value is ''Brooks''.\n:* ''K Option'' \u2013 (''Arithmetic'' or ''Geometric'') method used to calculate inter-cell hydraulic conductivities.\n:* ''Upper Option'' \u2013 method used to determine the hydraulic conductivity at the soil surface during ponded water conditions; the options are ''Normal'', ''Green Ampt'', and ''Average''.  ''Normal'' specifies that the normal cell-centered value of hydraulic conductivity be used, ''Green Ampt'' specifies that the saturated hydraulic conductivity of the soil in the cell be used, and ''Average'' specifies that an average of the two be used.  The default value is ''Normal''. For more information, see the [[Infiltration:Richards\u2019 Equation#7.1.4 Upper Boundary Condition|''GSSHA User\u2019s Manual'']].\n:* ''Max Iteration'' \u2013 the maximum number of iterations each time-step to determine water capacity and hydraulic conductivity. The typical range is 1 to 10 iterations. The default value is 1. \n:* ''Max Num'' \u2013 integer value, maximum number of cells in any unsaturated soil column.\n<noinclude>\n{{PrimNav|PNav11}}\n</noinclude>"
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