Deterministic Methods in Systems Hydrology - Chapter 7

Mô hình đơn giản của dòng chảy dưới bề mặt7.1 chảy qua MEDIA xốp Trong Chương 5 và 6, chúng tôi đã quan tâm đến phân tích hộp đen và mô phỏng bằng mô hình khái niệm của các phản ứng cơn bão trực tiếp, tức là phần trả về nhanh chóng của các lưu vực để đáp ứng lượng mưa. Những khó khăn phát sinh trong cách tiếp cận đơn vị thuỷ văn liên quan đến baseflow và giảm có thể có mưa với lượng mưa có hiệu quả, phát sinh từ thực tế rằng các quá trình này...
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Deterministic Methods in Systems Hydrology - Chapter 7 CHAPTER 7 Simple Models of Subsurface Flow 7.1 FLOW THROUGH POROUS MEDIA In Chapters 5 and 6 we have been concerned with the black box analysis and the simulation by conceptual models of the direct storm response, i.e. of the quick return portion of the catchment response to precipitation. The difficulties that arise in the unit hydrograph approach concerning the baseflow and the reduction of precipitation to effective precipitation, arise from the fact that these processes are usually carried out without even postulating a crude model of what is happening in relation to soil moisture and groundwater. Even the crudest model of subsurface flow would be an improvement on theGroundwater classical arbitrary procedures for baseflow separation and computation of effective precipitation used in applied hydrology. It is desirable, therefore, for the study of floods as well as of low flow to consider the slower response, which can be loosely identified with the passage of precipitation through the unsaturated zone and through the groundwater reservoir. In other words, it is necessary to look at the remaining parts of the simplified catchment model given in Figure 2.3 (see page 19). We approached the question of prediction of the direct storm response through the black-box approach in Chapter 4 and then considered the use of conceptual models as a development of this particular approach in Chapter 5. In the case of subsurface flow, we will take the alternative approach of considering the equations of flow based on physical principles, simplifying the equations that govern the phenomena of infiltration and groundwaterflow and finally developing lumped conceptual models based on these simplified equations. The basic physical principles governing subsurface flow can be found in the appropriate chapters of such references as Muskat (1937), Polubarinova-Kochina (1952), Luthin (1957), Harr (1962), De Wiest (1966), Bear and others (1968), Childs (1969), Eagleson (1969), Bear (1972), and others. The movement of water in a saturated porous medium takes place under the action of a potential difference in accordance with the general form of Darcys Law (7.1) V   Kgrad ( ) where V is the rate of flow per unit area, K is the h ydraulic conductivity of the porous medium and  is the hydraulic head or potential. If we neglect the effects of temperature and osmotic pressure, the potential will be equal to the p iezometric head i.e. the sum of the pressure head and the elevation: p Darcys Law   h   z   S  z (7.2)  where h is the piezometric head, p is the pressure in the soil water, y is the weight density of the water, S is soil suction and z is the elevation above a fixed horizontal datum. Since we are interested in this discussion only in the simpler forms of the groundwater equations, we will immediately reduce Darcys law to its one-dimensional form. The assumption is commonly made in groundwater hydraulics that all the streamlines are - 114 - approximately horizontal and the velocity is uniform with depth so that we can adopt a one- dimensional method of analysis. This is known as the Dupuit-Forcheimer assumption and it gives the one-dimensional form, of the equation (7.1)  (7.3) V ( x , t )   K [ h( x , t ] x where K is the hydraulic conductivity as before and h is the piezometric head. The above assumption leads immediately to the following relationship between the flow per unit width and the height of the water table over a horizontal impervious bottom as: ...