## 4 Modeling Raised-Field Agricultural Function: Introduction and Analysis  
To gauge the kind of analysis required to understand the workings and efficiencies of raised-field systems designed by the Tiwanaku engineers, a number of factors need to be considered to understand the geophysical environment in which raised fields operate. These include (1) the salinization of raised fields through incursion of saline Lake Titiaca water and cases in which the Titiaca lake level temporarily exceeds the local fresh groundwater table height and/or the groundwater table recession due to drought conditions, leading to saline water intrusion affecting berm soil fertility; (2) drainage of freshwater saturated soils into raised-field swales when the lake level is below the local groundwater table height, which thus dries berm soils, limiting agricultural production; (3) agricultural land area, which depends upon Titicaca lake level (given that the ground slope of lakeside land is shallow, a rise in lake level can extensively flood and reduce agricultural land area); (4) changes in the heat storage capacity of a raised-field system due to surface sediment deposits from erosive rainfall runoff and lake height coverage sediment deposits; (5) agricultural berm soil fertility change resulting from rainfall flood conditions, producing nutrient leaching and monocultural cropping, whose post-harvest waste comprising compost matter lacks critical mineral nutrients when remixed into berm soils. Many of these effects depend upon the variability of Lake Titicaca water level, which is influenced by rainfall levels and drought events. The relation between these five effects and the lake level, denoted as h\({}_{1}\), as measured from a given reference plane, is shown in Figure 5 in schematic form. In this figure, h\({}_{\text{MN}}\) < h\({}_{\text{MX}}\), where h\({}_{\text{MN}}\) and h\({}_{\text{MX}}\) represent minimum and maximum possible Lake Titicaca levels. The h\({}_{\text{MN}}\) value represents an extended drought period lake level, while the h\({}_{\text{MX}}\) value represents a maximum flood lake level. The 'normal' lake level h height fluctuation range is defined to be h\({}_{\text{N2}}\) < h < h\({}_{\text{N1}}\), involving rainfall amounts between h\({}_{\text{N2}}\) and h\({}_{\text{N1}}\), which represent the normal seasonal lake level variation. Other lake level fluctuations may occur due to long- or short-term climate cycles, involving varying rainfall amounts into the altiplano drainage or watershed zone, which channels groundwater and runoff into the lake. As the lake level increases, salinization, which is a function of (h\({}_{2}\)-h\({}_{1}\)), also increases (Figure 5). This reflects the fact that saturation by any means other than fresh groundwater increases as (h\({}_{2}\)-h\({}_{1}\)) decreases. The quantity h\({}_{2}\) is defined to be the groundwater average height above a reference plane. Similarly, drainage of groundwater varies with (h-h\({}_{1}\)), as the higher the groundwater level with respect to the lake level, the greater the drainage capability of preserving agriculture in the raised fields. This factor greatly affects the initiation and completion time of the growing season. The arrival of the maximum groundwater flow to the field systems near the lake edge occurs past the peak of the rainy season. This is due to the generally low flow percolation speeds of groundwater deposited at remote low slope eastern locations within the collection basin of the lake added to local rainfall absorption into berm soils. The local low ground permeability constants and low aquifer pressure gradients are then the source of the continuous arrival of groundwater from multiple sources to the lake edge, including significant groundwater flows in the dry season. Thus, the swales can serve as channels to help drain the berm ridges in dry as well as wet months when h\({}_{2}\) > h\({}_{1}\).