Why would the isohyetal method typically provide the most accurate average areal rainfall for a watershed with complex topography, compared to other standard methods?

The isohyetal method typically provides the most accurate average areal rainfall for a watershed with complex topography because it uniquely accounts for the highly non-uniform spatial distribution of precipitation that such terrain creates. Average areal rainfall represents the total volume of rainfall over a watershed's entire surface area, divided by that area, yielding a single representative rainfall depth. This value is critical for hydrological analyses like flood forecasting or water resource management. Complex topography refers to landscapes characterized by significant variations in elevation, such as mountains, valleys, and steep slopes, which profoundly influence atmospheric conditions and precipitation patterns. For example, moist air rising over mountains experiences orographic lift, cooling and condensing to produce heavy rainfall on the windward side, while creating a drier "rain shadow" on the leeward side. Rainfall can change dramatically over short distances in these environments. The isohyetal method involves plotting rainfall depths measured at individual rain gauges on a map. From these points, lines of equal rainfall depth, called isohyets, are interpolated and drawn across the watershed. Unlike simpler methods that might assume a uniform distribution or linear change in rainfall between gauges, the process of drawing isohyets allows a skilled hydrologist to graphically interpret and explicitly incorporate the known influence of topography on rainfall. For instance, the analyst can visually infer higher rainfall on windward slopes and lower rainfall in valleys or rain shadows, even in areas without direct gauge measurements, guiding the shape and spacing of the isohyets. After the isohyets are drawn, the watershed area is divided into sub-areas by these lines. The average rainfall for each sub-area is then determined by averaging the values of the two bounding isohyets. The product of this average rainfall and the corresponding sub-area is calculated for each segment. Finally, these products are summed and divided by the total watershed area to compute the overall average areal rainfall. This graphical, interpretation-driven approach directly incorporates the observed and inferred spatial variability of rainfall dictated by the complex terrain, producing a detailed rainfall map. This results in a highly representative area-weighted average that accurately reflects the true precipitation input across the watershed, making it superior to methods that rely on simpler spatial assumptions which would fail to capture these crucial topographical effects.