HESS Opinions “Topography driven conceptual modelling (FLEX-Topo)”

Heterogeneity and complexity of hydrological processes offer substantial challenges to the hydrological modeller. Some hydrologists try to tackle this problem by introducing more and more detail in their models, or by settingup more and more complicated models starting from basic principles at the smallest possible level. As we know, this reductionist approach leads to ever higher levels of equifinality and predictive uncertainty. On the other hand, simple, lumped and parsimonious models may be too simple to be realistic or representative of the dominant hydrological processes. In this commentary, a new approach is proposed that tries to find the middle way between complex distributed and simple lumped modelling approaches. Here we try to find the right level of simplification while avoiding over-simplification. Paraphrasing Einstein, the maxim is: make a model as simple as possible, but not simpler than that. The approach presented is process based, but not physically based in the traditional sense. Instead, it is based on a conceptual representation of the dominant physical processes in certain key elements of the landscape. The essence of the approach is that the model structure is made dependent on a limited number of landscape classes in which the topography is the main driver, but which can include geological, geomorphological or land-use classification. These classes are then represented by lumped conceptual models that act in parallel. The advantage of this approach over a fully distributed conceptualisation is that it retains maximum simplicity while taking into account observable landscape characteristics. Correspondence to: H. H. G. Savenije ([email protected]) 1 What is the issue? The hydrological world is complex and heterogeneous. Yet we know that the reductionist approach: combining so-called physically based small scale basic principles (such as the Darcy, Richards, and Navier-Stokes equations) with detailed distributed modelling, leads to equifinality and high predictive uncertainty, mostly because these methods ill account for heterogeneity, preferential pathways and structural patterns on and under the surface. This reductionist approach is not appropriate at the catchment scale, as has been observed by many (e.g. McDonnell et al., 2007). At the same time, we know that – in spite of the high apparent complexity – hydrological behaviour is often unexpectedly simple, whereby parsimonious conceptual models often outperform much more complex ones, and with much less predictive uncertainty. Apparently, catchments are intermediate systems: highly heterogeneous systems with some degree of organisation (Dooge, 1986), where relatively simple models can do the trick. Catchments belong to the realm of organised complexity (Dooge, 2005). Simple catchment-scale models apparently make use of emerging patterns of self-organisation implicit in naturally formed catchments and river basins. But obviously we cannot be satisfied by this. On the one hand we need simplicity, but on the other hand there is a limit to how simple a model can be (e.g. Dooge, 1997). Simple relationships that behave well in a certain catchment under certain conditions may be useless elsewhere or under different hydrological conditions. Prediction in ungauged basins requires that the relationships found can be transferred, and hence that they are based on objective and physically observable characteristics. Obviously topography is such a characteristic. Distributed models make use of topography, but in a rather unsophisticated way: as brute force. It would be much more fitting to extract from the topography the signatures of the landscape and to translate these into a conceptual architecture. This is Published by Copernicus Publications on behalf of the European Geosciences Union. 2682 H. H. G. Savenije: Topography driven conceptual modelling (FLEX-Topo) not dissimilar to what Beven (2001) suggested when he said that landscape characteristics need to be mapped into conceptual structures and relationships. The reason why we model is because we want to predict hydrological behaviour under unknown circumstances: either to predict an uncertain future in a gauged catchment (with a calibrated model), or to predict behaviour in an ungauged catchment with an uncalibrated model. In both cases, the question is: How to map topographical, geological, soil, land cover and rainfall heterogeneity on a conceptual representation of dominant physical processes? 2 The role of topography In solving this question, we need to zoom-out and apply a giant’s view, where we model the dominant processes at the relevant scale. The reductionist view of the ant, who observes physical processes at a microscopic scale, does not lead to predictive equations at the relevant scale of the catchment, mainly due to heterogeneity and the disregard of large-scale patterns (Savenije, 2009). Conversely, we need to model our catchments at the macro-scale based on macro-scale observables, one of which is the organisation of the landscape into topographically controlled “functional units”, as discussed by Zehe and Sivapalan (2009). Indeed, there is a lot of heterogeneity: in the landscape, in the soil, in the terrain, and in the rainfall. But at larger scales there are patterns with strikingly simple emergent behaviour. Winter (2001) used topgraphical features to distinguish hydrological landscapes. He suggested that the dominant feature of a hydrological landscape is an upland separated from a lowland by an intervening steeper slope. When driving through the European landscape, a well-developed landscape intensively used for agriculture, forestry and settlements, it occurred to me that hill slopes are mostly forested while the undulating plateaus with their modest slopes are used for agriculture. Where hill slopes are cultivated, they are generally used for fruit trees or vineyards, but the dominant land use of hill slopes is forest. The wetlands close to the rivers are not forested (since trees require unsaturated soils during most of the time). They are generally used for agriculture (seasonal crops), pasture or as wetland areas. Settlements occur both in the riparian zones and on the plateaus, while roads cut through the hill slopes. But the overall picture is: agriculture on the plateaus, forests on the hill slopes and meadows and wetlands on the riparian zones. At the same time, I have always had the feeling that forests are key to the hydrological dynamics of the European rivers, even though the area occupied by forests is seldom large. While driving through the French landscape and seeing the dense forests on the hill slopes, it suddenly all came together. Floods are for a large part generated on hill slopes. The undulating plateaus do not generate much runoff, only under extreme rainfall conditions where Hortonian overland flow occurs (but this is rare, otherwise the landscape would be dominated by erosion and badlands), and much of the Hortonian overland flow is re-infiltrated downslope. The processes on the plateaus are mainly vertical, where rainfall is to a large extent balanced by evaporation, with the remainder recharging the groundwater. This groundwater partly ends up in the river as base flow but can also be intercepted by trees at the toe of the hill slope, reducing the drainage from the plateau even more. As a result the amount of groundwater from the plateau reaching the stream is probably small, particularly if the distance to the stream is large. Besides the saturation overland flow generated in the wetlands and riparian zones, the floods and most of the runoff dynamics are generated on the hill slopes, and these are mostly forested. This implies that forests could very well be a dominant land cover when studying flood generation or when performing flood forecasting. In this regard it is worrying that not many rainfall stations are located in forests, on hill slopes, or in mountainous areas. The riparian zones, although they may be responsible for the early flood response through saturation overland flow, due to their limited extent and modest slope, are often not the largest contributor to flood volumes. For a forest ecosystem to survive on a hill slope there are two important life-support functions which seem to be contradicting. One is drainage, the other is moisture retention. Excess water needs to be drained off so as to maintain an aerated soil. However drainage needs to take place in a way that it does not erode the foundation of the ecosystem (i.e. the soil) and in a way that enough moisture is retained to bridge dry spells. Sub-surface drainage through preferential pathways is an efficient mechanism in this regard. It does not cause excessive erosion and it allows the wetting of stagnant pockets in the soil from which the roots can tap their water (e.g. Brooks et al., 2010). Zehe et al. (2010) demonstrated that this combination of wetting and preferential sub-surface drainage is the most efficient mechanism to achieve maximum entropy, which has evolved over time. An additional characteristic of hill slopes is that they have a sub-surface connection to the groundwater storage of the plateaus. As a result of the rapid drop in the topography the phreatic level of the ground water comes close to the surface near the toe of the hill slopes. As a result, trees at the hollow of a hill slope can tap into the groundwater reservoir of the plateau during dry periods. Hence, the runoff coefficient of hill slopes is high, higher than the vertical water balance of the hill slope (rainfall minus evaporation) would suggest. On top of this, hill slopes tend to behave similarly all over the world that is, they all show threshold-like response to storm rainfall totals. For events below a local rainfall threshold, subsurface stormflow does not occur. For events greater than this threshold, subsurface stormflow is initiated. Despite differences in the matrix-macropore partitioning and different individual flow pathways within the hill slope, the overall scale response is the same (Uchida et al., 2005). The Hydrol. Earth Syst. Sci., 14, 2681–2692, 2010 www.hydrol-earth-syst-sci.net/14/2681/2010/ H. H. G. Savenije: Topography driven conceptual modelling (FLEX-Topo) 2683 ecosystems on hill slopes have created an environment where sub-surface drainage is the dominant feature. This is a logical arrangement for ecosystem survival. Surface runoff would erode the mere basis for the ecosystem, while water logging would make it impossible for most plant species to survive. Only a system of sub-surface drainage that exceeds a certain storage threshold, which the ecosystem would need to retain, is the hydrological mechanism that can support an ecosystem. Such a system, termed by Jeff McDonnell during his Dalton lecture (2009) as “storage excess subsurface flow” (SSF), is a mechanism that occurs throughout the world in different ecosystems, different geologies and different climates. This is the dominant rainfall-runoff mechanism on humid hill slopes. This sub-surface drainage mechanism through preferential pathways also supports the moisture retention function of the hill slope, so that the hill slope facilitates the two essential functions: drainage and moisture retention. In the riparian zone, obviously, the dominant mechanism is “saturation excess overland flow” (SOF). In these areas where slopes are modest, open water is near and, hence, the groundwater level is close to the surface, the amount of soil moisture storage available is small. After continued rainfall, an ever-increasing part of the riparian zone will become saturated, partly because of hill slope and plateau groundwater contributing, and saturation overland flow will feed the streams. The plateaus, on the other hand, do not take an active part in the rainfall-runoff behaviour. They rather have a moisture retention and evaporation function. The phreatic water table is deep and hence the unsaturated storage capacity is large. Trees can develop deep root systems and, year-round, can tap water from the unsaturated, or even saturated layers. Because the distance to the streams is large and the groundwater is deep, water table slopes are modest. In addition, underlying rock may have low lateral permeability and the groundwater reservoir may supply water to the forest in the hollow of the hill slopes. As a result, the groundwater contribution from the plateaus to runoff is small. The runoff process associated with the plateau therefore is termed “deep percolation” (DP). In general, this process is predominantly vertical while the lateral flow component is small with long residence times. During extreme rainfall events, the plateaus can trigger “infiltration excess overland flow”, also termed “Hortonian overland flow” (HOF). But this is generally exceptional and linked to land use, otherwise the plateaus would demonstrate constant traces of erosion. Mutatis mutandis, the same applies to other intensively inhabited regions of the world. Steep hill slopes are not much use for agriculture and are often forested, either by natural forests, production forests or plantations. Riparian zones are used for pasture or seasonal agriculture. Even in Africa, where I have worked for many years, the situation is not much different, albeit that the plateaus are also often forested, but that does not change the image that plateaus hardly generate lateral runoff and that forested hill slopes determine both the flood behaviour and the water resources availability. Hence also in natural environments, forested hill slopes host the dominant drainage processes. In modelling the runoff behaviour of the Zambezi basin, we realised that less than 10% of the groundwater reservoir is active in the rainfall-runoff process (Winsemius et al., 2006). This is the groundwater situated in the near-stream hill-slopes. 3 The role of geology, soil and climate Until now, we have discussed topography as the main driver of hydrological behaviour. But what is the role of geology and soils? And how important is the spatial distribution of the rainfall and other climatic factors? In an evolutionary sense, geology is less important than it appears at first sight. As stated before, hill slopes behave very similarly all over the world in different geological settings. All “stable” hill slopes (as far as there is stability in geological terms) irrespective of their geology, have developed a sub-drainage system that conceptually functions as a “storage excess subsurface flow” system (SSF). If they had not developed subsurface drainage, they would have disappeared due to the erosion that results from Hortonian overland flow (HOF). So the mature hill slopes that we see have survived as a result of the sub-surface drainage structure, in symbiosis with the ecosystem living on it. Of course there are also hill slopes that are barren, such as in deserts. The dominant mechanism there is most probably Hortonian overland flow, as there is no ecosystem that facilitated the formation of sub-surface drainage. Although the conditions under which they were originally shaped may have been quite different under different climatic conditions. So, in arid climates where ecosystems have not had the opportunity to maintain themselves, the dominant mechanism on hill slopes is probably Hortonian overland flow. If sub-surface drainage through preferential pathways is present in all vegetated hill slopes, then the role of geology is probably limited to the interaction with deeper groundwater layers and to the feasible parameter ranges. For instance, Fenicia et al. (2010) showed that for different catchments in Luxembourg, having very distinct geological properties (e.g. one in schist, one in sand stone and one in marl), similar model approaches for rapid subsurface flow could be used, but that the main differences between the catchments were in the parameter ranges and in the interaction with the groundwater (in schist and marl this interaction is almost non-existent, whereas in sandstone it is the dominant mechanism). So it seems that topography is more important to distinguish between hydrological processes than geology. Soils influence hydrological behaviour significantly. What is important is the texture of the soil: the porosity, the permeability, the layering, the existence of preferential flow channels, the water repellence, etc. An interesting phenomenon www.hydrol-earth-syst-sci.net/14/2681/2010/ Hydrol. Earth Syst. Sci., 14, 2681–2692, 201