How to define hydrological functioning and how to connect it with structural catchment properties?

Thursday, 25 September 2014
Simon P Seibert1, Erwin Zehe1, Uwe Ehret1 and Conrad Jackisch2, (1)Karlsruhe Institute of Technology, Institute of Water and River Basin Management, Karlsruhe, Germany, (2)Karlsruhe Institute of Technology, Karlsruhe, Germany
Abstract:
The hydrologic community still lacks methods which allow regionalizing hydrological behavior. The main reasons for this are a) the lack of a commonly accepted and precise definition of functional characteristics in terms of quantitative descriptors and b) our limited understanding how functional characteristics are controlled by terrestrial system properties and the climate stetting. Nevertheless, there seems to be a common agreement upon the need for functional descriptors in order to characterize and classify our catchments; to identify minimum adequate model structures, and to support predictions based on a regionalization of hydrological behavior. To move a step forward we outline our theoretical concept on ‘hydrological functioning’. Based on our notion we developed a set of candidate descriptors which provide information on selected first order catchment controls on the headwater scale (< 150 km²).

Our concept relies partly on a thermodynamic perspective, which is helpful to separate the climatic and terrestrial properties which drive hydrological fluxes, from those, that control the different forms of storage and release. A necessary first step in this context is to express hydrologic processes and fluxes in thermodynamic terms. At a very basic level the second law of thermodynamics says, that gradients are depleted by the fluxes that are caused by these gradients. This applies regardless if we deal with fluxes of energy or mass (which includes water) (Kleidon et al. 2013). This interpretation of the second law of thermodynamics is the foundation for expressing hydrologic fluxes in a common way as a product of a conductance (or an inverse resistance, R) and a gradient ∇Φ.

q=-1/R·∇Φ(Eq. 1)

In hydrology both, resistances and gradients, typically do not occur as scalars but as fields. Hydrologically relevant fields of gradients are e.g. soil and air temperature, soil and plant water potentials, piezometric heads or surface water levels. These determine the (thermodynamic) forces which drive turbulent fluxes of latent and sensible heat and/or related fluxes of capillary soil water (sustaining evapotranspiration) and/or free water (sustaining the different components of runoff). The magnitude of these fluxes is constrained by hydrologically relevant resistances (again these are fields), such as inverses of either the soil heat conductance or the canopy resistances or the surface roughness or the soil hydraulic conductivity. These determine the dissipative losses of energy along the flow path. Resistance fields in larger control volumes (or areas) such as the critical zone of a hillslope or catchment (or its surface) are largely dependent on patterns of system states (i.e. soil moisture or the plant height) and the spatial covariance of textural properties (of the soil or of surface plant cover). Organized network like structures such as surface and subsurface preferential flow paths (surface rills, macropores, pipes) or vegetation and near surface atmospheric turbulent structures considerably reduce these flow resistances. Based on Eq. 1 and the associated mass- and energy balances we expect larger control volumes i.e. hillslopes or catchments to function similarly if they are similar with respect to terrestrial controls on the pair of gradient and resistance fields controlling either land surface energy exchange or stream flow generation (referred to rainfall runoff in the following).

Evapo-transpiration (ET) is as latent heat flux tightly related to the land surface energy balance. ET is the first essential form of how a catchment may release water (as vapor to the atmosphere). ET is fed by soil water which is stored against gravity due to the capillary binding. This is the first essential form of how a catchment can store water. ET is driven by radiative heating of the near surface atmosphere. Stream flow is the second essential form of how a catchment may release water (as free and liquid water into a connected river net). Runoff feeds from rainfall and/or direct runoff (free water) or from the other fundamental form of how a catchment can store water (free water in the aquifer). Contrary to ET, runoff is solely driven by gravity.

Functional descriptors should thus separately quantify the interplay of these different forms of ‘water release’, the related different forms of ‘water storage’ and of the underlying terrestrial and atmospheric controls (which are again essentially different).

A first assessment to judge the feasibility of candidate descriptors for instance for rainfall runoff/ free water release as stream flow is whether those descriptors a) discriminate among catchments which are “structurally” different, b) remain similar for “structurally” similar catchments and c) allow for disentangling climatic and terrestrial controls of functional similarity. Naturally, we might expect that catchments functional similarity with respect to free water release as stream flow might emerge at the time scale of rainfall events and at the annual time scale. This is because the former operates a short time scales, reflecting partly the high frequencies of the rainfall forcing. The latter is strongly controlled by slow flow, reflecting “low pass elements” in the catchments (which dampen high frequencies) such as snow pack and even glaciers melt and of course base flow from the aquifer. It is important to stress that equation 1 is immanently subjected to equifinality (Beven and Freer, 2001) as several combinations of gradients and resistances may yield the same flux of energy or mass. This implies that structural catchment descriptors must be grouped into teams of controlling the pair of driving gradient and resistance for both forms of water release. Gradients driving capillary water release by ET are controlled by radiative heating (slope, aspect and most important albedo), soil water retention properties (controlling capillary rise) and the plant water potentials. Vegetation (via the stomata conductance) and soil hydraulic conductivity control the resistance term as a function of plant water and capillary water storage. Gradients driving free water release as stream flow are largely related to topographic gradients and thus straight forward to determine – at lease for the surface. Resistances are determined by the aquifer permeability, soil hydraulic conductivity and apparent preferential flow paths in soil and in the aquifer. Although the latter are the big unknown, they leave fingerprints in event scale runoff as preferential flow and bypassing which is similar to Hortonian overland flow an (rainfall) intensity controlled threshold process. All other forms of runoff generation are expected to depend monotonously on accumulated water storage.

As a starting point we propose a set of candidate descriptors which addresses the following issues:

  • Storage: Motivated by the question of how to quantify fundamental storage (state) properties on the catchment scale we present attempts to approximate storage type(s), total active volume, temporal dynamics and the degree of (non-)linearity. By relating some of these methods to selected streamflow properties our descriptor candidates reveal (if present) information on empirical storage-baseflow relationships, the time span (lag) required for discharge to decline to baseflow after a precipitation input and simple storage-discharge relationships. The latter may help to find out whether runoff generation within a catchment is primarily storage controlled or (at least partly) intensity controlled.
  • The partitioning of precipitation on the land surfaced is fundamental to the interplay of runoff and evapotranspiration since the former is driven by gravity (comparably small energy fluxes are associated with large mass fluxes) whereas the latter is controlled by solar energy (comparably high fluxes of energy are associated with small fluxes of mass). Following the concept of the Budyko curve we introduce double and triple-mass curves which relate the mass to the energy balance, but with the difference that our concept assesses and interprets the dynamics of both, mass and energy, as a characteristic property of the system. We apply this concept to the long-term and to the seasonal time scale and with respect to different periods of the year (e.g. winter vs. period of vegetation). This way we capture the different forms of ‘water release’. In a second step we assess the impact of (grouped) structural catchment descriptors on the driving gradients and resistances. 

Basically, all of our methods are based on the rationale that different functional system properties need to be analyzed on the appropriate natural time scales (i.e. long-term mean vs. annual and/ or seasonal dynamics vs. behavior on the event-scale). For this purposes we combine both, continuous and intermittent data with different spatial and temporal resolution. Furthermore, several of our descriptors rest on subsets of the data with clearly defined temporal constraints like winter time, period of vegetation, night time, periods with extraordinary high mass and/ or energy input, and so on.

References

Beven, K., and Freer, J.: Equifinality, data assimilation, and uncertainty estimation in mechanistic modelling of complex environmental systems using the glue methodology, Journal Of Hydrology, 249, 11-29, 2001.

Kleidon, A., Zehe, E., Ehret, U., and Scherer, U.: Thermodynamics, maximum power, and the dynamics of preferential river flow structures at the continental scale, Hydrology And Earth System Sciences, 17, 225-251, 10.5194/hess-17-225-2013, 2013.

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