Flood prediction in ungauged basins — catchments without discharge records for calibration — can be attempted by transplanting parameters from a similar gauged donor basin. Kong, Li and Liu (2019) demonstrated this with the physically based distributed TOPKAPI model, transferring a parameter set calibrated on the gauged Xixian basin (upper Huaihe, China) to the adjacent, nominally ungauged Huangchuan basin with acceptable but degraded skill (average Nash-Sutcliffe efficiency about 0.67; qualified rate 69.23%), and posed four unresolved issues: prohibitive computation at fine (200 m) grids versus accuracy; the absence of systematic rules and criteria for successful parameter transfer; a systematic structural bias toward oversteep flood hydrographs and total-volume underestimation attributable to the confluence assumptions; and unknown applicability to dissimilar basins. Later work by the same group (Sheng et al. 2025) gave a multi-scale framework and scale-extrapolation transfer method for one reservoir catchment, partially treating the resolution issue. The remaining open problem is to establish validated, a-priori-applicable criteria for when and how parameter transplantation to ungauged basins succeeds for TOPKAPI-type physically based distributed models, including correction of the structural routing bias and extension along the basin-dissimilarity gradient.

Background

A river basin is called ungauged when no discharge measurements exist to calibrate a rainfall-runoff model, which is the standard situation in many mountainous and developing regions. Conceptual or lumped models (for example the Xin'anjiang model used widely in China) require historical discharge for calibration, so in ungauged basins one must either estimate their parameters indirectly or use models whose parameters can be derived from physical data. This is the core of the IAHS Predictions in Ungauged Basins (PUB) initiative, whose decade (2003-2012) review concluded that transferring model parameters from similar gauged catchments remains a central, unsolved challenge, with most transfer methodology developed for lumped conceptual rather than physically based distributed models (Hrachowitz et al. 2013). TOPKAPI (TOPographic Kinematic APproximation and Integration) is a physically based distributed rainfall-runoff model (Liu and Todini 2002) built by integrating the kinematic wave equation over a grid of cells, which converts soil, overland, and channel flow into three cascades of nonlinear reservoirs whose parameters — soil thickness, saturated hydraulic conductivity and water content, surface roughness, and channel Manning coefficients — are in principle scale-independent and obtainable from digital elevation, soil, and land-use maps. In the kinematic wave approximation the water surface slope equals the bed slope, which simplifies routing but neglects storage and backwater effects. The Manning coefficient of each channel reach is assigned by Strahler order, a stream-ordering rule in which headwater tributaries have order I and a reach formed by joining two reaches of equal order has that order plus one. GLUE (Generalized Likelihood Uncertainty Estimation) is a Monte Carlo method that runs thousands of random parameter sets, retains the behavioral ones that reproduce observations above a likelihood threshold (here Nash-Sutcliffe efficiency, NSE, exceeding 0.7), and diagnoses which parameters control the output; NSE measures hydrograph fit (1 is perfect). A qualified forecast in Chinese operational practice is one with volume or peak error within ±20%. Kong, Li and Liu (2019) calibrated TOPKAPI at 200 m resolution on 16 floods (1991-2003) in the Xixian basin (10,190 km²; average NSE 0.84) and transferred the parameters directly to the adjacent Huangchuan basin (1,989 km², treated as ungauged) for 13 floods (2003-2005), obtaining average NSE 0.67, absolute average volume and peak errors of 17.39% and 17.78%, and a 69.23% qualified rate. Their GLUE analysis (3,000 samples, 283 behavioral sets) ranked soil thickness and saturated soil water content as most sensitive, with the Manning coefficient of high-Strahler-order channels also important. The same paper listed the four unresolved issues that define this problem: the computational cost of fine grids versus accuracy; the lack of systematic rules and criteria for parameter transfer (aggravated by donor-target mismatches such as different soil composition — clay covers 71.48% of Xixian but 53.74% of Huangchuan — and Strahler-order channels that are not physically comparable between basins of very different size); the systematic tendency to simulate hydrographs with steeper rise and recession and to underestimate total flood volume, pointing to the kinematic-wave confluence assumptions; and the untested transferability to basins dissimilar in climate, soil, or topography.

Problem Statement

For physically based distributed rainfall-runoff models of the TOPKAPI type, elucidate and validate systematic rules and criteria under which a parameter set calibrated (or physically estimated) in a gauged donor basin produces flood forecasts of acceptable accuracy in an ungauged target basin, where acceptability is judged by operational metrics such as Nash-Sutcliffe efficiency and flood volume or peak error within ±20%. The question, as posed by its source, comprises four jointly supporting components that must be answered within one coherent body of evidence: (1) how grid resolution should be chosen given that fine meshes (around 200 m) make computation prohibitive, especially for large watersheds, while coarse meshes degrade the representation of topography, soil, and channel inputs — a component since advanced by the multi-scale and scale-extrapolation experiments of Sheng et al. (2025) in one reservoir catchment, but without a general resolution-selection rule; (2) which parameters transfer and how attributes that do not correspond between basins — for example Strahler-order channel classifications that are not physically comparable between catchments of very different size, or differing soil composition — should be mapped or adjusted; (3) how the model's systematic structural tendency to produce flood hydrographs with too-steep rising and recession limbs and to underestimate total flood volume, which the source traced to the underlying confluence assumptions, should be diagnosed and corrected; and (4) how transfer performance degrades as donor and target basins become more dissimilar in climate, soil, and topography, beyond the similar-adjacent-basin case tested so far. A complete answer addresses all four components and provides a set of a-priori-applicable criteria — usable before any local discharge data exist — demonstrated across a range of donor-target pairs that spans the dissimilarity gradient beyond the single similar-adjacent pair reported so far.

References

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