Sharing perceptual models of uncertainty: On the use of soft information about discharge data
Ida K. Westerberg, Reinert Huseby Karlsen · Hydrological Processes · 2024
Many hydrologists face the situation of having little or no information about the uncertainty in the hydrometeorological data they are using (e.g., Addor et al., 2020). Data uncertainty is rarely communicated by monitoring agencies and data providers—and is often not available on request. This means that data users typically treat data as if they are error-free, whereas in reality there can be large uncertainties and errors (McMillan et al., 2012). A striking example is that 50% of 1523 site-months of discharge data were found to be unreliable in a recent evaluation of the National Ecological Observatory Network streamflow estimates (Rhea et al., 2023). Such quality assurance of hydro-meteorological data requires substantial efforts (Meles et al., 2022). Therefore, lack of resources and/or sufficient data quality-assurance protocols frequently result in biases and errors remaining in delivered data (Tomkins, 2012; Viney & Bates, 2004; Westerberg et al., 2010; Wilby et al., 2017). However, the absence of metadata and 'hard' information about data uncertainty (i.e., estimated uncertainty bounds and underlying control measurements, see for example, Kiang et al., 2018) does not mean that there is no information about the data uncertainty. Instead, we can use 'soft' information to understand the likelihood that hydrometeorological data in a particular location are uncertain. Soft information can primarily inform us about epistemic data uncertainty, that is, related to lack of knowledge within the measurement process (see McMillan et al., 2018). Soft information can reveal factors that cause poorly known deviations from ideal monitoring conditions, or factors that make it likely that there is lack of knowledge about models used in the derivation of a data value from a measured proxy variable (such as rating-curve models used to derive discharge data from measured water level at river gauging stations). For example, if there are few high flow events, they are of short duration (i.e., a few hours), and/or the rainfall–runoff lag time is similarly short, it is practically difficult to manage to gauge high flows, leading to likely lack of knowledge about the high flow rating curve model and large uncertainty in the derived high flow data (Figure 1a). Conversely, if the catchment lake area and/or degree of river regulation is large, this leads to a dampened flow variability with longer and slower flow peaks that makes it easier to manage to gauge high flows and therefore likely leads to lower uncertainty in the high flow rating curve model and the discharge data (Figure 1b). A third example of soft information is if a river is ice-covered during the winter season: this leads to poorly known ice-impacts on the monitoring conditions and most of the winter discharge time series needs to be subjectively estimated, using procedures that may change over time (Hamilton & Moore, 2012). This practice leads to substantial uncertainty in winter low flows and makes the data unsuitable for many analyses such as recession (Stoelzle et al., 2013), drought (Brunner et al., 2021), or winter low flow change analyses (Juston et al., 2014). Such soft information about data uncertainty is well known by field hydrologists and data uncertainty experts but is not as commonly known in the wider hydrological community. In this commentary we focus on discharge data uncertainty with the aim to share—and to encourage sharing—of soft information about data uncertainty sources, to promote more informed decisions on data uncertainty in hydrological studies. Soft information about data uncertainty can be summarized in a perceptual model of uncertainty (Westerberg et al., 2017). A perceptual model of uncertainty mirrors the perceptual model of a hydrological system (Beven, 1991; Beven & Chappell, 2021), and summarizes our qualitative (and personal) understanding of the uncertainty sources involved in studying the system. It is a useful first step to identify and characterize uncertainty sources in any analysis of data uncertainty (McMillan et al., 2018). Here we formulate a generalized perceptual model that contains a smorgasbord of soft information about uncertainty sources that can be employed as pertinent to a particular dataset. We limit our example to discharge data uncertainty, but similar perceptual models can be made for other hydrometeorological variables such as precipitation or soil moisture. The soft information of interest partly depends on the monitoring technique, and here we focus on that relevant to the stage–discharge rating curve monitoring method (Rantz, 1982). It is the most common discharge monitoring method and uses a rating curve model of the stage–discharge relation at the river gauging site to calculate discharge time series from stage (i.e., water level) time series (Figure 1). The discharge is therefore not measured directly but is instead a derived data variable (Beven et al., 2012), impacted by uncertainty in the measurement of water level as well as uncertainty in the rating curve model. The rating curve model is typically a power-law function estimated from infrequent stage–discharge gaugings at different flow conditions. Uncertainty in discharge data is often epistemic in nature (McMillan & Westerberg, 2015), stemming from incomplete knowledge about the true stage–discharge relation at the gauging site. Factors including vegetation growth, erosion/sedimentation, hysteresis, backwater, ice, etc., cause deviations from the standard rating curve model assumption of a temporally invariant 1:1 stage–discharge relation. In addition, the relation is often ungauged and poorly known at extreme low/high flows leading to uncertain rating curve extrapolation (Di Baldassarre & Claps, 2011; Kiang et al., 2018 and Figure 1). We include three main categories of soft information in our generalized perceptual model of discharge data uncertainty: station characteristics, climate and flow regime, and catchment characteristics. The soft information in these categories can inform us about three types of uncertainty sources in discharge data from rating-curve models: uncertainty related to the hydraulic control, uncertainty related to ungauged extreme flows, and uncertainty due to measurement error. The perceptual model is presented in Table 1 and a graphical representation is provided in Figure 2. For each type of soft information in the three categories, we describe the related uncertainty sources and their impacts, sources of the soft information (e.g., photos, satellite images or land use data), and where available, references to example literature discussing the uncertainty source (and sometimes soft information). Because it is a general and qualitative model we only differentiate between low and high flows and the likelihood of there being low or high uncertainty magnitudes (Figure 2). Hydraulic control: More uncertain low flows, frequent debris blockages (e.g., by leaves or branches) lead to artificially high water levels and overestimation of discharge, largest relative uncertainty impact at low flows Station characteristics and local site-specific factors are often what first come to mind when considering discharge data uncertainty sources. This is because the stage–discharge relation is determined by the hydraulic control from the physical characteristics of the channel, that is, the shape of the river channel together with roughness elements such as vegetation and the riverbed material (Le Coz et al., 2014; Mansanarez, Westerberg, et al., 2019). Using soft information such as station photos, aerial images, site visits, topography, and elevation, we can start to understand any factors that complicate the hydraulic control and cause the stage–discharge relation to vary with time or over the flow range leading to epistemic uncertainty about the rating curve model (McMillan & Westerberg, 2015). We can use soft information about soil types, riverbed material and gauging station control structures to assess potential for erosion and sedimentation that causes time-variability in the stage–discharge relation due to change in river channel shape (Table 1). Temporal riverbed variability typically results in higher stage–discharge uncertainty for both high and low flows. However, impacts depend on the nature of the change (e.g., sudden shifts or continuous changes), which also determines if the rating curve needs to be frequently updated (Mansanarez, Renard, et al., 2019) or calculated with time-variable parameters (Guerrero et al., 2012; Morlot et al., 2014; Reitan & Petersen-Øverleir, 2011). The potential for temporal variability that results from seasonal changes in roughness due to weed and vegetation growth (Perret et al., 2021) can be assessed from photos, aerial images and site visits. Vegetation such as leaves and debris can often block small v-notch weirs, resulting in artificially raised water levels and temporally varying systematic overestimation. Sharp changes in river channel shape and roughness occur when a river overflows the channel and flows onto the flood plain, this causes an abrupt change to the high-flow rating curve and the out-of-bank part of the curve is often associated with significant uncertainty (Kiang et al., 2018). Soft information in the form of floodmarks, photos of the station in high flow conditions, elevation data, and aerial and satellite images can be used to assess the potential for out-of-bank flows. Knowledge about the purpose behind the design of gauging structures can also be used, for example, in the UK few stations are truly full range: there are common issues with insensitivity of gauging structures at low flows as well as unmeasured bypass flow and overtopped and drowned structures at high flows (Coxon et al., 2015; Harrigan et al., 2017). In addition to the physical characteristics at the gauging site and their impacts on uncertainty in the hydraulic control, the gauging data used to estimate the rating curve model play a critical role in determining discharge data uncertainty. To assess uncertainty in the rating curve model due to extrapolation for ungauged extreme flows, we can assess how likely it is that extreme flows are ungauged. For example, the remoteness of the station often impacts on the gauging potential as remote stations are typically visited less frequently and it is less likely that the station can be visited at short notice to gauge high flows of short duration. Photos or videos of a station during high flow conditions can show if gauging is unsafe or impossible due to turbulent flow. The instrumentation and age of the station can inform about gauging potential as well as measurement errors because equipment for both discharge gauging and water level recording have improved over time. Before the ADCP-age (e.g., introduced for large rivers in Sweden in 1995 and in the UK in 2002) high flows were much harder, or impossible, to gauge without cable ways or bridges from which to suspend current meters. Older water level data were typically recorded using one or a few daily manual readings (Hamilton & Moore, 2012; Lucas et al., 2023; Westerberg et al., 2011) or manually digitized from chart recorder papers sometimes only as a daily average value. Chart recorders frequently lead to poor data resolution (cm-scale) and temporally varying biases in water level due to poorly fitted/digitized paper, wet paper with spreading ink, or mechanical clock drift (Meles et al., 2022). Such errors will have detrimental impacts on baseflow and recession analyses but there could also be temporal errors in the timing of flow peaks. An obvious type of soft information about discharge data uncertainty we can derive from climate data is if the river is ice-covered during part of the year. Ice impacts on the hydraulic control, the possibility to gauge discharge, and the water-level measurement for river stations, whereas lake-outlet stations may remain ice-free even at high latitudes. Monitoring agencies typically subjectively estimate ice-impacted winter streamflow with the help of winter control gaugings, which often results in substantial low flow uncertainty (see the introduction section and Hamilton & Moore, 2012). The discharge during the ice-breakup period and rising limb of the spring flood hydrograph has particularly high uncertainty due to ice jams, drifting ice, and high velocities—that impede both control measurements and reliable discharge time series ice-impact corrections (Shiklomanov et al., 2006). Apart from ice impacts, the climate and flow regime can primarily inform us about uncertainty resulting from rating curve extrapolation for ungauged extreme flows. There are several factors we can determine from soft information that impact on the potential to gauge high flows: when peak flows occur (daytime/night-time), how many peak flows of different magnitudes there are, how predictable they are, and how long they last. For example, if peak flows have occurred during the night, they are very unlikely to have been gauged (Westerberg & McMillan, 2015). Depending on the flow regime there may only be one or a few high flows per year, and extreme high flows may only have occurred once in a multidecadal time series. Therefore, by just looking at the discharge time series (or a flow-duration curve) we can already start to understand the potential for discharge uncertainty due to rating-curve extrapolation for ungauged extreme flows, that is, few high flow peaks and a steep flow-duration curve leads to likely large uncertainty in high flows (Figure 1). The potential to gauge high flows is significantly increased where there are snowmelt-driven high flows as their occurrence is much more predictable than those driven by rainfall. Conversely, the gauging potential is decreased where high flows are of short duration, as it can be technically difficult to measure flows of short duration (i.e., a few hours) and change of flow during the gauging increases the measurement error. Upstream catchment characteristics influence the timing and magnitude of the runoff response and are therefore useful as soft information about uncertainty related to rating curve extrapolation for ungauged extreme flows. Catchment size and water body storage are key types of soft information, a small catchment without lakes or reservoirs and a short rainfall–runoff lag time has a flashy runoff response with high flow events of short duration that makes it difficult to gauge high flows. Conversely, a large catchment or a high proportion of lake coverage leads to a dampened flow variability, increased lag time, and attenuated peak flows (Hudson et al., 2021) that facilitates high-flow gauging (Figure 1). Similarly, soil hydrological characteristics control flow variability (Boorman et al., 1995). Well-drained, deep, and permeable soils can provide a large catchment water storage that sustains baseflow and dampens flow peaks. For example, Karlsen et al. (2016) found that catchments with deep sediment soils had a higher baseflow and more attenuated high flows compared to their shallower glacial till and peat soil counterparts. Hydrological signatures such as the baseflow index (BFI, e.g., Gustard et al., 1992) are useful to quantify flow variability behaviour (McMillan, 2020) and therefore as a source of soft information about discharge data uncertainty related to ungauged extreme flows. For example, a high BFI reflects a dampened flow variability with greater potential to gauge extreme flows. Accordingly, catchments with high BFI values were found to have the lowest discharge data uncertainty across the flow range in the study by Westerberg, Wagener, et al. (2016). Upstream catchment characteristics can also influence uncertainty in rating curves due to temporal variability in the hydraulic control. Catchments with mountainous topography or steep hillslopes often have unstable riverbeds, and therefore greater discharge data uncertainty, as drainage basin steepness plays an important role in controlling erosion rates (Chen et al., 2022; Summerfield & Hulton, 1994). In the absence of hard information, our generalized perceptual model (Table 1 and Figure 2) shows that we can have more information about discharge data uncertainty than we may at first think. Soft information such as a station photo, a catchment map, or the shape of the discharge time series itself can already give us important information about likely uncertainty sources and their potential impacts on our analyses. Thinking about soft information on data uncertainty and the monitoring preconditions behind the measurements (i.e., thinking like a field hydrologist!), can facilitate a deeper understanding of sources of data uncertainty and their possible impacts on our analyses and conclusions. With some basic understanding of hydrometric monitoring methods, many conclusions can be drawn using 'common sense', for example, "the highest flow occurred on Christmas day, it is therefore very unlikely to be gauged", or "high flow duration is only six hours with rapid change in flow, high measurement uncertainty and/or ungauged high flows is likely". In summarizing uncertainty sources with the perceptual model, we included three key types of uncertainty sources related to: the hydraulic control, the potential for ungauged extreme flows, and the measurement errors. Additional uncertainty sources could be included, for example, data management (McMillan et al., 2018) for which knowledge about monitoring and quality control procedures may be useful soft information. The generalized perceptual model can be seen as a smorgasbord of information about uncertainty sources, where the soft information can be considered as relevant to a particular dataset and can inform us if high or low data uncertainty is likely. In the absence of hard uncertainty information, a qualitative data uncertainty quantification based on soft information can be useful to analyse if the conclusions from a hydrological analysis are likely to be impacted by data uncertainty. This could be particularly useful in large-sample hydrology studies where hard data uncertainty information is typically not available (Addor et al., 2020). In application, it is important to note the 'softness' and uncertainty of the soft information: actual data uncertainty will also depend on monitoring and data production methods, gauging frequency, skill in measurement and data management, and to some extent luck in managing to gauge at the right flow ranges. Furthermore, note that uncertainties are often complex with several different sources active at the same time and/or at different flow ranges (McMillan et al., 2018), consequently stations often have different uncertainty magnitudes for low, middle, and high flows (Coxon et al., 2015). Perceptual models of hydrological processes are important tools to capture and communicate expert knowledge to the hydrologic community, but uncertainties are rarely explicitly included in perceptual model representations (McMillan et al., 2023; Wagener et al., 2021). Formulating perceptual models of uncertainty allows for an open and explicit treatment of uncertainty that can elicit different peoples' perspectives and helps to structure dialogue, communication and understanding of uncertainty (Westerberg et al., 2017). In the same vein, Seibert and McDonnell (2002) argue that communicating soft information on process understanding is important to improve the dialogue between field hydrologists and modellers. Both Graham et al. (2010) and McMillan et al. (2022) stress that this dialogue needs to include observational uncertainties and their possible impacts on process understanding and model inferences. We believe that one key benefit of the type of generalized perceptual model of data uncertainty that we have presented here, is to facilitate such dialogue on possible sources of observational uncertainties and their impacts. A generalized perceptual model can also be a useful starting point for data producers who want to catalogue and communicate the uncertainty sources in their data, creating site-specific metadata detailing uncertainty sources, uncertainty characteristics, and magnitudes. Finally, it is important to note the personal nature of the perceptual model and that it does not aim to be a complete description: our model summarizes the authors' experience in field monitoring, discharge data production, and data uncertainty analysis. We encourage others to complement our perceptual model of discharge data uncertainty, for example, for other discharge monitoring techniques such as index-velocity stations or drone/camera-based methods (e.g., Eltner et al., 2021; Hutley et al., 2023), and to share similar soft uncertainty information for other hydrometeorological variables—to promote more robust decisions in hydrological studies in the face of data uncertainty. We thank Mikael Lennermark and Maud Goltsis Nilsson at the Swedish Meteorological and Hydrological Institute for their insights on how monitoring methods and measurement uncertainties have changed over time in Sweden. Support for the authors was provided by The Swedish Research Council Formas (Svenska Forskningsrådet Formas) [2019-01094]. Data sharing is not applicable to this article as no new data were created or analyzed in this study.