1. Introduction
Difficulties in deriving accurate precipitation (P) estimation arise in many remote areas, particularly in complex terrain basins (Tao and Barros 2013; Tao et al. 2016). Consequently, satellite-based precipitation products have been increasingly developed to facilitate large-scale hydrological applications (Wu et al. 2012a, 2014). However, despite a wide range of hydrological studies applying satellite-based rainfall estimates for many years (Adler et al. 2000; Buarque et al. 2011; He et al. 2017; Huffman et al. 2001; Maggioni and Massari 2018; Meng et al. 2014; Nikolopoulos et al. 2013; Prakash et al. 2016; Stampoulis and Anagnostou 2012; Su et al. 2011; Wu et al. 2014; Yan et al. 2020; Zhong et al. 2019), the practical applications remain limited due to a number of error sources and uncertainties (Hossain and Anagnostou 2004; Sarachi et al. 2015). Reliable estimation of precipitation in space and time is highly desired for hydrological applications, as uncertainties in rainfall estimates can potentially lead to large errors in simulation outputs (Arnaud et al. 2002; Borga 2002; Courty et al. 2018; Morin et al. 2006; Nanding and Rico-Ramirez 2021; Rico-Ramirez et al. 2015; Smith et al. 2004; Tscheikner-Gratl et al. 2018; Wu et al. 2017; Younger et al. 2009; Zhang et al. 2018).
Many attempts have been conducted to quantify errors and uncertainties associated with satellite-based rainfall estimates to improve the understanding of precipitation physics (Behrangi et al. 2010; Hong et al. 2004; Liu and Fu 2010; Xu et al. 1999), retrieval algorithms (Bauer et al. 2001; Hossain et al. 2004; Moradkhani and Meskele 2010; Tong et al. 2014), measuring devices (e.g., infrared and microwave) (Hossain and Anagnostou 2004; Todd et al. 2001), and sampling frequencies (Iida et al. 2006; Nijssen and Lettenmaier 2004; Steiner et al. 2003). Since precipitation instruments have their own strengths and limitations in accuracy and spatial–temporal representativeness, the quality of satellite-based rainfall products were evaluated for defining the best available precipitation product in specific regions (Bitew et al. 2012; Chen et al. 2020; Collischonn et al. 2008; Cui et al. 2019; Diem et al. 2014; Dinku et al. 2010, 2008; Dos Reis et al. 2017; Feidas 2010; He et al. 2017; Le Coz and van de Giesen 2020; Meng et al. 2014; Monsieurs et al. 2018; Nicholson et al. 2019; Nikolopoulos et al. 2013; Stampoulis and Anagnostou 2012; Toté et al. 2015; Wu et al. 2017). These studies largely improve our understanding of the characteristics of errors and uncertainties in satellite rainfall estimates, which is crucial to improve future satellite rainfall products (Huffman et al. 2015) and hence their hydrological applications, such as global flood monitoring and forecasting (Wu et al. 2014).
Simulating the rainfall–runoff process using hydrological models can be useful for evaluating precipitation products at the river basin scale through comparison with an independent reference, e.g., discharge at river basin outlet (Beck et al. 2017b; Wu et al. 2017). Since rainfall is the most important driving component of the hydrologic cycle, the model performance depends heavily on the quality of precipitation inputs. However, due to the strong nonlinearity in hydrological processes, precipitation errors can be either amplified or dampened in simulated hydrological fluxes (mainly discharge) in different river basins (Artan et al. 2007; Bitew et al. 2012; Ehsan Bhuiyan et al. 2019; Gourley et al. 2011; Nikolopoulos et al. 2013). Therefore, propagation of precipitation errors through hydrological modeling has been identified as one of the critical issues in understanding the scale relationship between the errors in precipitation and in the corresponding hydrological simulations (Nikolopoulos et al. 2010).
The main characteristics of modeling experiments, datasets, and key findings in recent literature on precipitation–discharge error relationships are summarized in Table 1. Typically, a linear relationship between precipitation error and hydrological simulation errors was identified, and the errors in precipitation were translated into even larger errors in corresponding simulation outputs (Biemans et al. 2009; Decharme and Douville 2006; Kobold 2005; Maggioni et al. 2013; Nikolopoulos et al. 2010; Sharif et al. 2004; Wu et al. 2017). However, a few other studies demonstrated dampening effects of rainfall errors in discharge simulations (Falck et al. 2015; Mei et al. 2016). Moreover, propagation of precipitation errors through hydrological modeling varies with seasons (Biemans et al. 2009) and dampening or amplification of errors depends on rainfall products and basins sizes (Maggioni et al. 2013; Nijssen and Lettenmaier 2004; Nikolopoulos et al. 2010). Specifically, Nikolopoulos et al. (2010) demonstrated that the amplitude of dampening effect reduces with the increase of basin size. In contrast, Maggioni et al. (2013) reported a stronger dampening of precipitation errors for larger basins. However, there was no sign of dependency of error propagation on basin size in the study of Falck et al. (2015). Nikolopoulos et al. (2010) also reported that precipitation error propagation depends on the error metric, indicating that the propagation of rainfall errors into runoff volume result in completely different conclusions compared to the propagation from the same errors into runoff peaks.
A summary of relevant previous studies in terms of their study locations, adopted methods, and key findings (the current paper is included for comparison).
Although various studies have investigated error propagation of precipitation inputs through hydrological modeling (Fekete et al. 2004; Nijssen and Lettenmaier 2004; Serpetzoglou et al. 2010; Vivoni et al. 2007), how precipitation error propagates through a hydrological model remains unclear and sometimes controversial. Therefore, a systematic investigation on how errors in precipitation (P) translate into errors in hydrological predictions, in particular on precipitation–discharge errors, is crucial for better interpretation and use of various P products to derive simulations for hydrological applications, such as water resource management, flow storage, and flood control designs.
Specifically, building on the previous studies, such as Nikolopoulos et al. (2010) and Wu et al. (2017), this study aims to further examine the relationship between the errors in several widely used P products derived from different sources (i.e., gauge, ground-based radar, and satellite) and their simulated discharge over an extensive number of sites across the CONUS. Moreover, this study assesses how precipitation error propagates (amplification or dampening) into hydrological simulations as a function of several factors, including the type of P product, temporal scale, climate, basin size, and topography. It is worth mentioning that another motivation behind this study is that the P–Q error relations can be useful to estimate potential errors in flood predictions induced by precipitation errors when validation is not feasible. In particular, such relations can better inform the users of the Global Flood Monitoring System (GFMS) in their response to predicted flood events.
The rest of this paper is organized into the following sections. First, a description of the study basins and P datasets are presented in section 2, including the criteria for final selection of study basins. Section 3 provides a detailed description of modeling framework based on a distributed hydrological model, methodology of basins classification and definition of error metrics. Section 4 analyses the characteristics of precipitation error propagation through discharge simulations and P–Q error relationship, and their potential influencing factors including P product, climate type, discharge magnitude, temporal accumulation scale, seasonality, and basins topography (size, elevation, and slope). Finally, section 5 provides a summary and concluding remarks based on the study results.
2. Study domain and data
a. Study basins
The river basins are selected based on the availability of in situ gauges from the United States Geological Survey (USGS) Geospatial Attributes of Gauges for Evaluating Streamflow (GAGES-II) database (Falcone 2011). The GAGES-II dataset consists of 9322 streamflow gauges maintained by USGS over the CONUS with a large variety of geospatial and hydroclimate characteristics. A total of 1548 candidate river basins are identified for this study based on the following criteria: 1) each gauge has sufficient historic streamflow observations (i.e., at least 10 years of records between 2002 and 2013) at daily scale, and 2) there is a good agreement (within ±10% difference) between the hydrological model calculated drainage area and USGS National Water Information System (NWIS) reported area, the latter of which is considered as the reference value (following Wu et al. 2014; Alfieri et al. 2013). The spatial distribution of the selected GAGES-II sites is shown in Fig. 1b.
Maps of (a) elevation across the CONUS, (b) spatial distributions of GAGES-II sites matching with selecting criteria, (c) the Köppen climate type, and (d) MRVBF class of final selected 1548 river basins.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
b. Precipitation products
Multiple spatially gridded precipitation products are available across the CONUS, including Version 7 of the Tropical Rainfall Measuring Mission (TRMM) Multisatellite Precipitation Analysis for real-time (TMPA-3B42RT V7) and research (TMPA-3B42 V7) applications (Huffman et al. 2007), the NOAA/National Canters for Environmental Prediction (NCEP) Stage IV product (Lin and Mitchell 2005), the phase 2 of the North American Land Data Assimilation System (NLDAS-2) (Rui and Mocko 2013; Xia et al. 2012a), the CPC Unified (CPC-U) (Xie et al. 2007), the observation-corrected Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2) (Gelaro et al. 2017; Reichle et al. 2016), and the Multi-Source Weighted-Ensemble Precipitation, version 2.2 (MSWEP V2.2) (Beck et al. 2017a, 2019). These P products are mainly sourced from rain gauges (i.e., NLDAS-2 and CPC-U), ground-based radars (i.e., Stage IV), satellite-only (i.e., TMPA-3B42 V7 and TMPA-3B42RT V7) and reanalysis datasets (i.e., MERRA-2 and MSWEP V2.2). Precipitation products with higher temporal resolution (e.g., NLDAS-2, Stage IV, MERRA-2, and MSWEP V2.2) were simply aggregated to 3-hourly accumulations, while the CPC-U product at daily time scale was disaggregated based on the temporal distribution of 3-hourly TMPA-3B42 V7 product. A summary of the characteristics of these gridded P products, including their temporal and spatial resolutions, is provided in Table 2.
Overview of the precipitation products used in this study. Abbreviations in the data source(s) column are defined as follows: G, gauge; S, satellite; R, radar; and RA, reanalysis.
3. Methodology
a. Hydrological model
The Dominant River Tracing-Routing Integrated with VIC Environment (DRIVE) model (Wu et al. 2014) is used to simulate river discharges in this study. The DRIVE model, as the core of the real-time Global Flood Monitoring System (GFMS), couples a widely used land surface model, the Variable Infiltration Capacity (VIC) model (Liang et al. 1996, 1994), with a hierarchical Dominant River Tracing-Based Routing (DRTR) model (Wu et al. 2011, 2014). The VIC model solves full water and energy balances with good skill due to its characterization of both rainfall and snowmelt dominated runoff generation processes and soil frost dynamics (Christensen et al. 2004; Elsner et al. 2010; Hamlet et al. 2005). The DRTR is a gridded and physically based routing model, which allows the use of high-resolution subgrid information aggregated for coarser resolution routing simulation and integrates the grid-level drainage network with numerical schemes based on the Strahler ordering system (Wu et al. 2014).
Since this study aims to provide insights on error propagation of precipitation for GFMS applications, the DRIVE model setup is adopted directly from the existing GFMS configuration that runs at spatial and temporal resolution of 1/8° and 3-hourly, respectively. The VIC model runs in “water balance” mode. The hydrographic parameters (e.g., flow direction, drainage area, flow length, channel width, channel slope, overland slope, flow fraction, river order) for the DRTR runoff-routing scheme were derived by using the hierarchical Dominant River Tracing (DRT) river network upscaling algorithm (Wu et al. 2011, 2012b). The global soil and vegetation parameters were specified following Nijssen et al. (2001). Other atmospheric forcing data (i.e., air temperature and wind speed) were obtained from the NASA Modern-Era Retrospective Analysis for Research and Applications (MERRA) reanalysis (Rienecker et al. 2011). More detailed descriptions of the DRIVE model, forcing inputs, and model parameter setup are presented in previous studies (Huang et al. 2021; Wu et al. 2014; Yan et al. 2020). All forcing inputs are preprocessed at the same resolution in space and time that are consistent with model configuration.
To examine the error propagation of precipitation inputs through the hydrological model, the basic approach is to use the reference P and its simulated discharges to quantify errors in precipitation and their corresponding discharge simulations (Mei et al. 2016). Based on Xia et al. (2012b) and Wu et al. (2017), the NLDAS-2 and its DRIVE simulated discharges are defined as reference in this study. Note that the NLDAS-2 might not be among the best precipitation products over all the study basins. The absolute accuracy, however, does not impact the purpose of investigating the error propagation from precipitation through hydrological processes into discharge error, i.e., the relationship between errors in precipitation versus the errors in simulated discharge.
The hydrological model setups (e.g., initial states, parameters, atmospheric forcings other than precipitation) are kept the same for different P products. The same initial condition for each P product based DRIVE simulation is provided by the continuous NLDAS-2 based simulations for the period 1997/98 (with two years of spinning-up running before the start of the simulation of 1997). This removes the effects of differences in initial conditions among products and focusing only on rainfall–runoff process. Since the model simulation uncertainty results from the interactions between each source of uncertainty rather than individual ones, the decomposition of individual source of errors in model predictions remains challenging (Pianosi and Wagener 2016; Pianosi et al. 2016). Therefore, the design of this study is based on the assumption that the discharge errors are mainly due to precipitation errors and the interactions between different sources of errors and uncertainties are neglected. The DRIVE model runs between 1998 and 2013. Simulations during the period of 2002–13 are analyzed, while the first four years are treated as the spinup period. Note that the improvement of model performance per se is not within the scope of this study, and therefore further calibration of the DRIVE model is not conducted.
b. Basin classification
According to the Köppen climate classification (Beck et al. 2018; Köppen 1918; McKnight 2000), the 1548 river basins over the CONUS are categorized into three main climate groups (continental, temperate, and dry), as shown in Fig. 1c. A brief description of the nature of climate regimes, including precipitation, temperature, and hydrological characteristics of basins with dominant subclass are presented in Table 3. The description of the catchment hydrological characteristics is based on the assessment of regional patterns of seasonal water balance presented in Berghuijs et al. (2014).
Characteristics of Köppen climate regimes in precipitation, temperature, and hydrology.
Many studies have also identified catchment morphology, such as slope and flatness (Peña Arancibia et al. 2010; Uchida et al. 2005), as an influential factor on rainfall–runoff generation. To measure the combined impacts of elevation and slope on precipitation error propagation, the multiresolution index of valley bottom flatness (MRVBF) (Gallant and Dowling 2003) is calculated based on the HydroSHEDS (Lehner et al. 2008) global hydrography dataset at 1-km resolution (as shown in Fig. 1a) using the DRT algorithm, as in Wu et al. (2019). MRVBF identifies flat valley bottoms based on their topographic signature as flat low-lying areas at a range of scales. Flatness is measured by the inverse of slope, and lowness is measured by a ranking of elevation with respect to a circular surrounding area. The MRVBF indices are then grouped into seven general classes (Fig. 1d), where higher class numbers indicate cells with generally flatter and lower topography, consistent with Wu et al. (2019).
Hydroclimatic heterogeneity results in varying streamflow regimes across the CONUS (Berghuijs et al. 2014). In general, the total amount of annual precipitation decreases from east to west over the region (Fig. 2). There is no significant seasonal difference in precipitation amount in the eastern CONUS, while the western and central CONUS show stronger seasonality in precipitation accumulations. Specifically, precipitation is higher (lower) during winter (summer) in the western part, while central CONUS shows the opposite. In higher-latitude and mountainous regions streamflow regimes are dominated by snowmelt, which means precipitation is accumulated as snow in winter and released as runoff in spring leading to large variations in seasonal discharge (Berghuijs et al. 2016). In humid regions soil moisture supply and atmospheric demand play an important role (Novick et al. 2016; Yuan et al. 2019).
Maps of (a) mean annual precipitation (2002–13) estimated by NLDAS-2 and its hydrological performance with (b) NSE, (c) relative ABIAS (r_ABIAS), and (d) relative RMSE (r_RMSE) against the USGS observations at annual time scale.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
c. Error metrics
4. Results and discussions
a. Evaluation of DRIVE-NLDAS-2 simulated discharge
The evaluation of simulated discharge driven by NLDAS-2 precipitation against USGS observed discharge is to gain a basic understanding of the efficiency of NLDAS-2 based simulations. Hydrological performances of the DRIVE-NLDAS-2 simulated discharge vary largely across the CONUS (Fig. 2), reflecting the model efficiency in different regions. The result shows that the reference simulation generally represents a certain degree of observation fidelity in simulations with about 40% of gauge sites showing positive NSE scores with a mean (median) value of 0.47 (0.48) and maximum of 0.97 (USGS: 05474000). The spatial patterns of r_ABIAS and r_RMSE are similar, and the lower errors correspond to higher NSE values.
An overview of the distributions of different P products against the reference P (NLDAS-2) is shown in Fig. 3. The gauge-involved P products (i.e., CPC-U, MERRA-2, and MSWEP V2.2) agree better with the reference P for most of the regions, but they show overestimations in annual precipitation accumulations over the West Coast of the CONUS. Whereas the satellite-only TMPA-3B42RT product clearly overestimate the reference rainfall, and the situation is improved effectively after gauge adjustment in TMPA-3B42. Radar-based Stage IV shows underestimations of reference rainfall over basins in the western CONUS (Henn et al. 2018). This is because of difficulties in retrieving orographic precipitation due to beam blockage, and signal attenuation in mountainous regions (Bringi et al. 2011; Dai et al. 2015; Germann et al. 2006; Nanding and Rico-Ramirez 2021; Nanding et al. 2015; Rico-Ramirez 2012; Wang et al. 2015). The performances of these precipitation products vary between basins due to the strengths and limitations in their measuring devices. There is no single product outperforms the others in terms of both precipitation estimations and hydrological predictions for all study basins, including the reference product. In this study, the definition of reference for both precipitation and discharge is for comparing between the errors in precipitation and discharge directly in the model system.
Normalized precipitation bias (%) in mean annual precipitation estimated by different P products with respect to the reference P (NLDAS-2) over the CONUS.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
The following results focus on 1) the scale relationship between errors in basin-averaged precipitation and those in simulated discharges (hereafter referred to as P–Q error relationship), 2) error propagation from precipitation to simulated discharges, and 3) dependency of those of characteristics on a variety of factors.
b. P–Q error relationship
A strong positive linear relationship between errors in precipitation and simulated discharges is observed regardless of the P products and accumulation time scales in terms of r_RMSE (Fig. 4). The Stage IV product shows the strongest linearity in P–Q error relationship, followed by MSWEP V2.2, with the highest value of coefficient of determination. Remote sensing precipitation estimates (e.g., TMPA and Stage IV) tend to have larger errors in both precipitation and simulated discharges compared to gauge-based P products. Specifically, Stage IV mainly shows larger errors over basins in western regions of the CONUS (e.g., taking the 100th meridian west longitude as the approximate dividing line). This is due to the blockage in complex mountainous topography and the ground clutter contamination to radar signals. The lower skills were also reported in both precipitation estimation and discharge simulations (Maddox et al. 2002; Moreda et al. 2002; Nelson et al. 2016) reflecting the challenges in both data obtaining and modeling in complex terrain. However, although relative errors are much higher for basins on western edge, the P–Q error relationship of Stage IV shows strong (r2 > 0.5) positive linear behaviors for both the western and eastern CONUS (Fig. S1 in the online supplemental material). Gauge-adjusted satellite P products present lower errors, suggesting that the gauge-correction procedure can effectively reduce errors in satellite rainfall estimates and lead to better hydrological simulations, which is consistent with previous studies (Su et al. 2011; Wu et al. 2014). As shown in Fig. 4, the distributions of errors in precipitation and discharge tend to shift toward smaller errors at annual time scale (blue dots) compared to monthly time scales (gray dots), indicating that errors in precipitation are suppressed at larger time scale accumulation. Similar patterns in the P–Q error relationship are also observed for r_ABIAS (not shown). In general, linearity in the P–Q error relationship is stronger at annual time scale compared to monthly, in line with Wu et al. (2017). This is probably because of delays in the transformation of P to Q (due to channel routing and storage in snow, subsurface, lakes, etc.) are less important at annual than monthly time scales. Annual accumulations are more reliable to estimate hydrological water budget components (e.g., discharge) than monthly time scales (Berghuijs et al. 2014), assuming that changes in water storage (soil and surface) are negligible at annual accumulations for a closed watershed without significant streamflow diversions or impact of reservoirs (Adam et al. 2006).
Scatterplot of the r_RMSE in precipitation against the r_RMSE in estimated discharges at annual (blue) and monthly (gray) time scales, respectively.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
The relationship between the r_ABIAS in precipitation and NSE scores for discharge simulation tends to have negative linear behaviors with varying strength for different P products and accumulation time scales (Fig. 5). This negative linear relationship indicates that precipitation products with less bias or errors tend to have better hydrological performances in terms of NSE scores. The linear relationship between r_ABIAS in precipitation and NSE scores for discharge simulation is weaker than aforementioned P–Q error relationship. In particular, the satellite-based products show a much weaker linear relationship (r2 < 0.25) between errors in precipitation and NSE for discharge simulations though they have strong linearity (r2 > 0.5) in the P–Q error relationship. This can be explained by Eqs. (1) and (2) where NSE is more sensitive to larger errors, while the errors in precipitation tend to be translated into even larger errors in simulated discharge (Fig. 4).
Scatterplot of the r_ABIAS in precipitation against the NSE (ranging between 0 and 1) in estimated discharges at annual and monthly time scales, respectively.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
c. Error propagation
The relative errors in P products are generally translated into even larger relative errors in their simulated discharges (Fig. 6). The propagation factors are higher for annual accumulations than for monthly accumulations in terms of their mean values. This could be due to the fact that the spatially distributed precipitation errors are filtered out by averaging them to mean areal precipitation, while the error in the discharge at the outlet of a river basin is resulted from a cascade of numerical solutions for equations of various no-linear processes with spatially distributed precipitation inputs containing the original errors. Although the numerical solutions deployed by the hydrological model derive reasonably stable discharge simulations, there is inherent error propagation from precipitation input to discharge output which depends much more on the error pass and propagation among the numerical solution schemes than on spatial scales and seasonal changes. Therefore, the canceling effects for the precipitation error as a function of basin area and averaging time (Nijssen and Lettenmaier 2004) does not apply to the discharge error. This explains that the error propagation ratio between the discharge errors and precipitation errors tends to be greater than one, in particular at annual scale for a river basin with a stable hydrological water budget, while it varies significantly at monthly and shorter time scales.
Violin plot of propagation factors for r_RMSE and r_ABIAS at annual and monthly time scales; dots in colors represent the mean of propagation factors for each P product.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
However, the amplification effects of precipitation-to-discharge errors vary across P products. Stage IV consistently shows lower values in propagation factors at different accumulation time scales. This could be due to the better performance of the higher resolution radar-based product in moderating the precipitation errors in hydrological processes, as presented in Nikolopoulos et al. (2010). The errors in discharges simulated by satellite-based P products are more than double the errors in precipitation. Similarly, the errors in gauge-based P products are at least doubled in annual discharge, although they show relatively low errors in precipitation estimations (Fig. 4). Similar patterns are observed for the propagation of both r_RMSE and r_ABIAS.
Spatial patterns of error propagation factors also vary among P products, and accumulation time scales (Figs. 7 and 8). There are clear differences in error propagation patterns between P products over the study basins. Specifically, at annual time scale, the errors in TMPA-3B42 V7 simulated discharges are more than triple the errors in precipitation for about 33% (the highest) of basins, while a number of basins with the lowest proportion of 6% is obtained by the Stage IV (Fig. 7). The spatially distributed hydrological model used in this study takes into account the spatial variability of precipitation and calculates flow contributions from elementary grid areas. Therefore, the spatial variability in precipitation amounts and intensities between different P products in each river basin could be responsible for the variability in the distribution of propagation factors among different P products, which explains the different error propagation rates even if P products have similar basin-averaged precipitation accumulations.
Spatial pattern of propagation factor of r_RMSE at the annual time scale over 1548 river basins.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
As in Fig. 7, but for the monthly time scale.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
Compared to the annual scale, monthly accumulations show less amplification and more dampening effects of errors in most basins (Figs. 7 and 8). For example, the number of basins with dampening effect is 51 for Stage IV at annual accumulations, while a number is 111 basins for monthly accumulations. This decrease in the propagation factor at monthly time scales might be related to the fact that soil infiltration removes some of the short-term rainfall fluctuations by generating subsurface runoff, which contributes to the river channel discharge through a slower routing process. The filtering effects can be more visible in precipitation with higher errors (e.g., satellite-based P) particularly at monthly time scales and when subsurface soil layers are not saturated. This also partially explains the stronger linearity in annual P–Q error relationship compared to the linear relationship at monthly time scale (Figs. 4).
The sensitivity of precipitation error propagation patterns on reference data is also tested by using different P products and their simulated discharges as references, including satellite-based (TMPA-3B42RT V7 and TMPA-3B42 V7), radar-based (Stage IV), and reanalysis (MSWEP V2.2) products. Results based on TMPA-3B42 V7 are shown in Figs. S7 and S8. According to Fig. S7, there is a strong linear relationship between errors in precipitation and simulated discharges, regardless of P products and accumulation time scales. This is similar to the findings when NLDAS-2 is used as the reference. Moreover, Fig. S8 also shows that precipitation errors are less amplified at monthly time scale compared to annual time scale, which is also observed when using MSWEP V2.2 and Stage IV as the references. Moreover, similar analysis has also been done by only using 584 basins for which the NLDAS-2 DRIVE simulations show positive NSE scores, which leads to similar results that are obtained by using all basins (figures omitted). Therefore, the findings on changing patterns of precipitation error propagation are convincingly held.
d. Impact of hydroclimatic factors
With regard to the impacts of climate regime on P–Q error relationship, the differences in the strength of linearity are much smaller among P products and seasons in basins situated in temperate and continental climate regimes compared to those with dry climates (Fig. 9). Temperate and continental climate regimes have less seasonal streamflow variations, while large variations in storage and streamflow regimes over basins with dry climates are observed (Table 3). In dry climates, basins are mostly semiarid and have distinct seasonality in precipitation. For instance, basins in mountainous region in western CONUS receive most of precipitation during winter, while streamflow in these basins is mainly generated from snow melting (Berghuijs et al. 2014), suggesting a nonlinear behavior in P–Q error relationship during the warm season, particularly during April–June (AMJ) (Fig. 9).
Seasonality in slope and coefficient of determination (r2) of fitted regression line for the P–Q error relationship over the basins with different climate types from the perspective of r_RMSE. Different seasons are defined as January–March (JFM), April–June (AMJ), July–September (JAS), and October–December (OND).
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
A stronger linearity in the P–Q error relationship is also observed when considering all discharge magnitudes rather than considering only peak discharges, i.e., Q ≥ 99th percentile (Fig. 9). Stronger dampening effects are further observed when considering peak discharges compared to all discharge magnitudes at monthly time scale (Fig. 10), regardless of climate regimes and P products. The error in precipitation is calculated based on river basin average, while the translation of such precipitation error into discharge is based on a chain of rainfall–runoff generation and routing processes. That said, the precipitation error is temporally distributed along the whole hydrograph and the error in flood peak is associated to only part of the precipitation error. Stronger attenuation effects are observed for discharge peaks in basins with temperate and continental climates compared to dry climate basins (Fig. 10). In addition to precipitation, antecedent wetness conditions and water storage also play an important role in runoff generation in temperate and continental climates (Berghuijs et al. 2016). Although all P products tend to have more challenges in deriving accurate precipitation during extreme events, the error contributions to flood peak are from both the flood-causing precipitation and the antecedent wetness of the river basin. Therefore, the error dampening in the propagation can be caused by the reasonable model performance in continuous hydrological simulation of the wetness dynamics and filtering effects of the complex nonlinear rainfall–runoff processes.
Propagation factors of r_RMSE for basins with different climate regimes at monthly time scale when considering different discharge magnitudes.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
In terms of seasonality, there is no clear difference between the mean propagation factors for peak discharges during seasons of AMJ and OND in continental and temperate basins (Fig. 11). For arid/semiarid basins, however, the precipitation errors are clearly translated into even larger errors in discharges due to the high variability in precipitation during AMJ, whereas precipitation errors tend to be translated equally into discharge errors during OND. This is because the large water deficit during the dry period filters out the discharge errors and somehow similar to precipitation errors.
Propagation factors of r_RMSE for basins with different climate regimes for seasons of April–June (AMJ) and October–December (OND) when considering peak discharges (Q ≥ 99th percentile).
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
e. Impact of basin size and topography
The basin size also plays an important role in the P–Q error relationship and precipitation error propagation. Valley bottom regions (higher MRVBF class) are relatively larger in the plains of the eastern CONUS with less seasonal variations in precipitation and streamflow, except for a few basins in the northeastern and southeastern CONUS with strong seasonality. Basins at high elevations (lower MRVBF class) are mainly clustered in arid/semiarid regions with strong seasonality in streamflow. Thus, the role of topography in the P–Q error relationship and error propagation is studied together with the aforementioned hydroclimate classes (Figs. S2–S4).
The impact of basin size on the strength of P–Q error relationship varies between P products, seasons, and basin classes (Fig. 12 and Fig. S2). For example, with the Stage IV, large basins show strong positive linear P–Q error relationship for dry climate regime compared to small basins, while the basin size show no clear impact on the strength of P–Q error relationship for basins with temperate and continental climate regimes. With MSWEP V2.2, large basins show strong linearity in P–Q error relationship for temperate and continental climate regimes particularly for warm seasons, while small basins show relatively stronger P–Q error relationship than large basins for dry climate regime. Moreover, for temperate climate regimes (or MRVBF classes ≥ 5), small basins also show less variations in the strength of P–Q error relationship between seasons and P products compared to large basins. These results indicate that the impacts of basin size on the P–Q error relationship also depends on P product, season, and climate regime.
Seasonality in slope and coefficient of determination (r2) of fitted regression line for the P–Q error relationship over the basins with different climate types and sizes from the perspective of r_RMSE, when considering only peak discharges (Q ≥ 99th percentile). Seasons are defined as January–March (JFM), April–June (AMJ), July–September (JAS), and October–December (OND).
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
Figures 13 and 14 demonstrate the propagation factors of r_RMSE for basins with different size in each MRVBF class during seasons of OND and AMJ, respectively, when considering peak discharges. In terms of mean values, similar propagation factors are observed between small and large basins of each MRVBF class for each P product during the OND season (Fig. 13). For example, precipitation errors are translated into similar magnitude of discharge errors for both small and large basins with lower MRVBF class (steeper and higher elevated basins). With the increase of MRVBF class (lower and flatter basins), the mean of propagation factors increases for both small and large basins, particularly for reanalysis P products (e.g., MERRA-2 and MSWEP V2.2). In contrast, during the AMJ season, larger basins show amplification effects on precipitation errors propagation regardless of P products, MRVBF class and climate regimes, except the Stage IV product (Fig. 14 and Fig. S4). Moreover, large basins also show greater variations in error propagation between P products and seasons which in line with the variations in P–Q error relationship. Meanwhile, the larger uncertainty in propagation factors with wider distributions (shape of violin plot) for each P is observed for large basins compared to small basins, which indicates that factors like basin size other than P products, seasons, and climate regimes also control the magnitude of error propagation for basins with different climate regimes.
Propagation factors of r_RMSE for basins with different size and MRVBF classes for peak discharges (Q ≥ 99th percentile) during the OND season. The horizontal line indicates the propagation factors of one, while white dots represent the mean value.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
As in Fig. 13, but for the AMJ season.
Citation: Journal of Hydrometeorology 22, 8; 10.1175/JHM-D-20-0213.1
5. Conclusions
This study investigates the characteristics of precipitation error propagation and the P–Q error relationship by applying a distributed hydrological model to 1548 river basins across the CONUS. The NLDAS-2 precipitation and its DRIVE simulated discharge are used as the reference to quantify the relative errors (e.g., RMSE and ABIAS) in several P products and their corresponding discharge simulations for the period of 2002–13. The analysis focus on the dependency of precipitation error propagation and the P–Q error relationship on a variety of factors including P product, temporal scale, climate regime, and basin topography.
The results show the positive linear behaviors in P–Q error relationship at annual and monthly accumulations, and the linearity is stronger at larger accumulation time scale, suggesting that it is more reliable to estimate potential errors in hydrological simulation outputs due to precipitation errors at larger time scales. Precipitation errors are at least doubled in simulated discharge for annual accumulations, while dampening effects are more common in peak discharges. Moreover, the patterns of P–Q error relationship and error propagation are seasonal, and sensitive to the climate regimes of basins particularly for larger basins. The differences of linearity in P–Q error relationship are much smaller between seasons and P products for the basins in temperate and continental climate regimes compare to the basins with dry climates. Regarding to the role of basin topography, the role of basin size on precipitation error propagation and P–Q error relationship largely depends on climate regimes and seasons. Generally, during the OND season precipitation errors are translated into similar magnitude of discharge errors for both small and large basins in each climate regime and MRVBF class in terms of mean propagation factor, while during the AMJ season larger basins show amplification effects on precipitation errors propagation regardless of P products, seasons, and climate regimes. Large basins also show greater variations in error propagation and P–Q error relationship between P products and seasons.
This study quantifies the P–Q error relationship at annual and monthly scales based on existing P products, and investigates the precipitation error propagation in discharge simulations and its links to hydroclimate, topographic characteristics of river basins. It helps in understanding the quality (bias and uncertainty) of flood simulation outputs and their relation to precipitation inputs, thus also shed light on potential ways to improve precipitation estimation products. However, floods are also highly linked to daily and finer time scales, and such P–Q error relationships at finer time scales warrant further investigation with more complicated processes considered in future studies. It is worth noting that the current findings are only based on a given hydrological model, and therefore the results might change with different models with different numerical schemes for runoff-routing processes. However, this study advances the understanding of the P–Q error relationship and its propagation in hydrological models that are similar to the DRIVE model and the possible uncertainty that is associated to the global flood monitoring and forecasting systems such as the GFMS.
Furthermore, despite the findings revealed in this study fairly hold, the shortcoming is that the climate regimes are broadly classified into three main groups based on Köppen classification, but the diversity of climate and hydrological regimes remains considerable within each class resulting in varying patterns of P–Q error relationship and error propagation within each class. Therefore, the changing patterns of error propagation from precipitation to hydrological simulation outputs require further detailed study of subclusters or regions based on both climate and catchment characteristics including seasonal water balances.
Acknowledgments
This study was supported by the National Natural Science Foundation of China (Grants 41905101, 41861144014, 41775106, U1811464, and 41975113), National Key R&D Program of China (Grant 2017YFA0604300), and partially by the Program for Guangdong Introducing Innovative and Entrepreneurial Teams (Grant 2017ZT07X355). The authors thank the anonymous reviewers for their constructive comments and suggestions.
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