Edited by: Vimala D. Nair, University of Florida, United States
Reviewed by: Susana Bernal, Center for Advanced Studies of Blanes (CSIC), Spain; Peter Thorburn, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Australia
This article was submitted to Agroecology, a section of the journal Frontiers in Ecology and Evolution
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The quantification of solute and sediment export from drainage basins is challenging. A large proportion of annual or decadal loads of most constituents is exported during relatively short periods of time, a “hot moment,” which vary between constituents and catchments. We developed a new framework based on concentration-discharge (C-Q) relationship to characterize the export regime of stream particulates and solutes during high water periods when the majority of annual and inter-annual load is transported. We evaluated the load flashiness index (percentage of cumulative load that occurs during the highest 2% of daily load, M_{2}), a function of flow flashiness (percentage of cumulative Q during the highest 2% of daily Q, W_{2}), and export pattern (slope of the logC-logQ relationship for Q higher than the daily median Q, b_{50high}). We established this relationship based on long-term water quality and discharge datasets of 580 streams sites of France and USA, corresponding to 2,507 concentration time series of total suspended sediments (TSS), total dissolved solutes (TDS), total phosphorus (TP), nitrate (NO_{3}), and dissolved organic carbon (DOC), generating 1.5 million data points in highly diverse geologic, climatic, and anthropogenic contexts. Load flashiness (M_{2}) increased with b_{50high} and/or W_{2}. Also, M_{2} varied as a function of the constituent transported. M_{2} had the highest values for TSS and decreased for the other constituents in the following order: TP, DOC, NO_{3}, TDS. Based on these results, we constructed a load-flashiness diagram to determine optimal monitoring frequency of dissolved or particulate constituents as a function of b_{50high} and W_{2}. Based on M_{2}, optimal temporal monitoring frequency of the studied constituents decreases in the following order: TSS, TP, DOC, NO_{3}, and TDS. Finally, we analyzed relationships between these metrics and catchments characteristics. Depending on the constituent, we explained between 30 and 40% of their M_{2} variance with simple catchment characteristics, such as stream network density or percentage of intensive agriculture. Therefore, catchment characteristics can be used as a first approach to set up water quality monitoring design where no hydrological and/or water quality monitoring exist.
Quantifying solute and sediment export from drainage basins is important to understanding stream biogeochemical processes (Jarvie et al.,
Although solute and sediment export are related to climate, lithology, landscape structure, and land use (Burt and Pinay,
Despite these findings, the European Union's Water Framework Directive and other monitoring programs worldwide continue to recommend monthly sampling for most water quality monitoring, a timeframe often not suitable to accurately quantify loads or detect temporal trends (Skeffington et al.,
Analysis of the concentration (C) vs. river flow (Q), or C-Q relationship, is commonly used to estimate missing concentration values in discrete surveys, particularly for load calculations (Ferguson,
Our objective is to relate the flow duration curve and C-Q relationship to estimate load flashiness—an indicator of load variability and catchment export (M_{2}, percentage of cumulative load that occurs during the highest 2% of daily load values). We aim at combining a discharge-based metric (W_{2}, the percentage of cumulative discharge that occurs during the highest 2% of daily discharge values) with a metric extracted from C-Q analyses (b_{50high}, the slope of the C-Q relationship during high flows) to estimate the M_{2} of sediment, sediment-bound particulates or solutes. Furthermore, we examine how this M_{2} metric can be used to optimize the sampling frequency for reducing load uncertainty for a large range of catchment types. In order to achieve our objective, we quantify the relationship between W_{2}, b_{50high}, and M_{2} using long-term water quality and discharge datasets of 580 catchments of France and USA in highly diverse geologic, climatic and anthropogenic contexts. Then, we evaluate to what extent this relationship could characterize hydrological and biogeochemical export regimes for dissolved solutes and sediment-bound particulates across contrasting catchments. Finally, we determine the relevance of land cover and geological spatial attributes as predictors for M_{2} in drainage basins where no hydrological and or water quality monitoring exist.
Discharge (Q) and water quality data were obtained from stream databases in 580 catchments in France and the USA (
Summary of datasets.
Total suspended solids (TSS) | 474 | Min | 13 | 3,876 | 1.5 | 77 | 2.9 | 1.7 | 65.1 |
Median | 2,915 | 14,820 | 12.7 | 275 | 19.2 | 114.9 | 94.4 | ||
Max | 109,966 | 54,789 | 59.3 | 710 | 182.8 | 2,358.3 | 99.7 | ||
Total dissolved solutes (TDS) | 474 | Min | 13 | 3,876 | 1.5 | 81 | 36.3 | 43.4 | |
Median | 2,915 | 14,820 | 12.7 | 288 | 401.7 | 82.0 | |||
Max | 109,966 | 54,789 | 59.3 | 748 | 3,341.2 | 97.3 | |||
Total phosphorus (TP) | 475 | Min | 13 | 3,876 | 1.5 | 59 | 0.0 | 0.0 | 56.6 |
Median | 2,915 | 14,820 | 12.7 | 241 | 0.2 | 0.4 | 85.2 | ||
Max | 109,966 | 54,789 | 59.3 | 613 | 1.9 | 3.3 | 97.9 | ||
Nitrate-N (NO_{3}-N) | 475 | Min | 13 | 3,876 | 1.5 | 80 | 0.3 | 0.5 | 55.5 |
Median | 2,915 | 14,820 | 12.7 | 281 | 3.4 | 11.9 | 86.6 | ||
Max | 109,966 | 54,789 | 59.3 | 1,055 | 12.3 | 68.2 | 99.7 | ||
Dissolved organic carbon (DOC) | 448 | Min | 13 | 3,876 | 1.5 | 27 | 0.9 | 0.5 | 57.9 |
Median | 2,915 | 14,820 | 12.7 | 184 | 4.1 | 15.2 | 87.1 | ||
Max | 109,966 | 54,789 | 59.3 | 559 | 21.5 | 62.2 | 98.8 | ||
TSS | 54 | Min | 660 | 1,096 | 0.2 | 1,096 | 28.9 | 45.9 | 79.2 |
Median | 7,723 | 4,383 | 11.1 | 4,383 | 207.4 | 606.2 | 97.0 | ||
Max | 251,149 | 15,341 | 46.0 | 15,341 | 92,137.7 | 26,697.3 | 100.0 | ||
TDS | 33 | Min | 743 | 1,460 | 0.0 | 1,460 | 32.1 | No calculations | 61.4 |
Median | 13,177 | 2,920 | 3.7 | 2,920 | 643.2 | 74.7 | |||
Max | 1,061,441 | 9,855 | 52.3 | 9,855 | 3,866.9 | 90.4 | |||
TSS | 18 | Min | 11 | 1,096 | 9.0 | 1,096 | 21.52 | 145.00 | 70.1 |
Median | 1,085 | 6,940 | 19.4 | 6,940 | 43.48 | 596.73 | 89.1 | ||
Max | 19,218 | 16,071 | 40.2 | 16,071 | 108.59 | 1084.00 | 98 | ||
TDS | 16 | Min | 11 | 1,096 | 9.0 | 1,096 | 515.90 | No calculations | 65 |
Median | 1,085 | 6,940 | 19.4 | 6,940 | 688.32 | 78 | |||
Max | 19,218 | 16,071 | 40.2 | 16,071 | 1565.45 | 89 | |||
TP | 18 | Min | 11 | 1,096 | 9.0 | 1,096 | 0.08 | 0.20 | 85.5 |
Median | 1,085 | 6,940 | 19.4 | 6,940 | 0.18 | 0.86 | 89.4 | ||
Max | 19,218 | 16,071 | 40.2 | 16,071 | 0.36 | 5.76 | 97.6 | ||
NO_{3}-N | 18 | Min | 11 | 1,096 | 9.0 | 1,096 | 0.45 | 1.17 | 67.3 |
Median | 1,085 | 6,940 | 19.4 | 6940 | 2.95 | 2.83 | 88.5 | ||
Max | 19,218 | 16,071 | 40.2 | 16,071 | 8.22 | 52.16 | 97.5 |
Sampling site locations for the following datasets:
We selected sites in the USA (
We also selected other USA data to serve as validation sites. The validation dataset encompassed 18 tributaries of Lake Erie (
Formally, let
Illustration of flow and load flashiness indices for Portage River (1,109 km^{2}), Ohio, USA.
In practice
Note that the flashiness index is not restricted to flow variables.
The
Equation (4) allows the calculation of
Differences between
Daily flows follow a lognormal distribution, i.e., log(
Daily concentration can be derived from daily flow using the C-Q regression:
The
Where ϕ is the standard normal cdf and ϕ^{−1} its inverse (also known as the probit transformation):
Note that a “good” C-Q relationship would be characterized by a small residual standard deviation (η_{i,j}) compared with the standard deviation of input log-discharge (σ_{i}). In such a case,
Moatar and Meybeck (
The formulation proposed in Equation (7) is similar to that proposed by Moatar et al. (
We name this b_{50high} indicator as the “export pattern.” Negative b_{50high} values reveal that the cdf of load increases less rapidly than that of river discharge (
Equation (7), demonstrated mathematically, for
Since our stations also include intermittent rivers, we decided to use an equation similar to Equation (7), calibrating the parameter α for all stations and constituents (French database and USA database) together (Equation 9). We tested the model by comparing the M_{2} predictions with observed M_{2} based on a set of independent daily loads for TSS, TDS, TP, and NO_{3} (Erie database).
for site
This equation (Equation 9) explained 91% of M_{2} variance based on the French reconstructed daily loads using the C-Q relationship and the USA daily database with a root mean square error (RMSE) of 4% (
To calibrate the parameter α on Equation (9), we used “true M_{2},” calculated from daily load available for USA database with Equation (4) and “reconstructed M_{2}” calculated from monthly French database. Reconstructed M_{2} were determined after reconstruction of daily concentrations based on daily discharge using a segmented linear regression (Method SRC_{50} tested by Raymond et al.,
Q_{50} is the median discharge estimated from daily discharge. We tested statistical significance of C-Q correlation by Pearson product-moment correlation, with significant relationships (
To assess the robustness of M_{2} estimates derived from discrete surveys, we used two methods.
We validated the predictions of Equation (9) (M_{2} predicted) using the Erie database with “true M_{2}” for four parameters and 18 rivers.
We compared M_{2} estimates, obtained after the reconstruction of daily concentrations by segmented linear regression approach (Equations 8 and 10) with those obtained using the Weighted Regression on Time, Discharge, and Season approach (WRTDS; Q. Zhang pers. Comm.; Hirsch et al.,
Equation (9) has been used with M_{2}, W_{2}, and b_{50high} calculated from the entire set of data (between 20 and 40 years long). Since C-Q relationships can change with time, for example due to land use change, we assessed the stability of b_{50high} and M_{2} across decades. To do so, we used the French dataset in four successive series of 10 years, i.e., 1978–1987; 1988–1997; 1998–2007; 2008–2017. Tukey's range test was used for the comparison of M_{2}, b_{50high}, and W_{2} across four decades and for the whole 40-y period to find means that are significantly different from each other. Additionally, we analyzed annual b_{50high} variation for five stations in the Erie dataset where more than 35 years were available.
We investigated the sensitivity of period length on estimated b_{50high} and M_{2} considering monthly sampling (12 C-Q pairs per year). We used as reference the metrics computed from daily TSS, TDS, TP, and NO_{3}, surveyed for more than 30 years in four rivers from the Lake Erie dataset with various watershed scales (386–15,395 km^{2}). To mimic a classic long-term monthly monitoring, daily concentration time series were randomly subsampled following a normal distribution (30 days average ± 5 days). The metrics b_{50high} and M_{2} were then computed on subsampled data and compared to reference values. To assess potential variations due to varying sampling dates, this was repeated 100 times for each given period length. We investigated this from 2 years-long timeseries, up to 20 years.
We used the formulations proposed by Moatar et al. (
where e_{10} and e_{90} = lower and upper limits of precision; d = sampling interval in days; r, s, u, v values for calculating precision for different d are available in
Error nomograph (e_{10}, e_{90} vs. M_{2}) for annual loads calculated for discharge-weighted concentration method (adapted from Moatar et al.,
We analyzed the main geographical, geological and land cover characteristics of 475 French drainage basins. We then determined relationships between these variables and W_{2}, b_{50high}, and M_{2} for each of the water quality parameters. We performed generalized additive model (GAM) to assess potential non-linearity in relationships. The results showed that smoothing functions poorly improved the regression models. Hence, we assumed that classical multivariate regressions would be convenient to highlight and discuss simple relationships including their sign.
We used multiple linear regressions to evaluate the relationship between French dataset characteristics, i.e., catchment size, agricultural land use, lithology, wetland surface, stream network density, erosion indicator risk, as well as W_{2}, b_{50high}, and M_{2} for each of the water quality parameters, i.e., TSS, TDS, TP, NO_{3}, and DOC. These variables are listed with full details provided in
List of explanatory variables and their definitions, units, and data sources.
Area | Drainage area of the water quality monitoring station | km^{2} | |
Stream network density | Density of the natural stream network in the catchment | km/km^{2} | BDCarthage v4 IGN |
Wetlands | Percentage of potential wetland in the catchment | % | INRA – Beven index (Quinn et al., |
Crystalline rocks | Percentage of crystalline rocks in the catchment | % | BRGM 1/1,000,000 |
Low carbonate rocks | Percentage of low carbonate rocks in the catchment | % | BRGM 1/1,000,000 |
High carbonate rocks | Percentage of high carbonate rocks in the catchment | % | BRGM 1/1,000,000 |
Riparian vegetation | Percentage of riparian vegetation in a 10 m wide buffer on both sides of the stream | % | SYRAH_CE |
Forest | Percentage of forest in the catchment | % | CORINE Land Cover EEA 2012 |
Extensive agriculture | Percentage of extensive agriculture in the catchment | % | CORINE Land Cover EEA 2012 |
Intensive agriculture | Percentage of intensive agriculture in the catchment | % | CORINE Land Cover EEA 2012 |
Urban area | Percentage of urban land use in the catchment | % | CORINE Land Cover EEA 2012 |
Population density | Number of inhabitants divided by the catchment area | Inhabitant/km^{2} | INSEE 2011 |
Point source P | Sum of domestic and industrial phosphorus point sources loads | kg P/ha/year | AELB |
Soil P | Total phosphorus content in the surficial soil horizon. | g/kg | INRA (Delmas et al., |
Point source N | Sum of domestic and industrial nitrogen point sources loads | kg N/ha/year | AELB |
N surplus | Balance between nitrogen added to an agricultural system and nitrogen removed from the system per hectare of agricultural land | kg N/kg | NOPOLU 2010 (Schoumans et al., |
Erosion risk | Fraction of area with a strong to very high hazard erosion (derived from land use, topography, and soil properties) | % | INRA (Cerdan et al., |
The interannual flow-flashiness indicator of the study sites (W_{2}) ranged between 3 and 60%, with the majority between 5 and 30% (
The range of b_{50high} varied depending on the water quality variables considered; but for a given variable, the range obtained from monthly sampling data (French dataset) did not significantly differ from the ones obtained from daily sampled data (USA dataset;
TP, often transported with sediment, followed a similar pattern as TSS but with a smaller range of variation (
The variability of annual W_{2} differed depending on climate and catchment hydrology. Differences between maximal and minimal annual W_{2} values ranged between 40 and 60% for catchments exposed to a contrasting climate (e.g., small catchments in the Mediterranean area experiencing hot and dry summers and intense short rainy events in autumn; catchments with no storage capacity resulting in severe low-flow and quick runoff response to rainfall events). Ranges <20% were observed for streams fed by large aquifers (e.g., northern France) or in catchments where snow pack storage buffers the variability of daily flows.
Interannual load-flashiness indicator values ranged between 2% (TDS for Ill River at Strasbourg) and 98% (TSS at Santa Clara River)—close to the possible range (2–100%) (
Distribution of the 2,507 sample series (percentage) in each class of load flashiness depending on the solutes or particulates.
TSS | 0 | 6 | 33 | 52 | 8 |
TDS | 19 | 62 | 20 | 0 | 0 |
TP | 7 | 35 | 48 | 10 | 0 |
NO_{3} | 8 | 48 | 39 | 4 | 0 |
DOC | 6 | 39 | 49 | 7 | 0 |
Using Equation (9), we drew M_{2} isolines representing the five classes' limits on the W_{2}–b_{50high} relationship (
The two methods used to reconstruct daily concentrations led to similar results. The standard deviation of differences in the estimates of M_{2} calculated with daily concentrations reconstructed with the WRTDS and the segmented C-Q method (M_{2WRTDS}-M_{2SRQ50}) was around 4% for NO_{3} and TP for the four decades considered and 12% for TSS (Data presented in
For the French dataset, where we have up to 40 years of data, b_{50high} for TSS, TDS, NO_{3}, and DOC showed little variation across decades, while we found some noticeable, but not significant differences for TP. Overall, the variability between the four decades was limited for TSS (<5% for median M_{2} and <0.05 for median b_{50high}), TDS, DOC and nitrate (<1% for M_{2}). For TP, b_{50high} was higher in the last period (2008–2017) (+0.2) than in first and second periods (1978–1987 and 1988–1997). This was due to a more pronounced dilution of punctual sources which were more important in the 1978–1997. Therefore, the load-flashiness was lower (−5%) in the first period compared to the present time. However, the differences were limited.
For yearly variations in the Erie dataset, differences were more important across years, which was particularly true for Cuyahoga and mostly for TSS, TDS, and TP (
Sensitivity of period length necessary to derive reliable b_{50high} and M_{2} estimates from monthly monitoring was assessed via subsampling of daily timeseries (
The optimal sampling frequency needed to minimize the uncertainty associated with the estimation of solute and sediment loads increased with increasing M_{2} (
Sampling intervals required to achieve targeted errors (precision ± 10%) on annual loads as a function of b_{50high} and W_{2}. Each sampling interval corresponds to a level of load flashiness (M_{2}) calculated by error nomograph parameters (adapted from Moatar et al.,
The comparison of the optimal frequencies to calculate annual loads with <10% precision using our approach and the current sampling frequency recommended by the European Water Framework Directive is presented in
Distribution of optimal sampling intervals required for 475 French stations for each parameter. The vertical dashed lines represent the current sampling frequency, i.e., monthly, used by national monitoring survey based on European Water Framework Directive.
Catchment characteristics explained up to 38% of the total variance of W_{2}, b_{50high}, and M_{2} (
Relationships between W_{2}, b_{50high}, and M_{2} indicators and catchment characteristics: total percentage of variance explained by final regression models following a backward selection approach of explanatory variables (third column) and individual contributions (between 0 and 100%; next columns) of the selected variables according to hierarchical variation partitioning.
% |
% | 34.9 | 21.9 | 22.9 | 18.2 | 10.9 | 12.1 | 30.9 | 36.5 | 37.9 | 28.3 | 33.1 |
9.6 | 15.5 | 12.9 | 7 | 10.8 | ||||||||
11.7 | 20.6 | |||||||||||
% | 7.3 | 1.4 | 6.8 | 13.5 | ||||||||
% | 8 | 4.8 | 15.3 | 2.9 | 3.9 | 4.8 | ||||||
% | 11.6 | 6.8 | 4 | 8.4 | 14.4 | 13.7 | ||||||
% | 5.1 | 12.7 | 5.6 | 4.5 | 2 | |||||||
% | 4.6 | 5.8 | ||||||||||
10.2 | 12.8 | 20.5 | 4.2 | 8.2 | 10.1 | |||||||
% | 2.6 | 3.7 | 2.8 | 3.2 | 3.3 | 3.3 | ||||||
% | 8.9 | |||||||||||
% | 17.2 | 1.7 | 10.9 | 5 | ||||||||
3 | 11.2 | |||||||||||
9.8 | ||||||||||||
8.1 | ||||||||||||
7.8 | ||||||||||||
6.2 | ||||||||||||
% | 10.2 | 17.9 | 8.9 | 3.8 |
W_{2} was positively related to the stream network density and the percentage of intensive agriculture in the catchment (25 and 13% respectively) while it decreased with the size of the drainage basin (21%). The b_{50high} values of TSS, TP and DOC (between 31 and 44% of variance explained) decreased with the percentage of crystalline rocks in the catchments. We found a significant positive relationship between the percentage of wetland in the catchment and the DOC b_{50high} (21%), while a negative relationship was found for TSS b_{50high} (19%). The percentage of intensive agriculture in the catchment had a significant positive influence on TDS b_{50high} (18%). Load flashiness (M_{2}) decreased with the size of the catchment for all the water quality parameters, while it increased also for all the water quality parameters with the stream network density and the percentage of intensive agricultural practices.
We found that load flashiness (M2) can be inferred from flow flashiness (W2) and export pattern (b50high) based on a large dataset of stream concentration and discharge encompassing a wide range of climatic, geologic and land use conditions. We characterized the flashiness of solute and sediment export regime (M_{2}) using hydrological and biogeochemical indicators calculated for high flows, i.e., the flow flashiness (W_{2}) and the exponent of C-Q relationships during discharge higher than the median (b_{50high}). Following previous studies, we determined that stream export of solute and sediment during the highest 2% of time (M_{2}) was a good indicator of solute and sediment transport. We proposed to overcome the lack of high frequency concentration measurements by using the exponent of C-Q relationships during high flow periods (b_{50high}) as a proxy for export pattern, coupled with flow flashiness—a parameter more easily available, thanks to continuous discharge monitoring or new modeling development for ungauged catchments (Oudin et al.,
The theoretical proposed approach is based on two assumptions which have some implicit limitations. The first assumption (see
L = CQ = aQ^{b+1} which is a raw approximation. In particular, C-Q data typically show a large scatter around this power relationship. This scatter creates an additional source of variability that might play a non-negligible role on the variability of loads, and hence on the flashiness M_{2}. The regression formula of Equation (7) could therefore be augmented with an additional predictor describing the variability of the residuals around the C-Q power relationship.
Despite these assumptions, the theoretical model for perennial rivers (Equation 7), and the empirical model (Equation 9) provide good predictions of load flashiness (M_{2}). The empirical model (Equation 9) was parameterized based on an extensive monthly-sample data set from France (TSS, TDS, TP, NO_{3}, and DOC) and daily-sample data set from USA (TSS and TDS). The model was validated using an extensive daily-sample dataset (TSS, TDS, TP, and NO_{3}) from several rivers near Lake Erie. However, a more diverse validation dataset would have been desirable. Yet, daily concentrations with long-term time series are very rare.
M_{2} can be calculated by different methods depending on sampling frequency of concentration. When high-frequency concentration data are available, daily loads can be derived and Equation (4) can be applied. When discrete surveys are available, for example monthly samples, there are two options to characterize the M_{2}. One can apply Equation (4) after reconstruction of daily concentrations with a regression method like WRTDS (Hirsch et al.,
Our databases cover a wide range of climatic, lithological, land use and hydrological conditions found in the northern hemisphere between 30° and 50°N and range across river magnitudes from 10 km^{2} to 1 million km^{2}. The database displays extensive ranges of concentration and river flow which are close to those observed at the global scale for river basins of similar sizes (Meybeck and Helmer,
C-Q relationships are important signatures of catchment biogeochemical processes and export regime (Moatar et al.,
The relationship between discharge and concentration has significant implications for the inequality of solute export dynamics. Indeed, differences between cumulated percentage of load and flow associated with a specific duration or the ratios of Gini coefficients depend on the C-Q relationship (Jawitz and Mitchell,
Our framework for estimating load flashiness can be compared to the bivariate plot of beta and the coefficient of variations ratio proposed by Musolff et al. (
Our results provide a water quality monitoring strategy that can address the large range of M2 values measured in our dataset for different solutes and catchments (
Our study is the first to our knowledge that analyses the environmental factors controlling load variability (M_{2}). Although, the total explained variance is relatively low, i.e., 28–38% depending on the constituent (
Differences in load flashiness among the various waterborne materials align with catchment variations in the sources and fate of those materials. For example, the positive relationship between DOC flashiness and the percentage of wetlands confirms their significant contribution to stream DOC (Zarnetske et al.,
We were able to demonstrate that load flashiness (M_{2}), i.e., percentage of cumulative load that occurs during the highest 2% of daily load values is a useful proxy of solute and sediment export regimes. Our results emerged from a robust, long-term dataset of a wide range of discharge, solute and particulate sediments in 580 drainage basins in France and the USA and 2,507 sample series, representing over 1.5 million discharge-concentration couples. This indicator can be estimated from the common low-frequency national or regional monitoring surveys through the b_{50high} coefficient and the runoff flashiness indicator (W_{2}). We showed that if current water-sampling strategies undertaken by local, national, and international water authorities are not appropriate to directly calculate solutes and sediment loads; these data can nevertheless be used to calculate flow flashiness (W_{2}) and b_{50high}. We demonstrated that these two proxies are related to load flashiness (M_{2}) with a simple equation. We showed that load flashiness diagrams can be used to classify constituents and catchments by precision related to different sampling intervals and thus optimize stream water quality sampling procedures for a given transported constituent. Moreover, the analysis of our large dataset allowed the identification of significant correlations between easily accessible drainage basin characteristics (e.g., basin area, stream network density, and percentage of extensive agriculture), W_{2}, b_{50high}, and M_{2}. These characteristics can serve as a basis to classify non-monitored drainage basins as a function of their potential load flashiness and propose a sampling monitoring design for the most contributive ones. Regulatory monitoring in Europe, recommended by the WFD, promotes the monthly sampling for any monitored constituents (dissolved and particulate) and for any basin size. Such standardized monitoring does not take into account the actual variability of the constituent concentration and loads, particularly for the small (100–1,000 km^{2}) and very small (<100 km^{2}) basins. The load flashiness M_{2} can also be used to optimize monitoring frequency to reach a certain level of annual load uncertainty (here 10%) for loads trend detection required for instance by international conventions such as OSPAR and HELCOM.
The datasets generated for this study are available on request to the corresponding author.
FM, GP, MM, BR, and AG wrote the first draft. FM, MFl, CM, and MFe analyzed the data and made the figures. AC made the spatial calculations. The final manuscript was written by FM, GP, BR, AG, and KA with contributions from all co-authors.
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
We would like to thank Qian Zhang (University of Maryland Center for Environmental Science) for the calculations of daily loads on 238 French stations with WRTDS method. We also would like to thank two reviewers for their very thorough and constructive comments on an earlier version of the manuscript. Their insights helped us to improve this current version.
The Supplementary Material for this article can be found online at:
Predicted M_{2} vs. observed M_{2}.
Comparison analysis on 248 French stations of M_{2} estimates derived from segmented linear regression approach (Method SRC_{50}) on monthly TSS, TP, and NO_{3}, and daily discharge vs. M_{2} estimates derived from a Weighted Regression on Time Discharge and Seasonality (Method WRTDS, Q. Zhang pers. comm.).
Temporal evolution of yearly b_{50high} estimated for TSS, TDS, TP, and NO_{3} on five long-term and daily Lake Erie tributaries datasets.
Temporal evolution of yearly M_{2} and W_{2} estimated for TSS, TDS, TP, and NO_{3} on five long-term and daily Lake Erie tributaries datasets.
Error nomograph (e_{10}, e_{90} vs. M_{2}) for annual loads calculated for discharge-weighted concentration method. Lower limits (e10) and upper limits (e90) for sampling intervals of 3, 7,…, 60 days (Moatar et al.,
Percentage of sites with significant p-values for segmented C-Q regressions. Total suspended solids (TSS), total dissolved solutes (TDS), total phosphorus (TP), nitrate (NO3), dissolve organic carbon (DOC).
Assume that the distribution of daily flows
where ϕ is the standard normal cdf and ϕ^{−1} its inverse (also known as the probit transformation).
Since the Lorenz curve
Moreover, assume that the daily log-concentration log(
Daily log-loads can therefore be computed as follows:
This equation implies that daily loads
Some additional algebra [using the relation ϕ^{−1} (1 −
When the quality of the concentration-discharge regression is good (η ≪ σ), this relation simplifies to:
Note that the formula above are given for one particular catchment
percentage of cumulative discharge that occurs during the highest 2% of daily discharge values, termed as flow flashiness
percentage of cumulative load that occurs during the highest 2% of daily load values, termed as load flashiness
slope of the logC-logQ relationship for discharge higher than daily median discharge Q_{50}, termed export pattern
concentration-discharge
discharge
cumulative distribution function.