The calibration of macroscale hydrological models is often challenged by the lack of adequate observations of river discharge and infrastructure operations. This modeling backdrop creates a number of potential pitfalls for model calibration, potentially affecting the reliability of hydrological models. Here, we introduce a novel numerical framework conceived to explore and overcome these pitfalls. Our framework consists of VIC-Res (a macroscale model setup for the Upper Mekong Basin), which is a novel variant of the Variable Infiltration Capacity (VIC) model that includes a module for representing reservoir operations, and a hydraulic model used to infer discharge time series from satellite data. Using these two models and global sensitivity analysis, we show the existence of a strong relationship between the parameterization of the hydraulic model and the performance of VIC-Res – a codependence that emerges for a variety of performance metrics that we considered. Using the results provided by the sensitivity analysis, we propose an approach for breaking this codependence and informing the hydrological model calibration, which we finally carry out with the aid of a multi-objective optimization algorithm. The approach used in this study could integrate multiple remotely sensed observations and is transferable to other poorly gauged and heavily regulated river basins.

The past few years have witnessed an increase in the implementation of hydrological models to extensive domains, from large basins to a continental or even global scale

Some studies have explicitly dealt with the lack of in situ discharge time series by inferring discharge from satellite data. As shown in Fig.

Two approaches to the calibration of macroscale hydrological models with discharge data retrieved from satellite data.

Considering the increasing number of remotely sensed hydrological data that have become available over the last decades

To what extent is it possible and helpful to calibrate a macroscale hydrological model in ungauged catchments using remotely sensed data?

How do we deal with potential interactions between parameters used in data preprocessing (i.e., from remotely sensed data to reconstructed discharge data) and parameters of the hydrological models when doing model calibration?

Can we reduce the uncertainty from such interactions in model calibration results?

We answer these questions for an implementation of the VIC-Res hydrological model, a novel variant of the Variable Infiltration Capacity (VIC) model that includes a module for representing reservoir operations, for the Upper Mekong Basin

In this section, we provide information on our study site, the spatial domain of the hydrological model, and the availability of observed and remotely sensed discharge data.

Spanning an area of about 795 000 km

Panel

The Lancang accounts for 45 % of the river length, 21 % of the catchment area, and 16 % of the annual discharge of the entire Mekong

Because of the advantageous topography and abundant water availability, the Lancang River basin has become a hotspot for hydropower development. Indeed, the Lancang dam system – developed over the past 3 decades – consists of more than 35 hydropower dams

The spatial domain of our hydrological model is the light green area illustrated in Fig.

As mentioned above, the first gauging station with publicly available data is Chiang Saen, located in northern Thailand, about 350 km from Jinghong Dam (Fig.

To infer the discharge time series needed for model calibration, we sought locations around Chiang Saen where altimetry water level data are available (Fig.

Flowchart illustrating our numerical framework. The VIC-Res model (green boxes) includes a rainfall–runoff and a routing module; the latter explicitly simulates reservoir operations using data retrieved from satellite observations. The discharge data used to calibrate VIC-Res are estimated from altimetry water levels through a rating curve, which is based on Manning's equation and developed using multiple satellite data (Landsat images, altimetry water level, and a digital elevation model). All remote sensing items are represented by blue boxes. The relationship between the parameterization of Manning's equation (dark blue box) and the performance of VIC-Res is assessed and quantified via global sensitivity analysis

The numerical framework developed for our study consists of two main modeling components (illustrated in Fig.

Soil parameters controlling the rainfall–runoff process and routing parameters in VIC-Res. The last column shows the range of each parameter considered in this study and also adopted in previous studies (e.g.,

The hydrological model used in this study is VIC-Res

Improving on the VIC model, VIC-Res includes an explicit representation of water reservoir operations. For each reservoir in the study region, the model solves the storage mass balance and calculates the reservoir release. Specifically, we leverage information on modeled inflow and estimated storage (see Sect.

In our VIC-Res model, we calibrate seven soil parameters and two routing parameters (see Table

The data used in our VIC-Res model consist of climate forcing data, land use and cover, leaf area index (LAI), albedo, flow direction, and time series of reservoir storage volume. Climate forcing data include daily precipitation data retrieved from the CHIRPS-2.0 dataset, daily maximum and minimum temperature, and wind speed (retrieved from the ERA5 dataset). We collect land use and cover data from the Global Land Cover Characterization (GLCC) dataset and soil data from the Harmonized World Soil Database (HWSD). Monthly LAI and albedo are derived from the Terra MODIS satellite images, while the flow direction is calculated from the Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) data. The monthly time series of reservoir storage volume are reconstructed from satellite data, as explained below.

We finally note that the choice of the cell size could affect the rainfall–runoff and routing estimations, thereby impacting model calibration and simulated discharge

To capture the actual operations of reservoirs, we use monthly time series of reservoir storage volume reconstructed from satellite data by

To handle the lack of discharge data for model calibration, we again resort to satellite data. Specifically, we convert altimetry water levels (Jason-2/3) to discharge through a rating curve specified for the location of the virtual station (see Fig.

We construct the river cross-section at the virtual station using multiple satellite products (see Fig. S1a in the Supplement). First, we use a digital elevation model (SRTM DEM), which has a spatial resolution of 30 m, to obtain the portion of the cross-section above the water level at the observation time of the SRTM satellite (February 2000). To extend the information available to estimate the river cross-section, we then pair data on river widths at the virtual station with the corresponding water levels (nearest observations in time from the two satellites that provide river widths and water levels)

We construct the rating curve at the virtual station with Manning's equation (Eq.

The rating curve is constructed in two steps. First, we use Eq. (

We carry out a global sensitivity analysis ^{®} Xeon^{®} W-2175 CPU with 128 GB RAM running Linux Ubuntu 18.04. The total running time is about 200 h.

The performance metrics are calculated by comparing the simulated (by VIC-Res) and remotely sensed discharge at the virtual station. Because the temporal resolution of remotely sensed discharge is defined by the revisit time of the altimetry satellite (approximately 10 d for Jason-2/3), we calculate the performance metrics using the data of all days on which altimetry water levels are available. Among the several metrics available in literature

As we shall see, the global sensitivity analysis helps us understand the relationship between the performance of VIC-Res and the parameterization of the rating curve. Moreover, by identifying the parameter samples that map into high values of the performance metrics (here the top 25 %), the analysis helps us narrow down the range of variability in (at least some of) the model parameters. However, one may still want to complete the model calibration by further seeking for combinations of the VIC-Res parameters that optimize the performance metrics. To this end, we couple VIC-Res with

Here, we move across three steps. First, we illustrate the results leading to the estimation of a discharge time series at the virtual station, including the identification of the river cross-section and rating curve (Sect.

Figure

With the river cross-section at hand, we estimate the rating curve at the virtual station using Manning's equation (Eq.

Using the rating curve and water depth (converted from Jason-2/3 altimetry water level data), we estimate 298 discharge data points at the virtual station during the period from 2009 to 2018 (Fig.

The first fundamental step in our analysis is to understand whether co-estimating the Manning coefficient and the parameters of the hydrological model (see Fig.

The first column contains four parallel-coordinate plots. In each plot, the left axis is a model performance metric (i.e., NSE, TRMSE, MSDE, or ROCE) and the right axis is the Manning coefficient

Parallel-coordinate plot illustrating the 1000 parameterizations explored in this study. The first nine axes (green) represent the VIC-Res model parameters, while the last axis (blue) represents the Manning coefficient

In Fig.

The explanation behind this result must be sought in the different aspects of the simulated hydrograph that are captured by the four metrics (see Sect.

Having established that there can be a codependence between the performance of VIC-Res and the Manning coefficient, we now turn our attention to a potential solution. Ideally, one would like to calibrate a hydrological model that performs well with respect to multiple performance metrics

The left panel of Fig.

How does the new parameterization of

In panel

To complete the analysis, we compare the envelopes of variability in remotely sensed discharge data with the simulations of VIC-Res using the narrow range of

In our last step, we seek to reduce the uncertainty in simulated discharge presented in the previous section. To this end, we need to select a specific discharge time series to which we can calibrate the model. Albeit arbitrary, a reasonable choice is the remotely sensed discharge corresponding to the median value of

Simulated discharge at the virtual station used for calibration

In Fig.

Finally, we looked at the parameter values in the 12 parameterizations selected by the model calibration (Fig. S5a). Interestingly, these 12 parameterizations are all quite similar. On the other hand, the 58 parameterizations corresponding to the Pareto front span over a much larger variability range (Fig. S5b). Moreover, these 58 optimal parameterizations are in good agreement with the parameter ranges identified via sensitivity analysis (Sect.

Our study contributes an approach to calibrate macroscale hydrological models in poorly gauged and heavily regulated basins. The approach uses satellite data to infer both the discharge data used for model calibration and the reservoir operations included in the hydrological model. Unlike previous studies, our approach uses global sensitivity analysis to avoid the biases that could be introduced when co-calibrating the hydrological model and the rating curve used to reconstruct the discharge data

Looking at the specific results of the sensitivity analysis, there are two important points worth stressing here. First, we show that simultaneously estimating the parameters of the hydrological model and the Manning coefficient (by optimizing a set of model performance metrics) may significantly bias the reconstruction of the discharge values. Different combinations of performance metrics can result in different estimates of river discharge, thereby influencing the parameterization of the hydrological model. We saw, for example, that using the NSE for the joint calibration introduces bias in the Manning coefficient towards producing higher flows. Second, the sensitivity analysis specifically focused on the nine parameters of VIC-Res shows the existence of equifinality, meaning that different parameterizations can yield similar performance in terms of the NSE, TRMSE, MSDE, and ROCE. This equifinality issue is perhaps explained by the fact that we are using only river discharge data for calibration. Previous research

Our numerical framework seeks to reduce the pitfalls hidden in model calibration, but, like any other modeling study, is potentially affected by various errors and uncertainties. First, because of the unavailability of gauged rainfall data, we use a gridded product – a common approach for macroscale studies. However, gridded rainfall data inevitably carry errors, especially in regions (like Southeast Asia) where the number of rainfall gauges is limited

We note that the approach proposed in this study could be adopted for other basins, although there are a few specific caveats that should be kept in mind. First, the choice of the location for the virtual station (where we construct the river cross-section) should be driven not only by the availability of altimetry data but also by the site topography. In particular, the river banks should not be affected by levees, roads, or other interventions. This is because our approach works best for river banks under natural conditions, as it is possible to infer the relation between river widths and water levels for the portion below the lowest observed water level under the aforementioned conditions. Moreover, the virtual station should be located in a straight river segment with minimal discharge variation due to nearby tributaries and distributaries (both upstream and downstream), a setting in which our approach – based on Manning's equation – works best

Looking forward, we should consider expanding frameworks like the one presented here to even more complex modeling environments. For example, a modeling challenge that is often recurring in downstream applications is the presence of multiple human interventions, such as dams, irrigation withdrawals, and groundwater pumping. Understanding how data concerning the representation of all of these processes influence model calibration remains an open question. A similar comment applies to the calibration of multi-basin and global models. Bringing all of these elements together would be a major step towards a more reliable calibration of macroscale hydrological models.

The VIC-Res model codes are available at

The supplement related to this article is available online at:

DTV, TDD, FP, and SG conceptualized the paper and its scope. Data collection and all analyses were carried out by DTV and SG. DTV wrote the manuscript, with substantial input from all authors.

The contact author has declared that none of the authors has any competing interests.

Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

This article is part of the special issue “Representation of water infrastructures in large-scale hydrological and Earth system models”. It is not associated with a conference.

Dung Trung Vu is supported by the SUTD PhD fellowship.

This paper was edited by Yadu Pokhrel and reviewed by two anonymous referees.