Perturbed Synthetic SWOT Datasets for Testing and Development of a Kalman Filter Approach to Estimate Daily Discharge

1.     Introduction

Datasets are used to evaluate the performance of a Kalman filter approach to estimate daily discharge. This is a perturbed version of synthetic SWOT datasets consisting of 15 river sections, which are commonly agreed datasets for evaluating the performance of SWOT discharge algorithms (Frasson et al., 2020, 2021). The benchmarking manuscript entitled “A Kalman Filter Approach for Estimating Daily Discharge Using Space-based Discharge Estimates” is currently under review at Water Resources Research. Once the manuscript is accepted, its DOI will be included here.

2.  File description

The datasets are generally divided into two categories: river information (River_Info) and time series data (Timeseries_Data). River information provides fundamental and general river characteristics, whereas time series data offers daily reach-averaged data for each reach. In time series data, the data mainly contains three components: true data, perturbed measurements, and true and perturbed flow law parameters (A0, an, and b). For each reach, there are 10000 realizations of perturbed measurements per time step and there are 100 realizations of time-invariant perturbed flow law parameters through a Monte Carlo simulation (Frasson et al., 2023). Moreover, to support our proposed Kalman filter approach to estimate daily discharge, the datasets provide the median of the perturbed discharge, river width, water surface slope, and change in the cross-sectional area, as well as the uncertainty of the perturbed discharge and change in the cross-sectional area based on the interquartile range (Fox, 2015).

Datasets are contained in a .mat file per river. The detailed groups and variables are in the following:

River_Info

Name: River name, data type: char

QWBM: Mean annual discharge from the water balance model WBMsed (Cohen et al., 2014)

rch_bnd:   Reach boundaries measured in meters from the upstream end of the model

gdrch: Good reaches in the study. They were used to exclude small reaches defined around low-head dams and other obstacles where Manning’s equation should not be applied.

Timeseries_Data

t: Time measured in days since the first day or “0-January-0000” for cases when specific dates were available. Dimension: 1, time step.

A: Reach-averaged cross-sectional area of flow in m². Dimension: Reach, time step.

Q_true: True reach-averaged discharge (m³/s). Dimension: Reach, time step.

Q_ptb: Perturbed discharge (m³/s), including 10000 realizations for each measurement. Dimension: Good reach, time step, 10000.

med_Q_ptb: Median perturbed discharge (m³/s) across the 10000 realizations. Dimension: Good reach, time step.

sigma_Q_ptb: Uncertainty of the perturbed discharge (m³/s), calculated based on the interquartile range. Dimension: Good reach, time step.

W_true: True reach-averaged river width (m). Dimension: Reach, time step.

W_ptb: Perturbed river width (m), including 10000 realizations for each measurement. Dimension: Good reach, time step, 10000.

med_W_ptb: Median perturbed river width (m) across the 10000 realizations. Dimension: Good reach, time step.

H_true: True reach-averaged water surface elevation (m). Dimension: Reach, time step.

H_ptb: Perturbed water surface elevation (m), including 10000 realizations for each measurement. Dimension: Good reach, time step, 10000.

S_true: True reach-averaged water surface slope (m/m). Dimension: Reach, time step.

S_ptb: Perturbed water surface slope (m/m), including 10000 realizations for each measurement. Dimension: Good reach, time step, 10000.

med_S_ptb: Median perturbed water surface slope (m/m) across the 10000 realizations. Dimension: Good reach, time step.

dA_true: True reach-averaged change in the cross-sectional area (m²). Dimension: Good reach, time step.

dA_ptb: Perturbed change in the cross-sectional area (m²), including 10000 realizations for each measurement. Dimension: Good reach, time step, 10000.

med_dA_ptb: Median perturbed change in the cross-sectional area (m²) across the 10000 realizations. Dimension: Good reach, time step.

sigma_dA_ptb: Uncertainty of the perturbed change in the cross-sectional area (m²), calculated based on the interquartile range. Dimension: Good reach, time step.

A0_true: True baseline cross-sectional area (m²). Dimension: Good reach, 1.

A0: Perturbed baseline cross-sectional area (m²), including 100 realizations for each parameter. Dimension: Good reach, 100.

na_true: True friction coefficient. Dimension: Good reach, 1.

na: Perturbed friction coefficient, including 100 realizations for each parameter. Dimension: Good reach, 100.

b_true: True exponent coefficient. Dimension: Good reach, 1.

b: Perturbed exponent coefficient, including 100 realizations for each parameter. Dimension: Good reach, 100.