Short-term prediction of stream turbidity using surrogate data and a meta-model approach Bhargav Rele1 Caleb Hogan2 Sevvandi Kandanaarachchi23yand Catherine Leigh1z

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Short-term prediction of stream turbidity using

surrogate data and a meta-model approach

Bhargav Rele1, Caleb Hogan2, Sevvandi Kandanaarachchi2,3*†and Catherine Leigh1‡

October 13, 2022

1Biosciences and Food Technology Discipline, School of Science, RMIT University,

Bundoora VIC 3083, Australia.

2School of Science, Mathematical Sciences, RMIT University, Melbourne VIC 3000,

Australia.

3CSIRO’s Data61, Research Way, Clayton VIC 3168, Australia (Present address).

†ORCID: 0000-0002-0337-0395

‡ORCID: 0000-0003-4186-1678

* Corresponding author: sevvandi.kandanaarachchi@data61.csiro.au

Abstract

Many water-quality monitoring programs aim to measure turbidity to help guide

eﬀective management of waterways and catchments, yet distributing turbidity sensors

throughout networks is typically cost prohibitive. To this end, we built and compared the

ability of dynamic regression (ARIMA), long short-term memory neural nets (LSTM),

and generalized additive models (GAM) to forecast stream turbidity one step ahead, using

surrogate data from relatively low-cost in-situ sensors and publicly available databases.

We iteratively trialled combinations of four surrogate covariates (rainfall, water level,

air temperature and total global solar exposure) selecting a ﬁnal model for each type

that minimised the corrected Akaike Information Criterion. Cross-validation using a

rolling time-window indicated that ARIMA, which included the rainfall and water-level

covariates only, produced the most accurate predictions, followed closely by GAM,

which included all four covariates. However, according to the no-free-lunch theorems

in machine learning, no single model has an advantage over all other models for all

instances. Therefore, we constructed a meta-model, trained on time-series features of

turbidity, to take advantage of the strengths of each model over diﬀerent time points and

predict the best model (that with the lowest forecast error one-step prior) for each time

step. The meta-model outperformed all other models, indicating that this methodology

can yield high accuracy and may be a viable alternative to using measurements sourced

directly from turbidity-sensors where costs prohibit their deployment and maintenance,

arXiv:2210.05821v1 [stat.ML] 11 Oct 2022

and when predicting turbidity across the short term. Our ﬁndings also indicated that

temperature and light-associated variables, for example underwater illuminance, may

hold promise as cost-eﬀective, high-frequency surrogates of turbidity, especially when

combined with other covariates, like rainfall, that are typically measured at coarse levels

of spatial resolution.

Key words— ARIMA, LSTM, GAM, meta-model, time series forecasting, river, turbidity,

water quality

1 Introduction

Unnaturally high turbidity in rivers is a major aquatic ecosystem and human health con-

cern, which makes it an important and commonly monitored water-quality variable in river

management programs. High turbidity can indicate the presence of excess suspended sediment

and particulate contaminants that can adversely aﬀect water-dependent biota and ecosystem

condition while complicating water treatment processes. Inorganic particles released by

weathering aﬀect the pH, alkalinity and metallicity of water while organic particles such as

zooplankton and cyanobacteria can release toxins and odour components, potentially resulting

in poor taste, smell and appearance, which together with contaminants from human, livestock

and industrial waste can render water harmful for consumption (World Health Organisation

2017) and increase water treatment costs. Ecological processes such as bioturbation and

human-induced factors, such as agricultural or industrial activities that accelerate erosion

from catchments and increase sediment inputs to waterways, also contribute to turbidity prob-

lems (Leigh et al. 2019a). Along with direct concerns for human health, excessive turbidity

in freshwater ecosystems poses risks to aquatic organisms, for example by reducing light

penetration and visibility and causing smothering, both in river systems themselves and in the

receiving waters of downstream coastal and marine zones (Leigh et al. 2013).

A prerequisite to informing management and policy aimed at preventing and responding

eﬀectively to the aforementioned phenomena, is the accurate and timely measurement and

monitoring of turbidity. Turbidity is often measured in Nephelometric Turbidity Units (NTU)

using 𝑖𝑛-𝑠𝑖𝑡𝑢 sensors that determine light scatter through water, which can be costly in

terms of initial outlay, installation and maintenance (Trevathan et al. 2020, Shi et al. 2022).

Distributions of sensor networks require regular calibration and maintenance to reduce the

likelihood of errors in measurement (technical anomalies) that may alert water management

agencies incorrectly and potentially reduce public conﬁdence in the data (Leigh et al. 2019b).

Furthermore, high setup costs often mean sensors tend to be located sparsely across stream

networks, typically at outlets in lower reaches, which decreases the ability to understand and

manage water-quality dynamics across entire systems and spatially pinpoint turbidity issues

in a timely fashion.

A possible workaround is the development of models capable of predicting turbidity using

high-quality data from covariates (sometimes referred to as surrogates). Such data can be

acquired from lower-cost sensors installed at monitoring sites and/or from publicly available

data sources, thereby reducing reliance on expensive sensors. Several types of models and

surrogate variables have been explored and proposed in the literature, with rainfall and river

discharge (hereafter ﬂow) or water level commonly found as useful covariates (e.g. Tsai &

Yen (2017), Leigh et al. (2019a)). Heavy rainfall aﬀects turbidity via erosion and subsequent

runoﬀ, thereby increasing sediment loads in streamﬂow, which itself increases together with

water level and acts to re-suspend sediments. Hence, sudden increase in turbidity often follows

periods of high rainfall and sudden rise in water level (Leigh et al. 2019a). However, turbidity

may also increase when ﬂow and water level decline leading to an increased concentration of

particles (Iglesias et al. 2014), although this phenomenon typically occurs more slowly than

the increase in turbidity associated with sudden, fresh inputs of water.

Seasonal patterns in temperature may also be reﬂective of seasonal patterns in rainfall,

and thus ﬂow and water level, such that interannual variation in air and water temperature

may help to explain variation in turbidity. Iglesias et al. (2014), for example, found that

water temperature was the most important variable for estimating river turbidity in northern

Spain. Water temperature may also prove to be an informative covariate of turbidity given that

suspended particles absorb more heat than water molecules when exposed to solar radiation

(Paaĳmans & Takken 2008). As such we may expect that temperature correlates somewhat

with turbidity, particularly during the day. This further suggests that sensors capable of

recording underwater illuminance (the amount of light shining onto a surface, measured

in lux) may help identify highly turbid waters given that poor water clarity will decrease

light penetration. However, underwater illuminance will also be aﬀected by the amount of

solar irradiation and incident-light available, as dependent on, for example, time of day and

year, cloud cover and shading from vegetation or other structures above the stream. As

such, the relationship between light-associated variables (e.g. illuminance, irradiance, solar

exposure) and turbidity, despite its potential utility, may not be as straight forward as that

between rainfall, water level and turbidity. To our knowledge, the predictive ability of such

light-associated variables as potential covariates of turbidity is yet to be explored beyond

their potential use in determining light-attenuation (Droujko & Molnar 2022), but is worth

investigating given, for example, that low-cost 𝑖𝑛 −𝑠𝑖𝑡𝑢 sensors that can measure both water

temperature and illuminance are currently available (e.g. HOBO MX2202 data loggers;

https://www.onsetcomp.com/).

Our ﬁrst objective in this study was to assess the potential of variables that can be mea-

sured using low-cost 𝑖𝑛-𝑠𝑖𝑡𝑢 sensors or via readily available open-access databases (including

rainfall, water level, temperature, and illuminance or radiant exposure, as available), either

alone or in combination, to act as surrogates for the prediction of turbidity in rivers. We

aim to achieve this by developing and comparing the ability of diﬀerent models (dynamic

regression, long short-term memory, and generalised additive models) to forecast the one-step

ahead turbidity of Merri Creek, southeast Australia, using the aforementioned variables as

covariates. Our second objective was to develop and implement the novel use of a ensemble

machine learning method (meta-model) to select the most accurate model for turbidity predic-

tion at any one time-step. The establishment of an accurate model has the beneﬁt of providing

water management and monitoring agencies a cost-eﬀective tool for accurately predicting

turbidity using surrogates. The use of surrogates may also serve to detect technical-anomalies

within sensor-produced data via validation with model-produced data, enabling agencies to

distinguish between turbidity ﬂuctuations caused by natural phenomena and those caused by

technical errors. By comparing an erratic datum in observed data to predicted data, erratic-

behaviour not justiﬁed by the model can be ﬂagged for investigation. As such, potential

beneﬁts of using surrogate data provided by cheaper, readily available 𝑖𝑛-𝑠𝑖𝑡𝑢 sensors and/or

publicly available data sources include increased reliability as well as cost-eﬀectiveness.

2 Materials and Methods

2.1 Study area

Merri Creek is a roughly 70-km long tributary of the Yarra River, which ﬂows through

Wurrundjeri Country and the city of Melbourne, Australia, discharging into Port Phillip Bay.

Water along some sections of Merri Creek is piped and some wetland areas have been drained

and converted into channels or drains. Much of the catchment has been cleared of its native

grassland and woodland, with land use changing in a downstream direction from rural to

industrial to residential and urban. Monitoring turbidity is of interest to local government and

community groups, particularly as the creek is home to vulnerable species such as the Growling

Grass Frog (𝐿𝑖𝑡𝑜𝑟𝑖𝑎𝑟𝑎𝑛𝑖 𝑓 𝑜𝑟𝑚𝑖𝑠) and previously the platypus (𝑂𝑟𝑛𝑖𝑡 ℎ𝑜𝑟 ℎ𝑦𝑛𝑐ℎ𝑢𝑠𝑎𝑛𝑎𝑡𝑖𝑛𝑢𝑠)

for which elevated turbidity is considered a threatening process (Grant & Temple-Smith 2003,

The State of Victoria Department of Environment & Planning 2017).

2.2 Data collection

We sourced turbidity (NTU) and water level (m) data recorded hourly at Merri Creek

between January 2013 and 2014 from the State of Victoria (Department of Environment, Land,

Water and Planning) Water Measurement Information System (Department of Environment,

Land, Water and Planning, VIC 2014). These data were recorded at a long-term monitoring

site (St Georges Road, North Fitzroy) approximately 6 km upstream from the conﬂuence with

the Yarra River. Daily mean rainfall (mm), maximum air temperature (◦C) and total global

solar exposure data (i.e. the total irradiance over a day, in MJ/m2) recorded at Australian

Bureau of Meteorology weather stations that were closest to the North Fitzroy monitoring site

(Bureau of Meteorology 2014). The rainfall data were recorded at Somerton Epping, while

the temperature and solar exposure data were recorded at Melbourne Airport. Being only

20-25 km away, and in an upstream direction, from the monitoring site, rainfall, temperature

and solar exposure data were expected to reﬂect phenomena occurring at the monitoring site.

The temperature and solar exposure measurements are above-water measurements. Al-

though measurements of temperature and light taken underwater would be useful, such data

were unavailable due to unavoidable circumstances associated with the installation of new

sensors at the monitoring site. Therefore, it was deemed reasonable to assume that, beyond

the diel ﬂuctuations in temperature and light being more buﬀered underwater, the Merri Creek

water would be warmer on warmer days, given air temperature is a major factor controlling

water temperature (Cluis 1972), and more light would reach and penetrate into the water

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Short-termpredictionofstreamturbidityusingsurrogatedataandameta-modelapproachBhargavRele1,CalebHogan2,SevvandiKandanaarachchi2,3*yandCatherineLeigh1zOctober13,20221BiosciencesandFoodTechnologyDiscipline,SchoolofScience,RMITUniversity,BundooraVIC3083,Australia.2SchoolofScience,MathematicalSciences,RM...

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Short-term prediction of stream turbidity using surrogate data and a meta-model approach Bhargav Rele1 Caleb Hogan2 Sevvandi Kandanaarachchi23yand Catherine Leigh1z

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