Original: Quality Control in Weather Monitoring with Dynamic Linear Models
Revised: Quality Control in Weather Monitoring with Dynamic Linear Models

Original: Abstract
Revised: Abstract

Original: Decisions in agriculture are frequently based on weather.
Revised: Decisions in agriculture are frequently based on weather.

Original: With an increase in the availability and affordability of offthe-shelf weather stations, farmers able to acquire localised weather information.
Revised: With an increase in the availability and affordability of offthe-shelf weather stations, farmers able to acquire localised weather information.

Original: However, with uncertainty in the sensor and installation quality, farmers are at risk of making poor decisions based on incorrect data.
Revised: However, with uncertainty in the sensor and installation quality, farmers are at risk of making poor decisions based on incorrect data.

Original: We present an automated approach to perform quality control on weather sensors.
Revised: We present an automated approach to perform quality control on weather sensors.

Original: Our approach uses time-series modelling and data fusion with
Revised: Our approach uses time-series modelling and data fusion with

Original: Bayesian principles to provide predictions with uncertainty quantiﬁcation.
Revised: Bayesian principles to provide predictions with uncertainty quantiﬁcation.

Original: These predictions and uncertainty are used to estimate the validity of a sensor observation.
Revised: These predictions and uncertainty are used to estimate the validity of a sensor observation.

Original: We test on tem- perature, wind, and humidity data and achieve error hit rates above 80% and false negative rates below 11%.
Revised: We test on tem- perature, wind, and humidity data and achieve error hit rates above 80% and false negative rates below 11%.

Original: Introduction
Revised: Introduction

Original: Making decisions based on weather is common practice in agriculture.
Revised: Making decisions based on weather is common practice in agriculture.

Original: Government agencies such as the Australian Bureau of Meteorology (BoM) install weather stations across
Revised: Government agencies such as the Australian Bureau of Meteorology (BoM) install weather stations across

Original: Australia to monitor weather conditions.
Revised: Australia to monitor weather conditions.

Original: The data generated from these stations can be used for forecasting extreme heat, snow, frost and heavy rainfall, which directly affect farmers.
Revised: The data generated from these stations can be used for forecasting extreme heat, snow, frost and heavy rainfall, which directly affect farmers.

Original: Long-term weather forecasts can also be used understand climatic changes and it’s affects.
Revised: Long-term weather forecasts can also be used understand climatic changes and it’s effects.

Original: While the BoM weather stations provide sufﬁcient geographical coverage for large-scale weather modelling the coverage can be insufﬁcient for localised weather modelling.
Revised: While the BoM weather stations provide sufﬁcient geographical coverage for large-scale weather modelling the coverage can be insufﬁcient for localised weather modelling.

Original: For example, temperature, rainfall, and wind can be highly localised to small geographic regions.
Revised: For example, temperature, rainfall, and wind can be highly localised to small geographic regions.

Original: Furthermore,
Revised: Furthermore,

Original: BoM weather stations are often located to provide coverage of urban regions whereas farms are typically located in remote regions.
Revised: BoM weather stations are often located to provide coverage of urban regions whereas farms are typically located in remote regions.

Original: Farmers thus often install off-the-shelf weather stations on their farms; which we refer to as Third
Revised: Farmers thus often install off-the-shelf weather stations on their farms; which we refer to as Third

Original: Party Weather Stations (TPWS).
Revised: Party Weather Stations (TPWS).

Original: Unlike BoM weather stations, TPWS data may not be quality controlled, resulting in uncertainty on the reliability and correctness of the data.
Revised: Unlike BoM weather stations, TPWS data may not be quality controlled, resulting in uncertainty on the reliability and correctness of the data.

Original: For example, low cost sensors may be inaccurate or the weather stations may be incorrectly installed.
Revised: For example, low cost sensors may be inaccurate or the weather stations may be incorrectly installed.

Original: Incorrect data may cause a farmer take unnecessary costly actions or fail to take actions leading to disastrous consequences.
Revised: Incorrect data may cause a farmer take unnecessary costly actions or fail to take actions leading to disastrous consequences.

Original: We present an automated approach to detect unusual readings from TPWS data.
Revised: We present an automated approach to detect unusual readings from TPWS data.

Original: The approach uses the Dynamic Linear Model (DLM) and the Kalman ﬁlter.
Revised: The approach uses the Dynamic Linear Model (DLM) and the Kalman ﬁlter.

Original: It performs time series analysis and data fusion using Bayesian principles to provide predictions with uncertainty quantiﬁcation.
Revised: It performs time series analysis and data fusion using Bayesian principles to provide predictions with uncertainty quantiﬁcation.

Original: A key contribution is that we provide a means to automatically calibrate model.
Revised: A key contribution is that we provide a means to automatically calibrate model.

Original: We show that this approach is robust in that the same model, parameters, and hyper-parameters are used across various weather stations and variables to provide accurate results with error hit rates above 80% and false positive rates below 11%.
Revised: We show that this approach is robust in that the same model, parameters, and hyper-parameters are used across various weather stations and variables to provide accurate results with error hit rates above 80% and false positive rates below 11%.

Original: This work is especially relevant to those who seek a solution which is computationally efﬁcient, easy to implement, and easy to maintain.
Revised: This work is especially relevant to those who seek a solution which is computationally efﬁcient, easy to implement, and easy to maintain.

Original: Related Work
Revised: Related Work

Original: Quality control for weather sensing has been an active research topic for several years (Leung, Mateo, and Nadler 2007; Hubbard et al. 2007; Mateo and Leung 2008) and a recent surge has come about in relation to the so-called “citizen” or “crowdsourced” weather stations (Beele et al.
Revised: Quality control for weather sensing has been an active research topic for several years (Leung, Mateo, and Nadler 2007; Hubbard et al. 2007; Mateo and Leung 2008) and a recent surge has come about in relation to the so-called “citizen” or “crowdsourced” weather stations (Beele et al.

Original: 2022; Meier et al.
Revised: 2022; Meier et al.

Original: ; Napoly et al.
Revised: ; Napoly et al.

Original: The common approaches are heuristic, statistical, or regression based.
Revised: The common approaches are heuristic, statistical, or regression based.

Original: Heuristic approaches include thresholds, duplicate checks, and step-change tests.
Revised: Heuristic approaches include thresholds, duplicate checks, and step-change tests.

Original: Statistical approaches compare samples to the mean and standard deviations of cyclic data and previous extrema.
Revised: Statistical approaches compare samples to the mean and standard deviations of cyclic data and previous extrema.

Original: Regression approaches compare samples to neighbouring station interpolations, previous forecasts, and daily observations.
Revised: Regression approaches compare samples to neighbouring station interpolations, previous forecasts, and daily observations.

Original: Unlike the proposed approach, none of these approaches consider sub-daily dynamics of the variables in a time-series sense.
Revised: Unlike the proposed approach, none of these approaches consider sub-daily dynamics of the variables in a time-series sense.

Original: The more recent approaches tend to take advantage of the high spatial concentration of “crowdsourced” weather stations in urban environments.
Revised: The more recent approaches tend to take advantage of the high spatial concentration of “crowdsourced” weather stations in urban environments.

Original: High concentrations are however not likely in an agricultural setting.
Revised: High concentrations are however not likely in an agricultural setting.

Original: TheDLM (also called the linear dynamic system, linear Gaussian state-space model, or Kalman ﬁlter) is known for its ability for state estimation amongst noise (Murphy 2012).
Revised: TheDLM (also called the linear dynamic system, linear Gaussian state-space model, or Kalman ﬁlter) is known for its ability for state estimation amongst noise (Murphy 2012).

Original: It is also well equipped to perform outlier detection in time-series (e.g. (Ting, Theodorou, and Schaal 2007; Zhang and Liu 2009)).
Revised: It is also well equipped to perform outlier detection in time-series (e.g. (Ting, Theodorou, and Schaal 2007; Zhang and Liu 2009)).

Original: Furthermore, Kalman ﬁlters are well-known amongst the meteorological community (usually as Ensemble Kalman ﬁlters for NWP) (Roh et al. 2013; Evensen 2009).
Revised: Furthermore, Kalman ﬁlters are well-known amongst the meteorological community (usually as Ensemble Kalman ﬁlters for NWP) (Roh et al. 2013; Evensen 2009).

Original: However, little work has been done in developing it for quality control of weather sensors.
Revised: However, little work has been done in developing it for quality control of weather sensors.

Original: Methodology
Revised: Methodology

Original: A DLM is employed to make predictions of a given weather variable over time.
Revised: A DLM is employed to make predictions of a given weather variable over time.

Original: It fuses data from a TPWS and from a Numerical Weather Prediction (NWP) product, and also models the dynamics of the data over time.
Revised: It fuses data from a TPWS and from a Numerical Weather Prediction (NWP) product, and also models the dynamics of the data over time.

Original: The Kalman ﬁlter is used to perform inference in the DLM by updating the weather variable predictions at each time given past data.
Revised: The Kalman ﬁlter is used to perform inference in the DLM by updating the weather variable predictions at each time given past data.

Original: A weather variable prediction is the form of a Gaussian distribution.
Revised: A weather variable prediction is the form of a Gaussian distribution.

Original: If a given test observation is an outlier relative to the predicted Gaussian, it is classiﬁed as a suspect sample.
Revised: If a given test observation is an outlier relative to the predicted Gaussian, it is classiﬁed as a suspect sample.

Original: The DLM is automatically calibrated using an initial set of data with length T .
Revised: The DLM is automatically calibrated using an initial set of data with length T .

Original: This calibration is based on a noise estimate of this initial dataset.
Revised: This calibration is based on a noise estimate of this initial dataset.

Original: Dynamic Linear Model
Revised: Dynamic Linear Model

Original: The DLM is a linear-Gaussian state-space model (West and
Revised: The DLM is a linear-Gaussian state-space model (West and

Original: Harrison 2006; Murphy 2012).
Revised: Harrison 2006; Murphy 2012).

Original: It comprises a latent variable h t ∈ R H × 1 and an observed variable v t ∈ R V × 1 .
Revised: It comprises a latent variable h t ∈ R H × 1 and an observed variable v t ∈ R V × 1 .

Original: In this study, h t represents modelled time-series components the particular weather variable of interest and v t represents hourly TPWS observations and NWP data.
Revised: In this study, h t represents modelled time-series components the particular weather variable of interest and v t represents hourly TPWS observations and NWP data.

Original: The state-space equations are
Revised: The state-space equations are

Original: [Equation]
Revised: [Equation]

Original: where η h and η v are zero mean Gaussian distributions with covariances Σ h ∈ R H × H and Σ v ∈ R V × V respectively.
Revised: where η h and η v are zero mean Gaussian distributions with covariances Σ h ∈ R H × H and Σ v ∈ R V × V respectively.

Original: The matrix A ∈ R H
Revised: The matrix A ∈ R H

Original: × H is the state transition matrix and
Revised: × H is the state transition matrix and

Original: B ∈ R V × H is the measurement matrix.
Revised: B ∈ R V × H is the measurement matrix.

Original: The data is assumed to comprise an offset and a diurnal  periodic component with a period of τ = 24 hours.The
Revised: The data is assumed to comprise an offset and a diurnal (daily) periodic component with a period of τ = 24 hours.

Original:  DLM models this by combining a local-level and a freeform seasonal model (West and Harrison 2006) to produce the state transition matrix
Revised: The DLM models this by combining a local-level and a freeform seasonal model (West and Harrison 2006) to produce the state transition matrix

Original: [Equation]
Revised: [Equation]

Revised: [Equation]

Revised:  (3)

Original: Given τ and the structure of A , the latent dimension is H = 24 .
Revised: Given τ and the structure of A , the latent dimension is H = 24 .

Original: The DLM naturally performs data fusion when the observed variable comprises multiple data sources measuring the same latent variable.
Revised: The DLM naturally performs data fusion when the observed variable comprises multiple data sources measuring the same latent variable.

Original: With the TPWS and NWP data
Revised: With the TPWS and NWP data

Original: V = 2 , the observed variable is v t =
Revised: V = 2 , the observed variable is v t =

Original: [ x t y
Revised: [ x t y

Original: [Equation]
Revised: [Equation]

Original: ] (cid:62) , and
Revised: ] (cid:62) , and

Original: [Equation]
Revised: [Equation]

Original:  Σ v represents the covariance of the data noise and determines how sensitive the model is to a particular data source.
Revised: (4) Σ v represents the covariance of the data noise and determines how sensitive the model is to a particular data source.

Original: With an estimate of the data noise for the TPWS and NWP data given by (cid:15) =
Revised: With an estimate of the data noise for the TPWS and NWP data given by (cid:15) =

Original: [ (cid:15) x [Equation]
Revised: [ (cid:15) x (cid:15)

Original: [Equation] , the covariance matrix is 
Revised: y ] (cid:62) , the covariance matrix is [Equation]

Original: [Equation]
Revised: [Equation]

Original: We also consider a model that excludes the NWP data.
Revised: We also consider a model that excludes the NWP data.

Original: For this, V = 1 and the second dimension is removed in v t , B , and Σ v .
Revised: For this, V = 1 and the second dimension is removed in v t , B , and Σ v .

Original: Setting the values of Σ h generally lower than Σ v assumes that the data is more uncertain than the model’s dynamics contained in (1) 1 .We thus set 
Revised: Setting the values of Σ h generally lower than Σ v assumes that the data is more uncertain than the model’s dynamics contained in (1) 1 .We thus set Σ [Equation] I [Equation]

Revised: ( (cid:15)

Original: [Equation]
Revised: [Equation]

Original: where I is the H × H identity matrix.
Revised: where I is the H × H identity matrix.

Original: Noise Estimation
Revised: Noise Estimation

Original: The data noise (cid:15) used for the DLM model is estimated by extracting it from the data using a high pass ﬁlter.
Revised: The data noise (cid:15) used for the DLM model is estimated by extracting it from the data using a high pass ﬁlter.

Original: A 3 rd order Butterworth high-pass ﬁlter is used, which provides a roll off of -18 dB/decade (Oppenheim and Schafer 2010).
Revised: A 3 rd order Butterworth high-pass ﬁlter is used, which provides a roll off of -18 dB/decade (Oppenheim and Schafer 2010).

Original: A cut-off frequency of 5 /τ is used to remove low frequency components such as the diurnal cycle.
Revised: A cut-off frequency of 5 /τ is used to remove low frequency components such as the diurnal cycle.

Original: The noise of each data stream is then represented by the standard deviation of the high-pass-ﬁltered data stream and stored in (cid:15)= [ (cid:15)
Revised: The noise of each data stream is then represented by the standard deviation of the high-pass-ﬁltered data stream and stored in (cid:15)

Original: [Equation]
Revised: [Equation]

Original: In our experiments, we found that the approach can occasionally underestimate the true noise, resulting in over conﬁdent predictions.
Revised: In our experiments, we found that the approach can occasionally underestimate the true noise, resulting in over conﬁdent predictions.

Original: A lower threshold is thus applied to the noise estimate.
Revised: A lower threshold is thus applied to the noise estimate.

Original: The lower threshold is 0.7 for the TPWS data and 1.5 times the TPWS noise for the NWP data.
Revised: The lower threshold is 0.7 for the TPWS data and 1.5 times the TPWS noise for the NWP data.

Original: A higher
Revised: A higher

Original: NWP data noise encourages the model to rely more on the
Revised: NWP data noise encourages the model to rely more on the

Original: TPWS data.
Revised: TPWS data.

Original: Kalman Filtering
Revised: Kalman Filtering

Original: The Kalman ﬁlter performs inference on the DLM by computing the posterior ﬁltered distribution p ( h t | v t − T : t ) =
Revised: The Kalman ﬁlter performs inference on the DLM by computing the posterior ﬁltered distribution p ( h t | v t − T : t ) =

Original: N ( f t , F t ) , where f t is the ﬁltered mean, F t is the ﬁltered covariance, and N is the Gaussian.
Revised: N ( f t , F t ) , where f t is the ﬁltered mean, F t is the ﬁltered covariance, and N is the Gaussian.

Original: The Kalman ﬁlter operates in a two-step prediction-update process deﬁned by the following equations:
Revised: The Kalman ﬁlter operates in a two-step prediction-update process deﬁned by the following equations:

Original: Prediction step:
Revised: Prediction step:

Original: [Equation] [Equation]
Revised: [Equation] [Equation]

Original: Update step:
Revised: Update step:

Original: [Equation] [Equation]
Revised: [Equation] [Equation]

Original: The computed f t and F t can be transformed back to the observation space to provide an estimate of the variable of interest in the form N ( µ t , σ 2 t ) using
Revised: The computed f t and F t can be transformed back to the observation space to provide an estimate of the variable of interest in the form N ( µ t , σ 2 t ) using

Original: [Equation] [Equation]
Revised: [Equation] [Equation]

Original: where
Revised: where

Original: C =
Revised: C =

Original: 0] , which is identical to the ﬁrst row of B .
Revised: 0] , which is identical to the ﬁrst row of B .

Original: [Table]
Revised: [Table]

Original: At time t = 1 , the Kalman ﬁlter update equation requires f 0 and F 0 .
Revised: At time t = 1 , the Kalman ﬁlter update equation requires f 0 and F 0 .

Original: We set F 0 = 5 Σ h and f 0 is set using a sequence of T calibration data samples.
Revised: We set F 0 = 5 Σ h and f 0 is set using a sequence of T calibration data samples.

Original: Assuming T is divisible by τ , the i th element of f 0 is set as
Revised: Assuming T is divisible by τ , the i th element of f 0 is set as

Original: [Equation]
Revised: [Equation]

Original: Evaluation
Revised: Evaluation

Original: A test sample x t can be evaluated according to the predicted distribution N ( µ t , σ 2 t ) using to the two-sided p -value p two-
Revised: A test sample x t can be evaluated according to the predicted distribution N ( µ t , σ 2 t ) using to the two-sided p -value p two-

Original: [Equation]
Revised: [Equation]

Original: where Φ is the cumulative distribution function.
Revised: where Φ is the cumulative distribution function.

Original: The test sample x t is suspect if
Revised: The test sample x t is suspect if

Original: [Equation]
Revised: [Equation]

Original: Datasets and Testing
Revised: Datasets and Testing

Original: In this study data from BoM weather stations are used as
Revised: In this study data from BoM weather stations are used as

Original: TPWS data and the BoM’s ACCESS-R (Bureau of Meteorology 2010) provides the NWP data source.
Revised: TPWS data and the BoM’s ACCESS-R (Bureau of Meteorology 2010) provides the NWP data source.

Original: We consider daily minimum temperatures, daily maximum wind gusts, and relative humidity observations at 9am and 3pm.
Revised: We consider daily minimum temperatures, daily maximum wind gusts, and relative humidity observations at 9am and 3pm.

Original: Data are gathered for ∼ 100 stations across Australia, each with at least two years of data.
Revised: Data are gathered for ∼ 100 stations across Australia, each with at least two years of data.

Original: See Table 1.
Revised: See Table 1.

Original: The ACCESS-R data are only available for temperature, and thus the DLM for wind gusts and relative humidity considers the TPWS data streams only.
Revised: The ACCESS-R data are only available for temperature, and thus the DLM for wind gusts and relative humidity considers the TPWS data streams only.

Original: To test the approach, synthetic datasets are created where data samples are randomly perturbed.
Revised: To test the approach, synthetic datasets are created where data samples are randomly perturbed.

Original: A total of 2.7% of minimum temperatures perturbed with uniform distributions
Revised: A total of 2.7% of minimum temperatures perturbed with uniform distributions

Original: U ( − 6 ◦ C, − 2 ◦ C ) or U (2 ◦ C, 6 ◦ C ) .
Revised: U ( − 6 ◦ C, − 2 ◦ C ) or U (2 ◦ C, 6 ◦ C ) .

Original: Similarly, a total of 10% of maximum wind gusts perturbed with U (5 m/s, 14 . 6 m/s ) .
Revised: Similarly, a total of 10% of maximum wind gusts perturbed with U (5 m/s, 14 . 6 m/s ) .

Original: Directly perturbing relative humidity can violate the relative humidity range of [0%, 100%].
Revised: Directly perturbing relative humidity can violate the relative humidity range of [0%, 100%].

Original: Thus, the dew point temperature is perturbed with U ( − 10 ◦ C, − 4 ◦ C ) or
Revised: Thus, the dew point temperature is perturbed with U ( − 10 ◦ C, − 4 ◦ C ) or

Original: U (4 ◦ C, 10 ◦ C ) and translated to relative humidity according to (Bureau of Meteorology 2009):
Revised: U (4 ◦ C, 10 ◦ C ) and translated to relative humidity according to (Bureau of Meteorology 2009):

Original: [Equation]
Revised: [Equation]

Original: Here T d is the dew point temperature and
Revised: Here T d is the dew point temperature and

Original: T a is the dry bulb temperature.
Revised: T a is the dry bulb temperature.

Original: Similarly, the DLM is also applied to dew point temperature and the results are converted to relative humidity via (19).
Revised: Similarly, the DLM is also applied to dew point temperature and the results are converted to relative humidity via (19).

Original: [Table]
Revised: [Table]

Original: [Figure]
Revised: [Figure]

Original: During testing, the DLM is applied to the perturbed hourly data-streams for each TPWS and each weather variable.
Revised: During testing, the DLM is applied to the perturbed hourly data-streams for each TPWS and each weather variable.

Original: The perturbed test samples are compared with their corresponding DLM predictions and classiﬁed as valid or suspect according to (18).
Revised: The perturbed test samples are compared with their corresponding DLM predictions and classiﬁed as valid or suspect according to (18).

Original: The hit rate (number of true positives over the total number of positive cases) and false positive rate (number of false positives over the total number of negative cases) are computed from the classiﬁcations.
Revised: The hit rate (number of true positives over the total number of positive cases) and false positive rate (number of false positives over the total number of negative cases) are computed from the classiﬁcations.

Original: Results
Revised: Results

Original: The average hit rate, false positive rate, and accuracy for the various datasets are presented in Table 2.
Revised: The average hit rate, false positive rate, and accuracy for the various datasets are presented in Table 2.

Original: The high hit rates indicate that the model is able to detect the majority of the perturbed samples.
Revised: The high hit rates indicate that the model is able to detect the majority of the perturbed samples.

Original: The low false positive rates indicate a low probability of incorrectly classifying a valid sample as a suspect.
Revised: The low false positive rates indicate a low probability of incorrectly classifying a valid sample as a suspect.

Original: A plot of a true detection for temperature is illustrated in the top panel of Fig.
Revised: A plot of a true detection for temperature is illustrated in the top panel of Fig.

Original: The perturbed value is not signiﬁcantly lower than the predicted minimum, however it is still detected.
Revised: The perturbed value is not signiﬁcantly lower than the predicted minimum, however it is still detected.

Original: This particular TPWS provides a relatively smooth diurnal cycle and this has detected through the noise estimation.
Revised: This particular TPWS provides a relatively smooth diurnal cycle and this has detected through the noise estimation.

Original: As such, the DLM is conﬁdent in the data and produces a low variance in its predictions.
Revised: As such, the DLM is conﬁdent in the data and produces a low variance in its predictions.

Original: Small perturbations are thus able to be detected.
Revised: Small perturbations are thus able to be detected.

Original: Not all TPWS produce smooth diurnal cycles.
Revised: Not all TPWS produce smooth diurnal cycles.

Original: In general, the approach can fail when there is (1) a signiﬁcant difference between the TPWS and the NWP data, (2) a lack of a diurnal cycle, or (3) a severe non-linear change in the dynamics.
Revised: In general, the approach can fail when there is (1) a signiﬁcant difference between the TPWS and the NWP data, (2) a lack of a diurnal cycle, or (3) a severe non-linear change in the dynamics.

Original: Examples of this are illustrated in Fig.
Revised: Examples of this are illustrated in Fig.

Original: In the top panel the NWP data differs from the TPWS observations and there is also a poor diurnal cycle in the data.
Revised: In the top panel the NWP data differs from the TPWS observations and there is also a poor diurnal cycle in the data.

Original: The result is
Revised: The result is

Original: [Figure]
Revised: [Figure]

Original: that a high noise level is estimated and the model predictions are associated with high variance.
Revised: that a high noise level is estimated and the model predictions are associated with high variance.

Original: The model is thus desensitized to noise, reducing its ability to detect the perturbations.
Revised: The model is thus desensitized to noise, reducing its ability to detect the perturbations.

Original: In the bottom panel of Fig. 2, the NWP underestimates the minimum temperatures and the TPWS data contain non-linear changes in the dynamics, resulting in false positive detections.
Revised: In the bottom panel of Fig. 2, the NWP underestimates the minimum temperatures and the TPWS data contain non-linear changes in the dynamics, resulting in false positive detections.

Original: Plots of true and false detections for relative humidity and wind gust are presented in the middle and bottom panels of
Revised: Plots of true and false detections for relative humidity and wind gust are presented in the middle and bottom panels of

Original: Fig.
Revised: Fig.

Original: 1 respectively.
Revised: 1 respectively.

Original: These variables generally do not have as strong diurnal cycles as temperature and the data has a higher noise levels.
Revised: These variables generally do not have as strong diurnal cycles as temperature and the data has a higher noise levels.

Original: The DLM however generally performs better on these datasets.
Revised: The DLM however generally performs better on these datasets.

Original: This is mostly due to the model not using the NWP data.
Revised: This is mostly due to the model not using the NWP data.

Original: Using NWP data assists with identifying errors such as biases, but it can also have a negative affect when its predictions are not accurate.
Revised: Using NWP data assists with identifying errors such as biases, but it can also have a negative affect when its predictions are not accurate.

Original: This usually occurs when the NWP is a low resolution prediction and is not designed to predict highly localised weather affects.
Revised: This usually occurs when the NWP is a low resolution prediction and is not designed to predict highly localised weather affects.

Original: Selecting an accurate and high resolution NWP model is crucial.
Revised: Selecting an accurate and high resolution NWP model is crucial.

Original: Conclusion
Revised: Conclusion

Original: We present an approach to detect unusual readings from
Revised: We present an approach to detect unusual readings from

Original: Third-Party Weather Station data and test it on daily minimum temperature, maximum wind gust, and relative humidity.
Revised: Third-Party Weather Station data and test it on daily minimum temperature, maximum wind gust, and relative humidity.

Original: We show that the model is robust in that the same model parameters function over a range of weather stations and weather variables.
Revised: We show that the model is robust in that the same model parameters function over a range of weather stations and weather variables.

Original: Our approach involves Kalman ﬁltering and an initial model calibration via noise estimation.
Revised: Our approach involves Kalman ﬁltering and an initial model calibration via noise estimation.

Original: The approach is simple to implement and maintain, making it well suited to production environments.
Revised: The approach is simple to implement and maintain, making it well suited to production environments.

Original: Finally, given that the approach is a time-series based approach, we believe that it will complement the common statistical and heuristic approaches typically used for weather data quality control.
Revised: Given that the approach is a timeseries based approach, we believe that it will complement the common statistical and heuristic approaches typically used for weather data quality control.

Revised: In future work the approach could be tested on TPWS installed in remote regions.

Original: Acknowledgement
Revised: Acknowledgement

Original: We thank the BoM for their assistance in providing the data (including the perturbed data) and for the many discussions on quality control.
Revised: We thank the BoM for their assistance in providing the data (including the perturbed data) and for the many discussions on quality control.