Exploring causal factors of coastal chlorophyll-a dynamics and their potential contributions to near future forecasting

(≤ 250 words) 18 Harmful algal blooms have been causing significant damage worldwide, and Hong Kong is 19 no exception. To understand the drivers of algal bloom formation and forecast the dynamics 20 of chlorophyll-a (Chl-a), a proxy for algal abundance, in Hong Kong waters, this study 21 utilized nonlinear time series analysis, called empirical dynamic modeling (EDM), to 22 investigate Chl-a dynamics using in situ measurements and remote sensing data. We first 23 conducted causality tests of EDM to identify environmental factors influencing Chl-a at 24 different sites. As for the in situ measurement data, salinity was the strongest causal factor 25 among environmental factors. However, inputting the causal factors into the forecasting 26 model did not greatly improve the forecasting performance for Chl-a, suggesting that factors 27 not included in the current dataset, such as wind direction and current speed, may play a more 28 critical role in Chl-a dynamics. As for the remote sensing data, sea surface temperature (SST) 29 showed significant causal effect on Chl-a at most sites and the multivariate forecasting model 30 including Chl-a and SST outperformed the univariate model at most sites. This study is the 31 first to employ EDM to investigate Chl-a dynamics in Hong Kong waters, showcasing its 32 potential to identify causal factors and improve forecasting accuracy. The findings provide 33 scientific insights into Chl-a dynamics and water quality monitoring and modeling in a 34 coastal region. 35 36

(3–10 words): Causality test; Chlorophyll-a dynamics; Empirical dynamic 37 modeling; Hong Kong waters; Time series analysis; Water quality monitoring 38 39 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 3 1. Introduction 40 Harmful algal blooms (HABs), commonly known as “red tides,” refer to the discoloration of 41 coastal waters caused by the rapid growth and accumulation of harmful microscopic algae 42 (phytoplankton) (Zohdi & Abbaspour, 2019). These blooms can produce toxins triggering 43 foodborne illnesses, such as amnesic shellfish poisoning and ciguatera fish poisoning (Lopes 44 et al., 2019; Pradhan et al., 2022; Wang, 2008). Zooplankton, filter-feeding shellfish and 45 herbivorous fish consume these phytoplankton, acting as mediators for toxin transfer within 46 the food web, ultimately affecting humans. Even non-toxic blooms can indirectly harm 47 marine life by depleting oxygen during decomposition (Flewelling et al., 2005). Due to the 48 great impact on public health concerns, the seafood industry and tourism, the economic loss 49 is considerable. In Florida, for instance, red tides have been observed since the 1840s and the 50 annual losses reach millions of dollars (Kirkpatrick et al., 2004). To prevent such damage 51 caused by HABs in coastal ecosystems, it is essential to understand the mechanism and 52 predict the outbreaks of red tides. 53 The concentration of chlorophyll-a (Chl-a) is a common proxy for assessing 54 phytoplankton abundance. Thus, identifying the drivers of Chl-a dynamics contributes not 55 only to developing effective HAB monitoring plans but also to predicting HAB dynamics. 56 Previous attempts to identify drivers of the dynamics of Chl-a or phytoplankton community 57 composition mainly relied on correlation-based methods, for example, linear regressions, 58 Canonical-Correlation Analysis (CCA), and Redundancy Analysis (RDA) (Deconinck et al., 59 2025; Li et al., 2023; Yin, 2003). These methods assume that environmental variables are 60 independent and the effects of such variables are separable from each other, which are 61 features of linear systems. However, the effectiveness of these methods could be limited 62 when studying nonlinear systems such as marine ecosystems, where variables are 63 interdependent upon each other (Glaser et al., 2014). Moreover, correlation may misidentify 64 causal variables, as “correlation does not imply causation” (Berkeley, 1988). That is, 65 correlation can occur without causation, and causation may also occur in the absence of 66 correlation. 67 As an alternative non-parametric method, Empirical Dynamic Modeling (EDM) was 68 developed to analyze complex dynamics found in natural ecosystems (Anderson et al., 2021; 69 Glaser et al., 2014; Sugihara et al., 2012; Sugihara & May, 1990). Instead of deriving 70 equations to describe how the variables are related or how the system evolves, EDM 71 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 4 delineates a “trajectory” of the system evolution in a high-dimensional state space (i.e., a 72 manifold) (for example, see figures in Ye et al., 2015). EDM was originally developed to 73 make near-future forecasts for deterministic complex systems in the state space built by 74 lagged time series of a single variable (Sugihara & May, 1990). Eventually, several tools of 75 EDM were developed to analyze the relationships among multiple variables within the same 76 system (in HAB studies, it would be time series of Chl-a and environmental factors), enabling 77 detection of causalities among variables (Sugihara et al., 2012) and quantification of 78 interaction strengths (Deyle et al., 2016), and EDM tools have been applied to various 79 ecological time series to understand and forecast ecosystem dynamics (Deyle et al., 2022; 80 Tsai et al., 2024; Ushio, 2022; Ushio et al., 2018). 81 Hong Kong is a coastal city with a long historical record of HABs. Located to the east of 82 the Pearl River Estuary (PRE) and to the north of the South China Sea (Fig.1a), Hong Kong 83 is affected by fresh water and sea water at the same time (Wong et al., 2007). As a result, 84 there are significant spatial and seasonal variations in water circulation, stratification, salinity, 85 temperature, and nutrient levels there. In this study, we aim to detect causal factors of Chl-a 86 dynamics in Hong Kong waters and improve the near-future forecasting performance using 87 EDM tools. Our work is built on the long-term in situ observation of Chl-a and environmental 88 factors in 76 sites (Fig.1a) conducted by the Environmental Protection Department (EPD) of 89 the Hong Kong government. Additionally, remote sensing measurements collected by sensors 90 such as Sea-Viewing Wide Field-of-View Sensor (SeaWiFS) and Moderate Resolution 91 Imaging Spectroradiometers (MODIS) provide great support for monitoring Chl-a and other 92 parameters with high coverage and fine spatial resolution (Chen et al., 2013). In Hong Kong, 93 MODIS data at 4-kilometer resolution include 176 sites in total, of which 101 are located on 94 the water area (Fig.1b). The spatial resolution of remote sensing data is also fine, allowing for 95 daily or weekly observations. However, frequent occurrence of missing data in daily or finer 96 temporal resolution data complicates the understanding of spatiotemporal variations (Zhang 97 et al., 2025). Monthly-averaged data may mitigate the effect of missing data, but the 98 reliability of remote sensing data in coastal regions such as Hong Kong waters—where 99 particle suspension significantly impacts remote sensing images—has not been thoroughly 100 investigated for Chl-a monitoring, although the monthly remote sensing data is generally well 101 correlated with the in situ measurement data (Fig. 1c). Comparing the in situ measurement 102 data and remote sensing data would give us an opportunity to test the reliability of the remote 103 sensing data for Chl-a monitoring in coastal regions. 104 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 5 Here, using an in situ measurement dataset collected by EPD and remote sensing dataset 105 collected by MODIS, we apply two tools of EDM, unified information-theoretic causality 106 (UIC) (Osada et al., 2023) to detect causal environmental factors, and Multiview-distance 107 regularized S-map (MDR S-map) (Chang et al., 2021) to quantify interaction strengths of the 108 causal factors, and forecast dynamics of Chl-a in Hong Kong waters. In this study, we first 109 identified causal variables using UIC and quantified the causal effects using MDR S-map. 110 Then, we conducted near-future forecast of Chl-a dynamics in Hong Kong waters using the 111 time series of Chl-a and causal variables. For in situ measurement data, salinity showed the 112 strongest causal effect on Chl-a compared to other environmental factors. However, inputting 113 causal variables into the forecast model (i.e., multi-variable model) did not greatly improve 114 the performance compared to the Chl-a only model (i.e., single-variable model). For remote 115 sensing data, sea surface temperature (SST) showed a significant causal effect on Chl-a at 116 most of the sites and inputting SST improved the performance of the forecast model 117 compared to univariate model using Chl-a only. Lastly, we compared the results of the in situ 118 monitoring data and the remote sensing data and discuss the reliability of the remote sensing 119 data for Chl-a monitoring in Hong Kong waters. This study is the first to quantify the causal 120 effect of environmental factors on Chl-a dynamics in Hong Kong coastal waters using EDM, 121 providing perspectives for real-world environmental monitoring, management, and 122 forecasting. 123 124 125 126 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 6 127 Figure 1 Study sites of (a) in situ measurements conducted by EPD and (b) remote sensing collected by MODIS, represented by black points. In (a), there are ten water control zones declared by EPD, namely ①Tolo Harbour and Channel, ②Southern, ③Port Shelter, ④Junk Bay, ⑤Deep Bay, ⑥Mirs Bay, ⑦North Western, ⑧Western, ⑨Eastern and ⑩Victoria Harbour (https://cd.epic.epd.gov.hk/EPICRIVER/marine/?lang=en). (c) Comparison of Chl-a concentration (mg m-3) in the southern Hong Kong waters. The red line indicates data from a monitoring site of in situ measurement data, and the dashed line indicates remote sensing data from a monitoring site close to the in situ measurement site. Their locations are 22.1917˚N, 114.0790˚E and 22.18750˚N, 114.1042˚E. Remote sensing data shows a similar trend with the in situ monitoring data. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 7 2. Materials and methods 128 2.1 In situ measurement data 129 Monthly time series of Chl-a and environmental factors, including temperature, salinity, pH, 130 turbidity, total nitrogen (TN), and total phosphorus (TP) and silica (as SiO2), were collected 131 by Environmental Protection Department (EPD) in 76 sites in Hong Kong waters. Data were 132 downloaded from the EPD website (https://www.epd.gov.hk/epd/english/top.html) as of 2024 133 January. Each time series started from 2002 August and continued until 2022 July, containing 134 240 time points in each site. Sampling was carried out onboard a scientific vessel once a 135 month and samples were collected at 1 m below the sea surface. According to EPD, 136 temperature, salinity, pH, and turbidity were measured on site by CTD profiler (SEACAT19+ 137 Conductivity Temperature Depth, Sea-Bird Scientific, US). Chl-a, TN (the sum of Kjeldahl 138 nitrogen, nitrite nitrogen, and nitrate nitrogen), TP and silica were measured in the laboratory 139 as described in Annual Marine Water Quality Reports of EPD 140 (https://www.epd.gov.hk/epd/sites/default/files/epd/english/environmentinhk/water/hkwqrc/fi141 les/waterquality/annual-report/marinereport2024.pdf). N/P ratio was defined as TN divided 142 by TP. 143 144 2.2 Remote sensing data 145 Remote sensing data of Chl-a and sea surface temperature (SST) were derived from MODIS 146 (Moderate Resolution Imaging Spectroradiometer) onboard the Aqua satellite platform of 147 NASA (National Aeronautics and Space Administration). Data were downloaded from the 148 official website of NASA Ocean Color (https://oceancolor.gsfc.nasa.gov/) as of 2024 January. 149 Data used were monthly Level 3 data at resolution of 4 km. There were 176 sites in total 150 extracted between latitude 22.13°N and 22.58°N, longitude 113.82°E and 114.52°E, among 151 which 101 marine sites had been selected. Each time series started in August 2002 and 152 continued until July 2022, consisting of 240 time points for each site. Missing values of Chl-a 153 concentration were replaced with 0 because missing values usually indicate that the Chl-a 154 concentration was too low. 155 156 2.3 Unified information-theoretic causality (UIC) 157 To detect causal effects of environmental factors on Chl-a, unified information-theoretic 158 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 8 causality (UIC) was applied (Osada et al., 2023). UIC is a time series-based, nonparametric 159 causality test, which incorporates the advantages of both convergent cross-mapping (CCM; 160 Sugihara et al., 2012), a causality test in EDM, and transfer entropy (TE; Schreiber, 2000), an 161 information-theory based causality test. Here, TE from process y to process x, 𝑇𝐸!→#, 162 assesses how much uncertainty in predicting future value of y is reduced, given knowledge of 163 past values of x. This shares a similar idea with CCM, which regards y as a causal effect of x 164 if the neighborhood relationship of time series x is able to predict time series y by nearest 165 neighbor regression in the time-delay embedding. UIC quantifies information flow between 166 variables in format of TE determined by conditional probability (we call this measure TE, but 167 the mathematical definition of 𝑇𝐸!→# is different from that of Schreiber; see Osada et al. 168 2021 for details), which would be comparison of model performance of cross mapping in this 169 case: 170 𝑇𝐸!→# = 1 𝑁 ' log + 𝑝-𝑦$%$&|𝑥$, 𝑥$'( , … , 𝑥$'(*'+)( , 𝑧$4 𝑝-𝑦$%$&|𝑥$'( , 𝑥$'-( , … , 𝑥$'(*'+)( , 𝑧$45 . $/+ , 171 where x, y, and z are a potential effect variable, causal variable, and conditional variable (if 172 available), respectively. In our case, x, y, and z could be Chl-a, environmental factors, and the 173 other potential causal factors, respectively. 𝑝(𝐴|𝐵) describes conditional probability: the 174 probability of A given B. N is the length of the library (i.e., number of the vectors in the state 175 space) and E is and the optimal embedding dimension when conducting one-step forward 176 forecast in the state space. t, tp, and τ are the time point, time lag between effect variable and 177 causal variable, and time lag of the time series, respectively. To identify the delayed effect of 178 environmental factors on Chl-a, five time-lags, i.e., tp = 0, –1, –2, –3, and –4, were tested. 179 These lags suggest that the causal effects occur within the same month, one, two, three, or 180 four months earlier, respectively. For example, when the optimal embedding dimension is 181 five, there is one causal environmental variable, and tp = 0, the state vector is represented by 182 the information of an environmental factor of the current month (unlagged), one month ago, 183 two months ago, three months ago, and four months ago, which are used to predict the 184 current state of Chl-a (the numerator in the above equation, which is equivalent to “cross-185 mapping” in CCM, but is adjusted by the denominator in UIC). 186 To avoid misidentification of causality caused by seasonality (i.e., synchronized 187 dynamics), a seasonal surrogate test was carried out. For each Chl-a time series, 1000 188 surrogate time series were generated by computing a seasonal trend (= yearly trend) and 189 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 9 shuffling the residuals. If TE from an environmental factor to the original Chl-a time series 190 exceeds TE of over 950 surrogate time series, the environmental factor is regarded as having 191 a significant causal effect on Chl-a (i.e., p < 0.05). 192 For EPD data, causal effects of temperature, salinity, pH, turbidity, N/P ratio, and silica 193 on Chl-a were examined. For MODIS data, causal effects of SST on Chl-a were examined 194 due to the limitation of the availability of environmental variables. To ensure that all variables 195 with different units have the same level of magnitude for comparison and to avoid 196 reconstructing a distorted state space, the time series of all variables were normalized to have 197 a mean of 0 and a standard deviation of 1. This data preprocessing approach differed from 198 that used for our MDR S-map, where the first-differenced time series were normalized (see 199 the following section). Using the first-differenced and normalized time series for UIC showed 200 qualitatively the same results (see Tables S1–S4), but we show the UIC results of the 201 normalized time series in the main text and figures because the interpretation is more 202 straightforward. The computation was conducted using the package “rUIC” (version 0.9.13) 203 (Osada & Ushio, 2021) of R. 204 205 2.4 Multiview-distance regularized S-map (MDR S-map) 206 To conduct the near-future forecast of Chl-a dynamics, Multiview-distance regularized 207 S-map (MDR S-map; Chang et al., 2021) was applied. We analyzed the first-differenced and 208 normalized time series to maximize the forecasting accuracy of Chl-a dynamics and to 209 mitigate issues arising from temporal autocorrelation. Before conducting MDR S-map, time 210 series of Chl-a were taken first differenced and normalized and UIC was again conducted to 211 detect causal environmental factors on the differenced Chl-a at each site (Tables S1–S4). 212 Here, a significance test was conducted by a random-shuffled surrogate method (1000 213 surrogate time series were used to calculate the significance), as the first-differenced time 214 series did not show a clear seasonality. Only sites with significant causal environmental 215 factors were selected for further MDR S-map analysis. 216 MDR S-map links two existing EDM methods, multiview embedding (Ye & Sugihara, 217 2016) and regularized S-map (Cenci et al., 2019), which has been proposed to reconstruct 218 large interaction networks when the number of causal variables exceeds the optimal 219 embedding dimension (Chang et al., 2021). The first step of MDR S-map is to determine 220 “multiview distance” describing the “true” neighboring relationship in a high-dimensional 221 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 10 state space by ensembling various distances measured in numerous low-dimensional state 222 spaces at the optimal embedding dimension (Ye & Sugihara, 2016). Euclidean distance 223 between every pair of the vectors in the low-dimensional state space, which should be 224 reasonably reliable, is calculated. This procedure is repeated for numerous low-dimensional 225 state spaces, and “ensembled” Euclidean distances among the vectors are calculated by 226 calculating the weighted average among all these distances (the weight is based on the 227 forecast performance of each embedding). The ensembled distance is a good approximation 228 of the “true” distance in the high-dimensional system state. 229 The second step of MDR S-map is to construct a local linear model, Sequential locally 230 weighted global linear map (S-map, a fundamental tool of EDM; Sugihara, 1994), to fit the 231 time series and make a near-future forecast by including the causal effect from multiple 232 variables, 233 𝑦:(𝑡∗ + 𝑡𝑝) = 𝐶1 + 𝐶>+𝑌+(𝑡∗) + 𝐶>-𝑌-(𝑡∗) … + 𝐶>* 𝑌* (𝑡∗), 234 where t*, E, and tp represent the target time point, the embedding dimension, and forecasting 235 time step, respectively. 𝑦:, Yj, and C0 represent the predicted value of y, jth element of the 236 embedded time series (e.g., lagged Chl-a time series, environmental variables, and so on), 237 and the intercept of the local linear model, respectively. -𝐶>+, 𝐶>-, … , 𝐶>* 4 are local linear 238 coefficients. Such Jacobians of the locally approximated linear functions could be defined as 239 the causal effect (or interaction strength). To avoid an overfitting problem when dimension 240 (the number of variables in the linear model) is larger than the time series length, we used 241 regularization (e.g., ridge, lasso, or elastic-net; Cenci et al., 2019) to estimate the coefficients 242 for each time point, 𝐶> = (𝐶>+, 𝐶>-, … , 𝐶>* ), as follows: 243 𝐶> = 𝑎𝑟𝑔 𝑚𝑖𝑛2 FG√𝑾 (𝑌(𝑡 + 𝑡𝑝) − 𝒀(𝑡)𝐶)G- - + 𝜆[𝛼‖𝐶‖- - + (1 − 𝛼)‖𝐶‖+]Q , 244 where C represents local linear coefficients to be solved, λ is the penalized factor set to be 245 selected from 0, 0.001, 0.01, 0.1, 0.5, 1, and 2. α is the adjusted parameter set to be 0, 246 balancing the regularization using L1 (||.||1) or L2 (||.||2) norm of the parameter vector, which 247 means we used the ridge regression. t is the time point, and 𝑾 is the local weight matrix 248 based on the multiview distances. 𝒀(𝑡) = (𝑌+(𝑡), 𝑌-(𝑡), … , 𝑌* (𝑡)) is a N × E data matrix (N 249 is the number of time points and E is the number of nodes, i.e., optical dimension) collecting 250 the time series of all network nodes, and 𝑌(𝑡 + 𝑡𝑝) = (𝑦(𝑡+ + 𝑡𝑝), 𝑦(𝑡- + 𝑡𝑝), … , 𝑦(𝑁 +251 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 11 𝑡𝑝) )3 is N × 1 vector representing p-step forward time series data. The solution of the 252 equation depends on parameters λ and α. All combinations of the parameter values are tested 253 (i.e., grid search) and the best one for each site is determined by normalized mean square 254 error (NMSE) for one-step forward forecast. 255 In practice, univariate models are defined as models with only Chl-a time series (and its 256 time-lagged values). Under this circumstance, the state space is built by Chl-a and its lagged 257 values. Multivariate models are defined as models with Chl-a and environmental factors (and 258 their time-lagged values). For in situ measurement data, multivariate models tested included 259 Chl-a and temperature (“Chl-a + Temp”), Chl-a and salinity (“Chl-a + Sal”), Chl-a and pH 260 (“Chl-a + pH”), Chl-a and turbidity (“Chl-a + Turb”), Chl-a and N/P ratio (“Chl-a + N/P”), 261 and Chl-a and silica (“Chl-a + Sil”). For remote sensing data, the multivariate model tested 262 was built by Chl-a and sea surface temperature (“Chl-a + SST”). Then, the model 263 performance would be evaluated by NMSE. The time series of all variables were normalized 264 to have a mean of 0 and a standard deviation of 1. The computation was conducted using the 265 package “macam” (version 0.1.10) (Ushio, 2025) of R. 266 267 2.5 Data and code availability 268 All data used in this study was downloaded from public databases. All scripts and formatted 269 data used in this study are available on Github 270 (https://github.com/sxhuang00/causality_forecast_chl). 271 272 3. Results 273 3.1 Causal effects of temperature on Chl-a for in situ measurement and 274 remote sensing data 275 For in situ measurement data, several sites in Victoria Harbor showed significant and strong 276 causal effects of water temperature on the Chl-a dynamics (Fig. 2a; p < 0.05). Some specific 277 sites in western, southern, and eastern regions and Tolo Harbor also showed significant causal 278 effects of temperature. For remote sensing data, sea surface temperature (SST) exerted 279 significant and common causal effects on Chl-a dynamics in many monitoring sites (Fig. 2b; 280 p < 0.05). Some sites in the south and the east that are far from land showed stronger 281 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 12 causality of temperature on Chl-a. 282 283 284 3.2 Causal effects of salinity, pH, turbidity, and nutrients on Chl-a for in situ 285 measurement data 286 We examined the causal effects of other environmental factors for in situ measurement data 287 only, as such data was not available for the remote sensing data. The strengths of the causal 288 effects are summarized in Fig. 3a and the spatial patterns of the causal effects of the 289 environmental factors are shown in Fig. 3b-f. 290 First, we found that salinity causally influenced the Chl-a dynamics in most monitoring 291 sites in the southern regions and Victoria Harbor (Fig. 3b; p < 0.05). The causal effects, 292 measured by TE, of salinity were generally stronger than those of the other environmental 293 factors (average TE = 0.14 for salinity and average TE were 0.09, 0.05, 0.04, 0.07, and 0.05 294 for temperature, pH, turbidity, N/P ratio, and silica respectively; Fig. 3a). The causal effects 295 of pH were predominantly found in the monitoring sites that were close to shorelines and 296 were located far from oligotrophic regions, such as Mirs Bay in the eastern region (Fig. 3c; p 297 < 0.05); however, the causal effects of pH were generally weak (Fig. 3a). The causal effects 298 Figure 2. The spatial pattern of causal effect of seawater temperature on Chl-a for (a) in situ measurement data (EPD) and (b) remote sensing data (MODIS). Open circles indicate that the causal effect is not significant and filled circles indicate that the causal effect is significant. The circle size indicates the significance of the causal effect with a larger size representing a more significant effect. The circle color indicates the strength of the causal effect (transfer entropy; TE) with lighter color representing a stronger effect of temperature on the Chl-a dynamics. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 13 of turbidity were also generally weak but particularly strong in Deep Bay (Fig. 3d; p < 0.05). 299 Causal effects of the N/P ratio were common, especially in Tolo Harbor and Mirs Bay (Fig. 300 3e; p < 0.05). The causal effects of silica showed a similar spatial pattern to those of salinity, 301 particularly in Victoria Harbor and the southern region, but the effect strength was much 302 weaker than that of salinity (Fig. 3f; p < 0.05). 303 304 3.3 Forecasting Chl-a dynamics with univariate and multivariate models 305 using in situ measurement data 306 Using the first-differenced Chl-a time series, we tried to maximize the forecasting accuracy 307 of Chl-a dynamics using MDR S-map. For in situ measurement data, multivariate MDR S-308 map models with different combinations of embedding variables showed similar forecast 309 Figure 3. (a) The strength of significant causal effects (transfer entropy, TE) of environmental factors on Chl-a and the spatial pattern of causal effects of environmental factors on chlorophyll-a for in situ measurement data: (b) Salinity, (c) pH, (d) Turbidity, (e) N/P ration and (f) silica. Open circle indicates that the causal effect is not significant and filled circle indicates that the causal effect (TE) is significant. The circle size indicates the significance of the causal effect with the larger size representing a more significant effect. The circle color indicates the strength of the causal effect with lighter color representing a stronger effect of temperature on the chlorophyll dynamics. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 14 performance to the univariate model (Fig. 4). Mean NMSEs of “Chl-a”, “Chl-a + Temp”, 310 “Chl-a + Sal”, “Chl-a + pH”, “Chl-a + Tur”, “Chl-a + N/P”, and “Chl-a + Sil” were 0.660, 311 0.663, 0.666, 0.708, 0.656, 0.708, and 0.690, respectively. Although some sites showed better 312 forecast performance using the multivariate model than using the univariate model, the 313 improvement in the forecast performance when including causal environmental factors was 314 limited. 315 316 3.4 Forecasting Chl-a dynamics with univariate and multivariate models 317 using remote sensing data 318 As for remote sensing data, we analyzed sites showing significant causal effect of SST on 319 differenced Chl-a, and most of them exhibited better forecast performance with the 320 multivariate S-map model than with the univariate S-map (Fig. 5). The mean NMSE of the 321 univariate and multivariate model were 0.632 and 0.574, respectively. Importantly, compared 322 to the univariate model, the multivariate model was better at predicting the high peaks (i.e., 323 Chl-a concentration increases to a high level during algal bloom) and low peaks (i.e., Chl-a 324 concentration decreases to a low level after algal bloom) of Chl-a dynamics without delay or 325 Figure 4. Forecast performance of different MDR S-map models using in situ measurement data. The first column indicates the univariate model with differenced Chl-a time series input only. The other columns indicate different combinations of multivariate models with time series of Chl-a and lagged environmental factors input. Each point indicates a monitoring site. Note that the univariate model includes all in situ sites, while multivariate models only include sites showing significant causal effect of specific environmental factors on differenced Chl-a, and thus, the number of points for the multivariate models is smaller than that for the univariate model. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 15 lead (e.g., see Fig. 6). 326 327 328 Figure 5. Comparison of forecast performance of different MDR S-map models using remote sensing measurement data. (a) Jitter plot of NMSE of univariate model (with Chl-a time series input only) and multivariate model (with time series of Chl-a and lagged SST input. Note that only the sites with significant causal effect of SST on differenced Chl-a are shown). (b) Scatterplot of NMSE of univariate model and multivariate model. The solid line indicates the 1:1 line. Points below the 1:1 line indicate the NMSE of multivariate model is smaller than that of univariate model and these sites have better forecast performance using multivariate model. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 16 329 330 4. Discussion 331 In this study, we performed two statistical analyses to gain deeper insights into Chl-a 332 dynamics in Hong Kong waters using Empirical Dynamic Modeling (EDM) tools: (1) 333 identifying causal factors influencing Chl-a dynamics and (2) improving the forecasting 334 accuracy of Chl-a dynamics by incorporating these causal factors. Also, we used two datasets, 335 in situ measurements and remote sensing data, to briefly assess the reliability of remote 336 sensing data in a coastal region characterized by highly dynamic nature and high turbidity, 337 which often interfere with data accuracy. 338 339 4.1 Causal effects of temperature on Chl-a for in situ measurement and 340 remote sensing data 341 First, we found that a causal effect of temperature on Chl-a occurs in some inner corners of 342 semi-closed bays, for example, Deep Bay, Mirs Bay and Tolo Harbor derived from in situ 343 Figure 6. An example of predictions of multivariate model and univariate model of scaled 1st differenced Chl-a concentration time series with NMSE of 0.411 and 0.580, respectively. The original time series belongs to a site located at Port Shelter (22.31250°N, 114.3125°E). To clearly present the data, only the first 100 time points of the time series are displayed here. .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 17 measurement data. Temperature dynamics might reflect the occurrences of downwelling 344 inducing weak exchange between these water bodies and open water and long residence time 345 of the bay water (Harrison et al., 2008). Under such circumstances, these water bodies could 346 be considered as an incubator allowing sufficient time for phytoplankton to respond to local 347 nutrient inputs and change the dynamics of Chl-a. Additionally, we found that the strength 348 and spatial patterns of the causal effects of temperature on the Chl-a dynamics were different 349 between in situ measurement and remote sensing data (Fig. 2). This discrepancy might be 350 because in situ measurement and remote sensing monthly data were collected in different 351 ways. EPD conducted monitoring at irregular intervals, collecting data on different dates in 352 each month. In our analysis, this in situ data with irregular intervals was regarded as “regular 353 interval data,” where each data point represents one month. In contrast, monthly remote 354 sensing data was created by averaging daily measurements, potentially providing a more 355 accurate representation of monthly conditions. Thus, while the accuracy of temperature 356 measurement should be higher in the in situ data, the constant monitoring intervals of the 357 remote sensing data would be better suited for assessing the impact of temperature on Chl-a 358 dynamics, as EDM requires time series data of consistent intervals. 359 360 4.2 Causal effects of salinity, pH, turbidity, and nutrients on Chl-a for in situ 361 measurement data 362 Regarding the other environmental variables, we used the in situ data only because of the 363 limited data availability. The causal effects of salinity observed were concentrated in the 364 southern regions and Victoria Harbor (Fig. 3b) in accord with a previous study that showed 365 the establishment of a stable water column by the intrusion of the Pearl River freshwater 366 mass, which could promote algal blooms in these areas (Yin, 2003). The effect of salinity on 367 Chl-a dynamics is stronger than that of other factors (Fig. 3a), suggesting the importance of 368 freshwater discharge and physical processes in algal bloom formation in Hong Kong waters. 369 pH is related to the availability of inorganic carbon (HCO3–), which is necessary for 370 photosynthesis, and thus, changes in pH could affect algal growth (Liu et al., 2016). Causal 371 effects of pH are generally found in sites close to the shorelines (Fig. 3c). This might be 372 because pH levels in shorelines are less stable due to more intensive biological activities 373 compared to pH levels in the open ocean area (Duarte et al., 2013). 374 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 18 Primary production of phytoplankton is directly proportional to light availability, which 375 is influenced by turbidity (Domingues et al., 2011). Our results demonstrate that compared to 376 other environmental factors, turbidity generally has a weaker and less common causal effect 377 on Chl-a dynamics (Fig. 3d and a). This might suggest that light availability is a less 378 significant bottom-up factor for phytoplankton dynamics when compared to nutrients, at least 379 in Hong Kong waters. However, in Deep Bay, an estuarine oyster farming zone, turbidity 380 exhibits a notably stronger causal effect. As filter feeders, oysters consume phytoplankton 381 and are more efficient at filtering in clear water (Meeuwig et al., 1998). In oyster farming 382 areas, the impact of turbidity on Chl-a dynamics could be influenced not only by light 383 penetration but also by oyster herbivory, which might make this effect more pronounced in 384 Deep Bay than in other regions. 385 The causal effect of the N/P ratio was evident not only in eutrophic areas such as Tolo 386 Harbor but also in oligotrophic regions such as Mirs Bay and Port Shelter (Fig. 3e). This 387 indicates that nutrient limitation, which is indicated by the N/P ratio, may be a factor 388 controlling the Chl-a dynamics in these regions. The similar pattern of causal effect of silica 389 with salinity (Fig. 3f and b) could suggest that the availability of silica is affected by fresh 390 river discharge. A previous experimental study demonstrated that available silicon in benthic 391 sediments is subjected to release into the overlying water column for plankton uptake in 392 estuarine and continental shelf environments with lower salinity (Qin & Weng, 2006). 393 Overall, the causal effects of environmental factors on Chl-a are site-dependent. The 394 hydrodynamic conditions in each area should be taken into consideration when trying to 395 explain the Chl-a dynamics. As the climate in Hong Kong exhibits distinct dry and wet 396 seasons, the effects of rainfall and freshwater discharge (with salinity serving as an indicator) 397 on Chl-a may be temporally dynamic (Lee et al., 2006). Therefore, future studies could focus 398 on how changes in rainfall and freshwater discharge in different seasons control algal bloom. 399 Additionally, water column stability is related to tidal flush, upwelling and downwelling 400 induced by strong wind (Yin, 2003). However, tide current speed, wind speed, and wind 401 direction were not explicitly included in our study sites due to the limitation to accessing such 402 data. Thus, the possible causality of horizontal or vertical movement of water induced by tide 403 or monsoon could not be directly evaluated here. Further study could focus on datasets such 404 as those of Hong Kong Observatory (https://www.hko.gov.hk/en/index.html) for meteorology 405 parameters or Hong Kong Tidal Stream Prediction System 406 (https://current.hydro.gov.hk/main/download.php?lang=en) for oceanographic parameters to 407 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 19 draw a fuller picture of algal bloom mechanisms in different water districts. 408 409 4.3 Forecasting Chl-a dynamics with univariate and multivariate models 410 We combined the UIC-based causality detection and MDR S-map to conduct near-future 411 forecasting of Chl-a dynamics. For the in situ measurement data, multivariate models (i.e., 412 models with Chl-a and other environmental variables) showed similar forecast performance 413 with the univariate model (i.e., Chl-a only model) (Fig. 4). Possible explanations for this 414

include: 1) The monthly time series data could not effectively capture the fluctuations 415 in nutrient levels and the corresponding responses of Chl-a (or phytoplankton). It has been 416 shown that nutrients delivered by tidal currents and atmospheric inorganic nitrogen can be 417 rapidly consumed by phytoplankton within a timescale of just a few hours (Lo et al., 2025), 418 suggesting that finer temporal resolution data is necessary to make more accurate near-future 419 forecasting. 2) Although the duration of physical processes (e.g., stratification induced by 420 river discharge and downwelling caused by monsoons) usually lasts for a few months, neither 421 salinity nor temperature is a direct indicator of these processes. Incorporating “indirect” 422 indicators of these physical processes might not be sufficient to improve the forecasting 423 accuracy of the univariate model. Future efforts could explore various combinations of 424 factors across different sites at different time scales, considering that the mechanisms behind 425 algal bloom formation may differ in different water bodies. 426 For the remote sensing data, we found a significant improvement in forecast 427 performance of the multivariate MDR S-map compared to the univariate MDR S-map in 428 most of the sites (Fig. 5), which highlights the potential of EDM that utilizes multiple 429 variables and remote sensing data for monitoring and forecasting Chl-a dynamics. The 430 multivariate model with SST input was also better at capturing the high peaks and low peaks 431 than the univariate model (Fig. 6), suggesting that algal bloom outbreaks are affected by 432 temperature dynamics. The clear improvement in the multivariate model performance for 433 remote sensing data compared to in situ measurement data may be attributed to the robustness 434 of monthly average data derived from daily observations, even in the presence of missing 435 values. In contrast, the irregular monitoring interval of time series (EPD conducted sampling 436 on an irregular date of each month) may hinder the performance of EDM. 437 438 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 20 4.4 Comparison of the in situ measurement data and remote sensing data, 439 and perspectives for future Chl-a monitoring and forecasting 440 Although Chl-a dynamics of in situ measurement data and remote sensing data at some 441 neighboring sites showed similar trends (Fig. 1c), the causal effect of temperature on Chl-a 442 showed different spatial patterns using these two datasets (Fig. 2). The significant causal 443 effect of temperature was clearly stronger and more common for remote sensing data. Also, 444 the MDR S-map showed improved forecast performance only for remote sensing data. This 445 was expected since EDM is developed for recovering the trajectories of variables coupling 446 with each other and is supposed to demonstrate higher forecast performance if these variables 447 have stronger causal links. Our results reveal that different methods of collecting monthly 448 data can lead to different patterns. Therefore, a consistent sampling interval is recommended 449 to improve forecast performance when applying EDM. 450 Future efforts should focus on integrating other data resources and analysis methods, 451 including chlorophyll types and/or algae species information and neural network-based 452 algorithms. First, our analysis did not include any functional and/or species information of 453 algae. Different HAB species may have different physiological and population-level 454 characteristics (Chen et al., 2023), and including them in the model could provide better 455 forecasting performance and more detailed information about the algal dynamics (Xi et al., 456 2021). In addition, an advanced deep-learning model that utilized Chl-a data across a broad 457 spatiotemporal scale in a coastal ocean (Zhang et al., 2025) has provided a potential solution 458 for resolving the missing observation issue of remote sensing data. Further, we could 459 integrate time series data of Chl-a concentrations with historical algal bloom incidents. By 460 employing classifiers such as support vector machines (Keerthi et al., 2001, a machine 461 learning method), we can identify patterns of Chl-a and environmental factors prior to algal 462 bloom outbreaks. This approach could ultimately enhance our ability to predict algal bloom 463 events. 464 465 5. Conclusions 466 In the present study, we revealed causal effects of environmental factors on Chl-a and 467 their potential for improving the performance of forecasting Chl-a in Hong Kong waters 468 utilizing a nonlinear time series analysis called Empirical Dynamic Modeling (EDM) and two 469 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 21 parallel sets of twenty-year time series data from in situ measurements (provided by the 470 Environmental Protection Department; EPD) and remote sensing data (from MODIS). For in 471 situ measurement data, salinity exhibited the strongest causal effect on Chl-a compared to 472 other environmental factors, suggesting the importance of oceanographic processes, such as 473 stratification induced by freshwater discharge, in algal bloom formation. As for remote 474 sensing data, SST showed a significant causal effect of Chl-a at most sites and a multivariate 475 model including Chl-a and SST outperformed the univariate model at most sites, highlighting 476 the potential of the multivariate models of EDM. Although the in situ measurement data and 477 remote sensing data showed similar Chl-a dynamics in Hong Kong waters, our causal 478 analysis and forecasting model revealed several differences between the two datasets. These 479 findings suggest that accounting for data characteristics (e.g., monitoring intervals) is 480 essential for achieving more efficient and effective monitoring. Overall, this study 481 demonstrates the application of nonlinear time series analysis, EDM, to monthly Chl-a 482 dynamics derived from in situ measurements and remote sensing and shows how such 483 approaches can provide insights into Chl-a dynamics in Hong Kong waters. To enhance the 484 water quality monitoring and improve forecasting HAB occurrence in Hong Kong waters, 485 future studies may consider incorporating physical dynamics, developing methods to mitigate 486 the effects of irregular sampling intervals, including species and/or population characteristics, 487 and exploring the potential of other data analysis approaches such as deep learning. 488 489 .CC-BY 4.0 International licenseperpetuity. 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It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint Causal factors of coastal chlorophyll-a dynamics and near future forecasting 30 Data and Code Accessibility: All data used in this study was downloaded from public 637 databases. All scripts and formatted data used in this study are available on Github 638 (https://github.com/sxhuang00/causality_forecast_chl). 639 640 Declaration of generative AI use: We used generative AI tools to polish the English 641 language and improve the clarity of the text. All AI-generated suggestions were manually 642 reviewed and verified for accuracy and clarity. 643 644 Acknowledgments: We thank Takamitsu Ohigashi and Yining Xu for their assistance in data 645 analysis. We thank Mengqiu Wang for her valuable advice on the use of remote sensing data. 646 This research was supported by The Hong Kong University of Science and Technology 647 Startup Fund to MU. 648 649 Author contributions: SH and MU conceived research; SH and MU designed research; SH 650 analyzed the data with help from MU; MU wrote a custom function to perform the MDR S-651 map; SH and MU wrote the first draft, discussed the results, and completed the manuscript. 652 653 Conflicts of Interest declaration: The authors declare no conflict of interest. 654 .CC-BY 4.0 International licenseperpetuity. It is made available under a preprint (which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in The copyright holder for thisthis version posted January 8, 2026. ; https://doi.org/10.64898/2026.01.07.698127doi: bioRxiv preprint