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Earth system models for regional environmental management of red tide: Prospects and limitations of current generation models and next generation development


Earth system models (ESMs) serve as a unique research infrastructure for quality climate services, yet their application for environmental management at regional scale has not yet been fully explored. The unprecedented resolution and model fidelity of the Coupled Model Intercomparison Project Phase 6 (CMIP6) simulations, especially of the High-Resolution Model Intercomparison Project (HighResMIP) focusing on regional phenomena, offer opportunities for such applications. This article presents the first venture into using the HighResMIP simulations to tackle a regional environmental issue, the Florida Red Tide. This is a harmful algae bloom caused by the dinoflagellate Karenia brevis, a toxic single-celled microscopic protist. We use CMIP6 historical simulations to establish a causal agreement between the position of Loop Current, a warm ocean current that moves into the Gulf of Mexico, and the occurrence of K. brevis blooms on the Western Florida shelf. Results show that the high-resolution ESMs are capable of simulating the phenomena of interest (i.e., Loop Current) at the regional spatial scale with generally adequate data-model agreement in the context of the relation between Loop Current and red tide. We use this case study to elaborate on the prospects and limitations of using publicly available CMIP data for regional environmental management. We highlight the current gaps and the developmental needs for the next generation ESMs, and discuss the role of stakeholder participation in future ESMs development to facilitate the translation of scientific understanding to better inform decision-making of regional environmental management.

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Data availability

Data and codes that support the findings of this study are publicly available. Elshall (2021) documents and provides the K. brevis data, CMIP6 model data, CMEMS reanalysis data, and the python codes for data analysis and visualization that are used in this study.


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This work is funded by NSF Award #1939994. The views expressed in this article are those of the authors and do not necessarily reflect the views or policies of the U.S. Environmental Protection Agency.

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Correspondence to Ming Ye.

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We process zos data to determine Loop Current position (i.e., LCN and LCS) to obtain the zos anomaly per time interval

$$h_{t} = \mathop {\max }\limits_{{h_{t,n} }} \left( {\mathop \vartriangle \limits_{m} \left[ {\mathop E\limits_{l} \left[ {\mathop E\limits_{k} \left[ {\mathop E\limits_{j} \left( {h_{t,n,m,l,k,j} |M_{k} } \right)} \right]} \right]} \right]} \right)$$

such that the expectations \(\mathop E\limits_{j}\), \(\mathop E\limits_{k}\) and \(\mathop E\limits_{l}\) of zos data are taken for all model runs with index \(j\) of each ensemble member \(M_{k}\), all ensemble members \(M_{k}\) with index \(k\), and all data points with index \(l\) along each segment (i.e., north and south segments in Fig. 1b), respectively. Then the difference \(\mathop \vartriangle \limits_{m}\) between the north and south segments with index \(m \in \left[ {1,2} \right]\) is taken resulting in \(h_{t,n}\) with \(n \in \left[ {1,6} \right]\) because we have monthly zos data, and we use 6-month interval. Finally, for each of the 6-month intervals \(t\) starting from 1993 to 2015, the maximum \(h_{t,n}\) is selected resulting in zos anomaly values \(h_{t}\) such that \(t \in \left[ {1,44} \right]\). There are 44 \(h_{t}\) values because we use a 6-month interval (i.e., half a year) and given the 22-year study period. As the Loop Current position is a cycling event, taking the maximum value \(\mathop {max}\limits_{{h_{t,n} }} \left( . \right)\) in each time interval is more robust than the average value that may dilute the signals of the LCS.

To evaluate the predictive performance and compare the model results and reanalysis data we use the following four metrics:

Loop Current position ratio (\(y_{1}\)): This is the ratio of the frequency of LCS to LCN.

$$y_{1} = \frac{{\sum\nolimits_{t = 1}^{T} {H_{LCS} (h_{t} )} }}{{\sum\nolimits_{t = 1}^{T} {H_{LCN} (h_{t} )} }}$$

such that \(\sum\nolimits_{t = 1}^{T} {H_{LCS} (h_{t} )}\) and \(\sum\nolimits_{t = 1}^{T} {H_{LCN} (h_{t} )}\) are the count of LCS and LCN intervals given the total number of intervals \(T = 44\), with indicator function for LCS.

$$H_{LCS} (h_{t} ) = \left\{ {\begin{array}{*{20}c} {1,\;\;\;\;h_{t} \ge 0} \\ {0,\;\;\;\;h_{t} < 0} \\ \end{array} } \right.$$

and LCN

$$H_{LCN} (h_{t} ) = \left\{ {\begin{array}{*{20}c} {1,\;\;\;\;h_{t} < 0} \\ {0,\;\;\;\;h_{t} \ge 0} \\ \end{array} } \right.$$

Temporal match error (\(y_{2}\)): For reanalysis data and model predictions, the temporal match with respect to LC position for LCS.

$$y_{2,LCS} = \frac{{\sum\nolimits_{t = 1}^{T} {H_{LCS} \left( {h_{t,obs} } \right) - \sum\nolimits_{t = 1}^{T} {\left( {h_{t,obs} < 0^{ \wedge } h_{t} < 0} \right)} } }}{{\sum\nolimits_{t = 1}^{T} {H_{LCS} \left( {h_{t,obs} } \right)} }}$$

for LCN.

$$y_{2,LCN} = \frac{{\sum\nolimits_{t = 1}^{T} {H_{LCN} \left( {h_{t,obs} } \right) - \sum\nolimits_{t = 1}^{T} {\left( {h_{t,obs} \ge 0^{ \wedge } h_{t} \ge 0} \right)} } }}{{\sum\nolimits_{t = 1}^{T} {H_{LCN} \left( {h_{t,obs} } \right)} }}$$

and both positions.

$$y_{2} = \frac{{T - \sum\nolimits_{t = 1}^{T} {\left( {h_{t,obs} \ge 0^{ \wedge } h_{t} \ge 0} \right) - \sum\nolimits_{t = 1}^{T} {\left( {h_{t,obs} < 0^{ \wedge } h_{t} < 0} \right)} } }}{T}$$

where \(\sum\nolimits_{t = 1}^{T} {H_{LCS} (h_{t,obs} )}\) and \(\sum\nolimits_{t = 1}^{T} {H_{LCN} (h_{t,obs} )}\) are for reanalysis data \(h_{t,obs}\)(Eq. A1). In Eqs. A57, \(\sum\nolimits_{t = 1}^{T} {\left( {h_{t,obs} \ge 0^{ \wedge } h_{t} \, \ge 0} \right)}\) and \(\sum\nolimits_{t = 1}^{T} {\left( {h_{t,obs} < 0v^{ \wedge } h_{t} < 0} \right)}\) present the temporal match counts of reanalysis data and model simulation for LCS and LCN, respectively. The logical conjunction \(\wedge\) of \(\left( {h_{t,obs} \ge 0^{ \wedge } h_{t} \ge 0} \right)\), for example, yields one when \(h_{t,obs} \ge 0\) and \(h_{t} \ge 0\) are both true, and yields zero otherwise.

K. brevis error (\(y_{3}\)): When LCS coincides with a large bloom, this is a false-negative prediction of red tide.

$$y_{3} = \frac{{\sum\nolimits_{t = 1}^{T} {\left( {h_{t} < 0^{ \wedge } H\left( {z_{t} } \right) = 1} \right)} }}{{N_{bloom} }}$$

where \(H(z_{t} )\) is an indicator function with zero and one for no bloom and large bloom and, respectively, and \(N_{bloom}\) is the number of large-bloom.

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Elshall, A.S., Ye, M., Kranz, S.A. et al. Earth system models for regional environmental management of red tide: Prospects and limitations of current generation models and next generation development. Environ Earth Sci 81, 256 (2022).

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