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In this study, the HFLUX model was coupled with the SCEM-UA algorithm for analyzing the uncertainties of the model inputs. The specific procedures started with selecting the inputs of the HFLUX model. With the linked HFLUX and SCEM-UA model and implementation of an iteration scheme, the uncertainty of each of the selected inputs was obtained based on the ranges (minimum and maximum values) of the input data/parameters and the Latin hypercube sampling. The simulations were then compared against the observed data to evaluate the performance of the SCEM-UA algorithm. These steps are depicted in Fig. 1.Figure 1Flowchart for the uncertainty analysis.Full size imageRiver water temperatures simulated by the HFLUX modelRiver water temperature affects the water quality and the ecosystem health, and hence control of river water temperature is important to mitigation of its adverse effects1. The HFLUX model was used to simulate the streamflow temperatures at different locations and times. The model is highly flexible in terms of choosing the solution methods for solving the governing equations and selecting the energy budget terms such as shortwave solar radiation, latent heat flux, and sensible heat transfer flux. The model input data include the initial spatial and temporal temperature conditions, stream geometry data, discharge data, and meteorological data8. The water balance and energy balance equations are respectively given by8:$$frac{partial A}{{partial t}} + frac{partial Q}{{partial x}} = mathop qnolimits_{L}$$
(1)
$$frac{{partial left( {Amathop Tnolimits_{w} } right)}}{partial t} + frac{{partial left( {Qmathop Tnolimits_{w} } right)}}{partial x} = mathop qnolimits_{L} mathop Tnolimits_{L} + R$$
(2)
$$R = frac{{Bmathop varphi nolimits_{total} }}{{mathop rho nolimits_{w} mathop Cnolimits_{w} }}$$
(3)
where A is the cross section area of the stream (m2), x is the distance along the stream (m), t is the time (s), Q is the discharge of the stream (m3/s), qL is the lateral inflow per unit stream length (m2/s), Tw is the stream temperature ((^circ C)), TL is the temperature of the lateral inflow ((^circ C)), R is the energy flux (source or sink) per unit stream length ((^circ C) m2/s), B is the width of the stream (m), (mathop varphi nolimits_{total}) is the total energy flux to the stream per surface area (W/m2), (mathop rho nolimits_{w}) is the density of water (kg/m3), and (mathop Cnolimits_{w}) is the specific heat of water (J/kg (^circ C)). Equation (3) is based on a thermal datum of 0 (^circ C) and the impact on the absolute value of the advective heat flux term. In Eq. (2), if qL is negative, the first term on the right-hand side of the equation becomes a loss of qLTw. Also, dispersive heat transport that is omitted in Eq. 2 is negligible when the longitudinal change in water temperature is small in comparison to the temporal changes8.SCEM-UA algorithmThe SCEM-UA algorithm provides posterior distribution functions for the model parameters and input data by generating an initial sample from the parameter space. First, the indicators of n, q, and s that are respectively dimension (the number of investigate inputs), number of complexes (the population to be divided), and population (the number of sample points) are determined for the algorithm. Then, the algorithm searches the sampling points in the feasible space and sorts the points according to the density. The algorithm determines the sequence and complexes based on those points. The sequence is the first q points of the population and complexes are a collection of m points from the population. Note that m = s/q. In the next step, the points of each complex are sorted based on the density, which can be mathematically expressed as20:$$left{ {begin{array}{*{20}c} {mathop alpha nolimits^{k} le T,,,,,,,,,mathop theta nolimits^{t + 1} = Nleft( {mathop theta nolimits^{t} ,,mathop Cnolimits_{n}^{2} mathop Sigma nolimits^{k} } right)} \ {mathop alpha nolimits^{k} > T,,,,,,,,mathop theta nolimits^{t + 1} = Nleft( {mathop mu nolimits^{k} ,,mathop Cnolimits_{n}^{2} mathop Sigma nolimits^{k} } right)} \ end{array} } right.$$
(4)
where k = 1,2,…,q, α is the ratio of the mean posterior density of the m points of complexes to the mean posterior density of the last m generated points of sequences, (theta) is the points of complexes, ({c}_{n}=frac{2.4}{sqrt{n}}) , (T={10}^{6}), (mu) is the mean, and ∑ denotes the covariance. To investigate the new points created by the algorithm, the points of complexes are replaced by20:$$left{ {begin{array}{*{20}l} {Omega ge Zquad replace,best,member,of,mathop Cnolimits^{k} ,with,mathop theta nolimits^{t + 1} } \ {Omega < Zquad mathop theta nolimits^{t + 1} = mathop theta nolimits^{t} ,,,,,,,,,,,,,,,,,,,,,} \ end{array} } right.$$ (5) where (mathop Cnolimits^{k}) is the Kth complex, Z is drawn from the uniform distribution in the range of 0–1, and Ω is calculated by20:$$Omega = frac{{Pleft( {left. {mathop theta nolimits^{t + 1} } right|y} right)}}{{Pleft( {left. {mathop theta nolimits^{t} } right|y} right)}}$$ (6) where (Pleft( {left. {mathop theta nolimits^{t + 1} } right|y} right)) and (Pleft( {left. {mathop theta nolimits^{t} } right|y} right)) are the posterior probability distributions for (mathop theta nolimits^{t + 1}) and (mathop theta nolimits^{t}), respectively. Then, the algorithm examines the following condition for each complex. If it is rejected, the algorithm replaces the worst member ({c}^{k})(the point with the lowest density) with ({theta }^{t+1}) 20.$$mathop Gamma nolimits^{k} le T,,and,,Pleft( {{{mathop theta nolimits^{t + 1} } mathord{left/ {vphantom {{mathop theta nolimits^{t + 1} } y}} right. kern-nulldelimiterspace} y}} right) < ,Pleft( {{{mathop Cnolimits_{m}^{k} } mathord{left/ {vphantom {{mathop Cnolimits_{m}^{k} } y}} right. kern-nulldelimiterspace} y}} right)$$ (7) where ({Gamma }^{k}) is the ratio of the posterior density of the best (the point with the highest density) to the posterior density of the worst member of ({c}^{k}). The last step is to examine (beta) and L. Note that (beta) = 1 and L = m/10. If (beta < L), (beta = beta + 1) and the algorithm returns to sort complex points. Otherwise, the algorithm examines the Gelman and Rubin convergence6, and eventually provides the posterior distribution functions20. The value of the Gelman and Rubin convergence should be less than 1.2. The Gelman and Rubin convergence is examined by:$$R = sqrt {frac{g - 1}{g} + frac{q + 1}{{q.g}}frac{B}{W}}$$ (8) where g is the number of iterations within each sequence, B is the variance between the q sequence means, and W is the average of the q within-sequence variances for the parameter under consideration20.Study AREAMeadowbrook Creek was selected to test the methods proposed in this study8. The creek flows through the City of Syracuse in New York. Thus, this catchment consists of high residential and industrial land covers, which contribute runoff to the main channel. The creek is about 4 km long. A portion of this creek (475 m long) was selected for the modeling for a period of June 13–19, 2012 in this study. The upstream boundary condition in the HFLUX model was set based on the water temperature of the creek observed at the upstream station8. The uncertainty of the model inputs was examined at three selected points as shown in Fig. 2. Note that the input values at these three points had greater relative changes than the changes at other locations, which provided the possibility to improve the evaluation of the algorithm performance. In addition, these three locations had the same sampling of the selected input data. During the simulation period, the streamflow velocity varied within a range of 0.06–0.63 (m/s). The daily temperature changed between 8.9 and 28.2 °C. The relative humidity, used to calculate the total energy flux to the stream per surface area, changed from 36 to 93%. The creek bed mainly consisted of clay, cobbles, sand, and gravel materials. The basic statistics of the data/variables used in the HFLUX model are presented in Table 1. Figure 2 shows the study area, the creek, and the three selected points for analysis.Figure 2Study area and the locations of three evaluation sections (the gray enlarged map shows the State of New York), the map in this Figure is created by Google Earth 7.0.2.8415 (https://google.com/earth/versions).Full size imageTable 1 Basic statistics of the data/variables used in the HFLUX model.Full size tableEthical approvalAll authors accept all ethical approvals.Consent to participateAll authors consent to participate.Consent to publishAll authors consent to publish. More

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Study sitesWe conducted this study in three protected areas in Sabah, Malaysian Borneo: Danum Valley Conservation Area (DVCA), the Lower Kinabatangan Wildlife Sanctuary (LKWS), and Tabin Wildlife Reserve (TWR) (Fig. 4). The minimum and maximum daily temperatures and annual precipitation among the three study sites did not differ significantly (annual temperature: 22–33 ℃, annual precipitation 2400–3100 mm; Mitchell37; Matsuda et al.39; South East Asia Rainforest Research Partnership Unpublished data. https://www.searrp.org/) although there is no recent precise climate data of TWR.Figure 4Location of the three study sites in Borneo.Full size imageThe DVCA (4° 50′–5° 05′ N, 117° 30′–117° 48′ E) is a Class I Protection Forest Reserve established by the Sabah state government in 1996 and managed by the Sabah Foundation (Yayasan Sabah Group) covering 438 km2. Approximately 90% of the area is comprised of mature lowland evergreen dipterocarp forests34. The study area is an old-growth forest surrounding the Borneo Rainforest Lodge (5° 01′ N, 117° 44′ E), a tourist lodging facility.The LKWS (5° 10′–5° 50′ N, 117° 40′–118° 30′ E), is located along the Kinabatangan River, which is the longest river flowing to the east coast, reaching 560 km inland and with a catchment area of 16,800 km2. Designated as a wildlife sanctuary and gazetted in 2005, the LKWS consists of ten forest blocks totaling 270 km2, comprised of seasonal and tidal swamp forests, permanent freshwater swamps, mangrove forests, and lowland dipterocarp forests35,36. The southern area of the Menanggul River is extensively covered by secondary forest. However, the northern area has been deforested for oil palm (Elaeis guineensis) plantations, except for a protected zone along the river. The TWR (5° 05′–5° 22′ N, 118° 30′–118° 55′ E) is located approximately 50 km northeast of Lahad Datu, eastern Sabah, and covers approximately 1225 km2.The TWR is exclusively surrounded by large oil palm plantations. Most parts of the TWR were heavily logged in the 1970s and the 1980s, leaving mainly regenerating mixed dipterocarp tropical rainforests dominated by pioneer species such as Neolamarckia cadamba and Macaranga bancana37,38. The study area was near the Sabah Wildlife Department base camp located on the western boundary of the TWR (5° 11′ N, 118° 30′ E). The study area includes heavily logged secondary forests and a small patchy old forest (0.74 km2).Data collectionWe set up 15, 30, and 28 infrared-triggered sensor cameras (Bushnell, Trophy Cam TM) in the DVCA (July 2010–August 2011 and May 2014–December 2016), LKWS (July 2010–December 2014) and TWR (May 2010–June 2012), respectively. As a result, the cumulative number of camera operation days in DVCA, LKWS, and TWR were 14,134, 18,265, and 4980, for a total of 37,379 days. Although it was impossible to record the animals during certain months because of adverse weather conditions, such as heavy rain, flooding, battery failure, other malfunctions mainly caused by insects nesting inside the cameras, or logistical problems, the cameras remained continuously activated. Due to these reasons, camera operating days differed among the cameras in each site. In this study, we used photos of animals, and we did not handle animals directly. All cameras were placed at heights of 30–50 cm above the forest floor and were tied to tree trunks using fabric belts to reduce damage to the trees.Because the terrain and level of regulations to conduct this study differed by the study site, we employed different layouts of camera stations at each study site. In the DVCA, T. K. and three trained assistants placed 15 cameras along six forest trails totaling 9000 m, which were established and maintained by the tourist lodging facility. Because it was prohibited to establish new trails and to place cameras at sites where tourism activity would be disturbed in the study area; therefore, the trails that were longer than 1 km and relatively easily accessible were selected as camera locations to maintain consistency of trail characteristics. Cameras were placed on each trail at 50 m intervals, alternating right and left to avoid bias of photo-capture frequency caused by terrain differences. Each station was at least 25 m away from each other on the different trails (Fig. 5a). The operating days differed among the 15 cameras, i.e., mean = 942.2; SD = 152.0; range = 682–1229.Figure 5Maps of camera locations at each study site. (a) Trails and camera stations at DVCA; (b1) trails and camera stations and (b2) trail locations at LKWS; (c) a trail and camera stations at TWR.Full size imageIn the LKWS, I. M. and two trained assistants had planned to install 30 cameras, but a maximum of only 27 cameras were in operation during the study period in the LKWS, probably owing to malfunctions caused by high humidity and rain in the tropical rainforest. All cameras were placed on the trails in the riverine forest along the Menanggul River. As part of a project on the primates of the riverine forests along the Menanggul River and to assist their observation and tracking in the swampy habitat in the LKWS39, trails 200–500 m long and 1 m wide were established at 500 m intervals on both sides of the river. Of the 16 trails, we selected ten trails that were all 500 m long and placed three cameras at the points from the riverbank to the inland forest in each trail, that is, 10 m, 250 m and 500 m from the riverbank (Fig. 5b1); cameras were set up 50 m away from the trails (Fig. 5b2). Consequently, the number of operating days differed among 30 cameras, i.e., mean = 608.8; SD = 531.4; range = 28–1315.In the TWR, M. N. and A. M placed 28 and three cameras on camera stations created by overlaying a 750 × 500 m grid in May and August 2010, respectively. Cameras were placed at each grid point at 250 m intervals (Fig. 5c). The operating days differed significantly among the 28 cameras, that is, mean = 177.9; SD = 123.2; range = 26–539.Temporal activity analysisWe defined non-independent photo capture events as consecutive photos of the same or different individuals of the same species taken within a 30-min interval and removed these photos from the analysis. We plotted the activity patterns of each species using a von Mises kernel40,41 using the package activity42 in R version 4.0.243. We estimated the activity level of animals with more than ten independent photo-capture events as indicated in the previous studies26,44. For our analysis, we pooled the images from all study sites if the photo number of a species was less than 10 in any study locations. If that was not the case, we used the package activity42 to compare species activity levels across the three research sites using a Wald test with Bonferroni correction for multiple pairwise comparisons. When there were significant differences, we separately estimated activity levels by the study sites. When there were no significant differences among the sites, we pooled the photo numbers to estimate activity levels.We divided a day into three periods: nighttime (19:00–04:59 h local time (GMT + 8)); daytime (07:00–16:59 h); and twilight (05:00–06:59 h and 17:00–18:59 h). During the study period, twilight hours essentially corresponded to 1 h between sunset and sunrise, at 5:54–6:25 and 17:50–18:25 in DVCA, 5:51–6:23 and 17:47–18:25 in LKWS, and 5:50–6:21 and 17:46–18:22 in TWR (data from https://www.timeanddate.com). After converting the time data of each photo-capture event into radians, we fitted a circular kernel density distribution estimated by 10,000 bootstrap resampling to radian time data, and we estimated the percentage of active time in each period. We then categorized the activity patterns of photo-captured carnivore species into four categories: nocturnal (active at night); crepuscular (active during twilight periods); diurnal (active during daytime); and cathemeral (active in all periods). We defined the activity pattern of the species as showing a statistically higher proportion of photo-captures at nighttime, daytime, and twilight periods than at other periods, such as nocturnal, diurnal, and crepuscular, respectively. When photo-capture proportions showed no differences among the three periods, we defined the activity pattern as cathemeral. For species with substantial sample size (50  More

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