Predictive accuracy of temperature-nitrate relationships for the oceanic mixed layer of the New Zealand region

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112,, doi: /2006jc003562, 2007 Predictive accuracy of temperature-nitrate relationships for the oceanic mixed layer of the New Zealand region V. Sherlock, 1 S. Pickmere, 2 K. Currie, 3 M. Hadfield, 1 S. Nodder, 1 and P. W. Boyd 3 Received 20 February 2006; revised 3 November 2006; accepted 5 February 2007; published 15 June [1] Nitrate concentrations are a major factor controlling phytoplankton growth, hence the recent interest in using remotely sensed sea surface temperature (SST) and chlorophyll concentrations (Chla) to infer nitrate concentrations and substantially improve spatiotemporal estimates of nitrate in the surface ocean. Regression models which predict mixed-layer nitrate concentrations as a function of temperature and climatological salinity are derived for the subtropical and subantarctic waters of the New Zealand region (30 50 S, 154 E 160 W). These models are then validated using independent in situ measurements of temperature and nitrate concentrations and remotely sensed SST and Chla. Root mean square (RMS) nitrate prediction errors vary with water mass and exhibit seasonally dependent biases. RMS errors range from 0.8 to 1.8 mm in subtropical waters, 1.6 to 1.9 mm in the Subtropical Front, and 1.4 to 2.5 mm in subantarctic waters, depending on the spatiotemporal sampling characteristics of validation data sets. Prediction errors are correlated with observed chlorophyll concentrations, and a linear chlorophyll correction reduces seasonally dependent prediction biases significantly. Nitrate prediction errors for the New Zealand region are comparable with nitrate prediction errors reported for the North Atlantic and Equatorial and North Pacific, and the regression models give a substantially better description of the seasonal variation of nitrate in the New Zealand region than an existing nitrate climatology. A comparison of predicted nitrate-depletion temperatures with other published studies highlights the importance of detailed regional validation of temperature-nitrate regression models. Citation: Sherlock, V., S. Pickmere, K. Currie, M. Hadfield, S. Nodder, and P. W. Boyd (2007), Predictive accuracy of temperaturenitrate relationships for the oceanic mixed layer of the New Zealand region, J. Geophys. Res., 112,, doi: /2006jc Introduction [2] Light, temperature, and nutrient concentrations are major factors controlling phytoplankton growth rates, community structure, and primary production in the surface mixed layer of the ocean [Parsons et al., 1977; Arrigo, 2005]. Nitrate is an important, preferentially utilized source of nitrogen which supports new production [Dugdale and Goering, 1967], and phytoplankton maintain surface waters in nitrate-depleted conditions over much of the annual cycle in many of the world s oceans [Fanning, 1989; Levitus et al., 1993]. Variations in environmental forcing (such as surface radiative and freshwater fluxes and surface wind stress) will affect turbulent mixing and advective supply of nitrate to the surface ocean and are therefore an important 1 National Institute of Water and Atmospheric Research (NIWA) Ltd., Wellington, New Zealand. 2 NIWA, Hamilton, New Zealand. 3 NIWA Centre of Physical and Chemical Oceanography, University of Otago, Dunedin, New Zealand. Copyright 2007 by the American Geophysical Union /07/2006JC factor governing nitrate availability and new production [Dugdale and Goering, 1967; Eppley and Peterson, 1979]. However, quantitative estimates of seasonal and interannual variability in nitrate budgets and primary production on basin scales require a spatiotemporal sampling frequency which can seldom be achieved using water sampling methods (referred to hereinafter as in situ, as opposed to remote sensing, measurement techniques). [3] In situ data sets generally show a relatively strong negative correlation between temperature and nitrate concentrations in the mixed layer, which reflects the covariation of temperature (and hence density and stratification) and the processes of nutrient depletion (biological uptake) within and supply (vertical and lateral advection and mixing) to the mixed layer [Garside and Garside, 1995; Kamykowski, 1987, and references therein]. This correlation has been exploited in a number of recent studies to derive regression models which predict nitrate concentrations using remotely sensed sea surface temperatures (SST) [Gong et al., 1995; Garside and Garside, 1995; Kamykowski et al., 2002; Switzer et al., 2003] or SST and chlorophyll-a (Chla) concentrations [Goes et al., 1999, 2000] and thus capitalize on the sampling frequency of the remote-sensing data to 1of13

2 improve spatiotemporal estimates of nitrate concentrations in the surface mixed layer. Several of these regression models have already been used to estimate new production and interannual variability in carbon export in the North Pacific [Goes et al., 2000, 2004] and to infer nutrient availability on global scales based on the difference between the remotely sensed SST and the local nitratedepletion temperature (NDT, the temperature at which nitrate concentrations become undetectable by conventional measurement techniques) derived from temperature-nitrate regression relationships [Kamykowski et al., 2002; Switzer et al., 2003; Kamykowski and Zentara, 2003, 2005]. [4] We would like to apply this same methodology to use remote-sensing data streams to infer mixed-layer nitrate concentrations and investigate the relationships between environmental forcing and interannual variability in nitrate availability and primary production in the New Zealand region (30 50 S, 154 E 160 W). To do so, we must first derive and validate regression models which account for the complex geographic distribution and distinct physical, biological, and chemical characteristics of the subtropical and subantarctic water masses and the subtropical front (STF) within our study domain. The results of these first steps, and the conclusions we have drawn regarding the current and required accuracy of nitrate estimates in the New Zealand region, are the topic of this paper. [5] In section 2, we describe the derivation of our regression models, which predict mixed-layer nitrate + nitrite concentrations (referred to hereinafter as nitrate) as a function of temperature and climatological salinity for the subantarctic and subtropical water masses of the New Zealand region. In section 3, we present a number of model validation studies. We characterize the seasonal and spatial variation of errors in mixed-layer nitrate concentrations predicted using the observed in situ temperatures for the regression data and three independent data sets and compare the relative skill of the temperature-nitrate relationships and the Commonwealth Scientific and Industrial Research Organisation (CSIRO) Atlas of Regional Seas (CARS) nitrate climatology [Ridgway et al., 2002] in describing the seasonal and spatial variation of nitrate in the New Zealand region. We quantify the contribution of SST errors to the total error budget for nitrate predictions using remotely sensed SST, and we analyze the correlation between nitrate prediction errors and remotely sensed Chla to assess the potential utility of Chla as a regression model predictor in the New Zealand region. Finally, in section 4, we compare our regression model results with published error characteristics of regression models for the North Atlantic and North Pacific, and with NDT predictions of Kamykowski et al. [2002] and Switzer et al. [2003] for the New Zealand region. Section 5 concludes with an assessment of the current predictive accuracy in the New Zealand region and future model developments. 2. Regression Model Development 2.1. Overview of the Oceanography of the New Zealand Region [6] The physical, chemical, and biological oceanography of the New Zealand region is complex (for a detailed overview, see the work of Heath [1985]). To assist the reader, in Figure 1, we illustrate the spatial sampling characteristics of the data used in this study and the boundaries of the four salinity classes which are used in subsequent error analyses. These salinity classes, which are defined in Table 1, can be interpreted schematically in terms of water masses, the class S1 represents oligotrophic waters of the subtropical gyre which are advected southwards within the East Australia Current-Tasman Front-East Auckland Current system, the class S2 represents seasonally oligotrophic subtropical waters, the class S3 spans the STF, and the class S4 represents the subantarctic waters to the southeast of New Zealand. To the east of New Zealand, the STF is bathymetrically locked to the Chatham Rise, giving corresponding bathymetric constraints to the southern and northern boundaries of the subtropical and subantarctic water masses, respectively. [7] Nitrate is depleted before phosphate and is generally depleted before silicate within the subtropical waters and the STF in the New Zealand region. Excess nitrate concentrations at silicate depletion are observed however, particularly in the STF (the works of Zentara and Kamykowski [1981], Kamykowski and Zentara [1986], Chang and Gall [1998], Kamykowski et al. [2002], and unpublished analysis of the data sets used in this study). The adjacent subantarctic waters are classified as High Nitrate Low Chlorophyll (HNLC), with light, iron, and silicate availability and grazing all potentially factors limiting phytoplankton growth [Dugdale et al., 1995; Banse, 1996; Boyd et al., 1999] Regression Data Sets [8] Quality-controlled profiles of temperature, salinity, and nitrate concentrations measured in the New Zealand region (30 50 S, 154 E 160 W) were extracted from the National Oceanographic Data Center (NODC) World Ocean Database 2001 [Conkright et al., 2002] and the Australian CSIRO Marine Research archives [Ridgway et al., 2002]. Stations on the continental shelf (delimited for the purpose of this study by the 200 meter isobath) were excluded from the current analysis because terrestrial freshwater and nutrient fluxes and shelf circulations and phytoplankton populations are expected to modify temperature-nitrate covariance in the coastal zone [Switzer et al., 2003]. [9] In order to derive and apply the regression relations (using remotely sensed SST), we assume observations within the mixed layer are representative of surface values and vice versa. Profile data were processed to identify the mixed-layer depth (using a potential density threshold of 0.01 kg/m 3 and a reference level z 0 within 15 m of the surface [Thomson and Fine, 2003]) and select data records for observations from depths 75 meters within the mixed layer. [10] The resulting regression data set comprises 795 data records from 472 stations. The spatial distribution of the selected stations is illustrated in Figure 1a Regression Model Formulation [11] As the NODC and CSIRO data sets sample the distribution of nitrate in the New Zealand region sparsely and inhomogeneously in space and time, we have cumulated observations from all seasons and years to derive climatological annual regression relations, with the understanding that this may lead to seasonal biases in nitrate predic- 2of13

3 Figure 1. Spatial sampling characteristics of (a) the regression data set and (b) the independent validation data sets used in this study. The water mass characteristics of the salinity classes S1, S2, S3, and S4 are described in Table 1. Table 1. Definition of the Salinity Classes Used in Error Analyses, Range of Observed Nitrate Concentrations, and Water Masses They Nominally Represent a Class Salinity Range, psu Nitrate Range, mm Water Mass Descriptor S1 S > Subtropical Seasonally oligotrophic b S S Subtropical Seasonally oligotrophic S S Subtropical Spans the Subtropical Front S4 S < Subantarctic HNLC waters southeast of NZ a Classification is based on the CARS annual mean surface salinity field. b This class represents oligotrophic subtropical gyre waters advected within the East Australian Current-Tasman Front-East Auckland Current system. 3of13

4 Figure 2. Temperature-nitrate scatter plots and derived regression relationships for the regression data set. Regression relations are illustrated for the range of salinities (grey shading) associated with each water mass class (defined in Table 1). tions if the temperature-nitrate relationship has a marked seasonal dependence [Kamykowski and Zentara, 1986; Henson et al., 2003]. [12] Temperature-nitrate scatterplots are illustrated in Figure 2 for the regression data set. The covariance of mixed-layer temperature-nitrate in HNLC subantarctic and seasonally oligotrophic subtropical and STF waters is sufficiently different that we cannot derive a single regression model which gives adequate predictions in both water masses for regression and independent data sets. We have therefore derived separate regression models for the subantarctic water mass southeast of New Zealand (S4) and the subtropical and STF waters (S1 S3 combined) in the remainder of our study domain. We use the CARS annual mean salinity climatology and a simple threshold criteria (S < 34.4 psu, based on observed temperature-salinity relationships over Chatham Rise) to define the S4 water mass class. [13] As in previous studies, our regression models predict nitrate as a polynomial function of temperature. We were unable to include chlorophyll as a predictor in our models because simultaneous chlorophyll measurements are available for too few stations in our regression data set. [14] The principal spatial variation of mixed-layer temperature and nitrate in the New Zealand region is latitudinal, although the oceanic circulation of the region gives rise to marked longitudinal variability in these parameters. We tested latitude and salinity (as a water mass tracer) as predictors in regressions to account for the observed spatial variability in mixed-layer temperature and nitrate in the New Zealand region. While both gave improved fits to regression data for subtropical and frontal waters, salinity proved to be the better predictor (neither gave a statistically significant reduction in variance for the S4 data set, but the sample size for this class is very small (26 observations)). As there is currently no remote-sensing measurement of salinity, the CARS annual mean salinity climatology at the data locations was used to derive (and apply) the regression models. [15] Regression models were determined by stepwise regression. At each step, regression relations were determined by nonlinear least squares fitting using the Marquardt- Levenberg algorithm implemented in the Gnuplot routine fit Regression Models Derived for the New Zealand Region [16] The resulting nitrate prediction equations are illustrated in Figure 2. In subtropical and frontal waters (S1 S3) dno 3 ¼ MAX 0; 34:61 9:59bT þ 0:44bT 2 0:007bT 3 þ 2:99S ; and in subantarctic waters (S4) dno 3 ¼ 43:91 5:20z þ 0:18z 2 with z ¼ bt for bt T? and z ¼ T? for bt > T? ; where dno 3 (x, tjbt, S) is the nitrate concentration (in mm) predicted based on the estimated temperature bt (in C) and climatological salinity S at the location (latitude, longitude, and depth) x and time t and T* = 14.4 C is the turning point of the quadratic function. Note negative predicted values of ð1þ ð2þ 4of13

5 Figure 3. Nitrate-depletion temperatures predicted by the smallest real root of the nitrate regression relations for the New Zealand region. The hashed region represents the subantarctic water mass class S4, where the regression model predicts nitrate is never depleted. dno 3 are reset to zero in equation (1) while dno 3 is reset to the value predicted for T? for all bt > T? in equation (2). [17] If T(x, t) and NO 3 (x, t) are the true values of temperature and nitrate the nitrate prediction error cno3 (x, t) is given by NO 3 (x, t) dno 3 (x, tjbt, S). This error is composed of the inherent regression model error NO 3 (x, t) dno 3 (x, tjt(x, t), S) and a contribution due to the temperature error bt = bt(x, t) T(x, t). The associated (first order) temperature error sensitivity is given dno 3 which increases with decreasing temperature. Error sensitivities are 1 mm/ C at 15 C and 0.3 mm/ Cat20 Cfor predictions in subtropical and frontal waters. Error sensitivities are 1.6 mm/ C at 10 C and 0.2 mm/ Cat14 Cfor predictions in subantarctic waters Regression Model Predictions of Nitrate-Depletion Temperatures [18] The smallest real root of the cubic regression relation for the subtropical and STF water mass classes defines the NDT for a given climatological salinity (the CARS annual mean surface salinity in this instance). The regression model predicts NDT in the range C, increasing monotonically with salinity. The corresponding latitudinal and longitudinal distribution of the regression model NDTs are illustrated in Figure 3 and reflect the spatial structure of the surface salinity climatology (which results from the largescale oceanic circulation of the New Zealand region). The regression model for subantarctic waters predicts that nitrate is never depleted (represented by the hashed region in Figure 3). [19] Comparison of predicted NDT with observed temperatures where nitrate concentrations are less than 0.1 mm suggests that the model NDT predictions overestimate the minimum observed NDT by 1 3 C, which is to be expected, as the regression procedure will tend to place the cubic root near the middle of the range of temperatures associated with low or undetectable nitrate concentrations. The bias in predicted NDT appears to increase monotonically with salinity, that is, the regression model These effects are not corrected for in Figure Regression Model Validation 3.1. Independent In Situ Data Sets [20] Hydrographic and nutrient data sets from 2 repeat transects and 13 research voyages undertaken by the National Institute of Water and Atmospheric Research (NIWA) between 1992 and 2004 provide independent data to validate the predicted seasonal and spatial variation in mixed-layer nitrate, albeit for a limited spatial domain. The locations sampled by these independent data sets are illustrated in Figure 1b. [21] The Biophysical Mooring Transect (BMT) along the E meridian between two biophysical moorings, the subtropical mooring at 41 S and the subantarctic mooring at 47 S [Nodder et al., 2005], is repeated every 3 6 months. During these transects temperature, salinity and nutrient concentrations are measured quasi-continuously from water samples drawn from the RV Tangaroa s scientific intake at 5-meter depth on the underway transects and vertical profiles of these same parameters are made at each mooring site. The analysis in this paper is based on eight transects in August and December 2001, March, July, and November 2002, July and November 2003, and June 2004, and an additional transect in October 2000 when profile measurements were made at 31 stations along the transect. [22] The Munida transect runs from Taiaroa Head (45.77 S E) 60 km offshore to S E and is repeated every 1 2 months. The analysis in this paper is based on profile measurements of temperature, salinity, and nitrate made at the outermost five stations of the transect (nominally sampling the STF and subantarctic water mass) from 41 transects made between January 1998 and November [23] Profile measurements of temperature, salinity, and nitrate made during 13 research voyages in the waters east and west of the South Island of New Zealand between April 5of13

6 1992 and October 2000 were extracted from the NIWA data archive to form the third validation data set. [24] Temperature and salinity profiles were measured using Seabird Conductivity-Temperature-Depth (CTD) casts. Underway temperature was measured using a Seabird SBE21 thermosalinograph. Underway temperature traces have been cross-calibrated with the CTD temperature measurements at the mooring sites and agree to within 0.2 C. Underway and profile (bottle) nutrient samples were analyzed using an Astoria Pacific International (API) 300 microsegmented flow analyzer with digital detector. Nitrate was reduced to nitrite using cadmium metal and determined (as nitrate + nitrite) using an azo dye (API method 305-A177). The estimated accuracy of the nitrate measurements is 0.1 mm, and the estimated precision for the range of nitrate concentrations observed in the mixed layer is 0.15 mm (1% of the highest calibrant). The nitrate detection limit is mm. [25] All profile data sets were processed to extract observations in the mixed layer as described in section 2.2. Underway data (5-meter depth) is assumed to sample the mixed layer Nitrate Predictions Using In Situ Temperature Measurements [26] The predictive accuracy of the regression model is characterized using standard statistical measures, namely the root mean square error (RMSE) and the fraction of observed nitrate variance explained by the temperaturenitrate relationship (FEV): FEV cno3 S 2 NO3 c ¼ 1 S NO 3 NO 3 RMSE 2 NO3 c 2 ¼ 1 varðno 3 Þ : ð3þ Nitrate prediction errors are also binned by month and represented graphically using Tukey box and whisker plots with representation of outliers. [27] Regression model errors (i.e., the errors for nitrate predictions made with observed in situ temperatures T(x, t)) are tabulated in Table 2 for the regression and independent data sets Predictions for the Subtropical Water Mass and STF [28] Nitrate prediction errors for the regression data set in the water mass classes S1 S3 range from 0.8 to 1.6 mm. Prediction errors and the fraction of explained variance increase with latitude south (cf. quasi-linear decrease in salinity with latitude) because the annual variation in nitrate concentrations is more important at higher latitudes, particularly in the STF. A month-by-month decomposition of prediction errors (not shown) shows no marked seasonal bias in nitrate predictions, except in the class S2, where nitrate concentrations in July and August are underestimated by 1 2 mm (20 40%). [29] We now consider the results for the independent data sets in the water masses classes S2 and S3. The regression model explains 70 80% of the observed variance and RMS nitrate prediction errors are comparable with the regression set errors for the BMT data sets and the NIWA archive data in S3. The RMSE for the NIWA Archive data set in the S2 water mass class (1.75 mm) is higher than either Data set Class a N b Table 2. Summary of Nitrate Prediction Errors for Regression and Independent NIWA Data Sets and Comparison With the CARS Nitrate Climatology RMSE c FEV RMSE FEV dno 3 d NO 3,clim Regression S S S S BMT S S S e NIWA Archive S S S Munida S a The water mass classes used in these error characterizations are defined in Table 1. b Number of observations. c RMSE in units of mm. d RMS difference between observed nitrate concentrations and the CARS seasonal nitrate climatology, and corresponding FEV. e FEV 0 are indicated by the symbol. the regression or BMT data sets (1.16 and 0.9 mm, respectively), and the FEV is lower (16%) accordingly. This is due to large variability (2 7 mm) in observed nitrate concentrations on small spatial scales which is not correlated with temperature, and hence not predicted by the temperature-nitrate relationship, for data from one voyage in July This is in contrast to the BMT data set, where small-scale spatial variations in wintertime nitrate concentrations are generally well predicted by the temperaturenitrate relationship. [30] A seasonal decomposition of nitrate prediction errors for the BMT data set in subtropical and frontal waters is illustrated in Figure 4. In subtropical waters (S2), observed nitrate concentrations are underestimated by 1 mm (20%) in midwinter (July), and they are typically overestimated by 2 3 mm in November and, to a lesser extent, in October. A similar pattern of seasonal prediction biases is apparent in the STF (S3). In October and November, there is substantial reduction in nitrate (of 2 3 mm) within the mixed layer (which we attribute to the growth of diatom phytoplankton species [Chang and Gall, 1998]) prior to any significant increase in the mixed-layer temperature and which is therefore not predicted by the temperature-nitrate relationship. [31] Month-by-month decompositions of prediction errors for the NIWA Archive data set in classes S2 and S3 (not illustrated) also show that the temperature-nitrate relationship overestimates nitrate concentrations in October and November by 2 4 mm, although neither class shows marked bias in predicted midwinter nitrate concentrations Predictions for Subantarctic Water Mass Southeast of NZ [32] Temperature-nitrate relationships, seasonal nitrate variability, and nitrate prediction errors for the BMT, Munida, and NIWA archive sets are illustrated in Figure 5 for the S4 water mass class. [33] Despite the very small regression set for this class, the regression model gives a reasonable description of the mean temperature-nitrate covariance in the S4 water mass (model predictions do not show significant systematic 6of13

7 Figure 4. Temperature-nitrate scatter plots and Tukey box plots of nitrate prediction errors (observed minus predicted nitrate concentrations) for the Biophysical Mooring Transect data set in water mass classes S2 and S3. Misclassified data discussed in section are circled and labeled *. biases although there is a tendency to underestimate observed nitrate concentrations at very low temperatures). However, the independent data sets are characterized by high variability in nitrate at any given temperature which is reflected in high RMSE ( mm) and reduced FEV (50 65%) compared to predictions for subtropical and STF waters or the S4 regression set. [34] Higher nitrate prediction errors are to be expected for the subantarctic water mass because nitrate availability is not the principal factor limiting phytoplankton growth. If there was a correlation between mixed-layer temperature and the limiting factor, the temperature-nitrate covariance might still yield useful (accurate) predictions. Based on the observed covariance, this does not seem to be the case in the S4 water mass (this is also consistent with the results of Boyd et al. [2004] who found no strong evidence that variations in vertical mixing (and hence mixed-layer temperature) could account for the observed interannual variability in remotely sensed chlorophyll concentrations in late summer (February to March) in the S4 region) Water Mass Misclassification Errors [35] Water mass misclassification errors arise when the salinity climatology and threshold criterion do not give an accurate description of the actual location of the STF and subantarctic water mass, and the wrong regression relation is applied in nitrate predictions. Large prediction errors result when mixed-layer temperatures in the STF and subantarctic water mass are greater than 11 C, because the regression relations for the subtropical and subantarctic water masses differ significantly at these temperatures. [36] The subset of low nitrate concentrations observed in January on the Munida Transect (see Figure 5) can be attributed to misclassification of frontal (S3) waters based on observed salinity. Similarly, the gross prediction errors for the subset of BMT data at temperatures of 15 C with anomalously high nitrate concentrations in the water mass S3 observed on voyages in December and March (see Figure 4b) can be attributed to misclassified subantarctic (S4) waters based on the latitudinal covariation of temperature, nitrate, phosphate, and silicate concentrations (problems with the thermosalinograph salinity measurements have precluded their use in this study). These errors make a significant contribution to the RMSE for the BMT S3 water mass class. [37] The clustering in the BMT S4 temperature-nitrate scatterplot is due to BMT temporal sampling of the seasonal variation of nitrate in the S4 water mass (rather than the presence of two distinct water masses), the latitudinal covariation of temperature and nutrient concentrations observed on each BMT voyage supports the subantarctic water mass classification for all BMT S4 data illustrated Comparison With the CARS Climatology [38] A further characterization of regression model performance which is of interest is a measure of predictive skill relative to climatology. Accordingly, we have extracted the climatological nitrate NO 3,clim (x, d) from CARS for the day of the year and location of our in situ data sets (interpolating spatially as necessary) and calculated the RMSE and FEV for the climatological nitrate errors NO3,clim (x, t) =NO 3 (x, t) NO 3,clim (x, d). These statistics are reported in the last two columns of Table 2 for the regression and independent data sets. [39] For the regression data set, the temperature-nitrate relationships have slightly poorer predictive accuracy than 7of13

8 Figure 5. Temperature-nitrate scatter plots and nitrate prediction errors the independent data sets sampling the S4 water mass class. Misclassified data are circled and labeled *. the CARS climatology in classes S1 and S2, comparable predictive accuracy in class S3, and substantially better predictive accuracy than the CARS climatology in class S4. [40] For the independent data sets, the tabulated results show that the temperature-nitrate relationship has significantly better predictive accuracy than the CARS climatology in the region sampled by the independent data sets in all water mass classes, with the exception of data extracted from the NIWA archive in the S2 class. Month-by-month error decompositions (not shown) reveal a number of consistent seasonal biases which account for the higher climatological nitrate errors for the independent data sets. These are: [41] 1. An overestimation of nitrate concentrations in the S2 and S3 classes between October and December (which is more important than the corresponding bias in temperaturenitrate predictions) [42] 2. An underestimation of nitrate concentrations between June and August in the S3 class east of New Zealand (which is more important than the corresponding bias in temperature-nitrate predictions) [43] 3. And significant underestimation (3.5 mm) of nitrate concentrations in the subantarctic water mass east of New Zealand (S4) between February and November (corresponding biases for temperature-nitrate predictions are of the order of mm) Nitrate Predictions for the BMT Using Remote-Sensing SST and Chla Data Predictions Using Remote-Sensing SST [44] We have assessed the accuracy of three day and monthly SST composites for the prediction of the seasonal variation of nitrate for the BMT data set. [45] Temporal SST composites were derived from AVHRR radiances observed during each of the BMT voyages (3-day composites) and during the corresponding month (monthly composites) using the NIWA SST archive [Uddstrom and Oien, 1999]. To estimate the SST at the transect sample locations, we calculated the median value of 8of13

9 Table 3. Summary of Temperature and Nitrate Prediction Errors for the Biophysical Mooring Transect Data Set for Predictions Using 3-Day and Monthly Mean Remote-Sensing SST Composites Class N bt RMSE a dno 3 RMSE b FEV Three-Day Composites S (1.16) c S (1.63) 0.77 S (1.46) 0.47 Monthly Composites S (0.90) 0.72 S (1.86) 0.80 S (1.43) 0.65 a RMS temperature error in C. b RMS nitrate prediction error in mm. c Values in brackets are the corresponding RMSE for nitrate predictions using the observed in situ temperature at only those sampling locations where remote-sensing SST data are available. SST observed within ±0.5 degrees longitude of the transect for 0.1 degree latitude bins along the length of the transect and interpolated the median SST data to the latitudes of the underway samples wherever valid SST data was available. [46] As noted previously, when predictions are made using SST, we implicitly assume SST is representative of the mixed-layer temperature. Uddstrom and Oien [1999] report root mean square error of 0.7 C and a bias of 0.1 C for comparisons of SST retrievals and drifting buoy estimates of bulk mixed-layer temperature. Statistics for the difference between BMT in situ temperatures and SST estimates are generally consistent with these drifting buoy comparison statistics, RMSE range from 0.4 to 0.9 C depending on water mass and temporal composite, and are tabulated in Table 3 for reference. Biases make a small contribution to the total RMSE (i.e., random errors predominate) and are not discussed further here. [47] The error characteristics of nitrate predictions using three day and monthly mean remote-sensing SST composites derived from daytime and nighttime overpasses are tabulated in Table 3 and may be compared with corresponding errors for predictions using the observed in situ temperature at all sample locations where remotesensing SST estimates are available (bracketed values in Table 3) to quantify the contribution of SST errors in the nitrate prediction error budget. For predictions using 3-day SST composites, there is an increase of mm inthe RMS and mm in the interquartile range (not tabulated) of nitrate prediction errors. Monthly temporal compositing reduces random SST retrieval errors (without apparently introducing any significant representation error), leading to smaller increases ( mm) in the interquartile range of nitrate prediction errors and even a slight reduction ( mm) in RMS error (because SST errors partially compensate regression model errors for some of the largest prediction errors). [48] In order to characterize the effect of possible errors in SST estimates of mixed-layer bulk temperatures due to daytime near-surface stratification and heating, we also characterized the accuracy of predictions using SST composites derived from nighttime overpasses only. We found no significant difference in predictive skill, which we attribute to reduced prediction temperature-error sensitivity in warmer mixed layers (where daytime near-surface stratification and heating is expected to occur more frequently). [49] Thus, based on this preliminary analysis, we conclude that the use of remotely sensed SST to estimate mixed-layer temperature errors do not make a significant additional contribution to the current error budget for predictions of the seasonal variation of nitrate concentrations on the transect. SST errors may, however, become an important limitation when attempting to predict interannual and/or small-scale spatiotemporal variability in nitrate concentrations (particularly in months when mixed-layer temperatures are coldest because of the temperature dependence of nitrate prediction errors described in section 2.4) Correlation Between Nitrate Prediction Errors and Remote-Sensing Chla [50] Goes et al. [1999] have demonstrated that polynomial functions of surface chlorophyll concentrations are beneficial predictors in regression models for the northern and equatorial Pacific, accounting for local and regional differences in temperature-nitrate relationships due to phytoplankton nitrate uptake. Although we were unable to introduce chlorophyll as a model predictor (because of lack of available in situ data), we have analyzed the correlation between BMT nitrate prediction errors and remotely sensed Chla to assess to potential utility of Chla as a regression model predictor in the New Zealand region. [51] NASA Global Area Coverage SeaWiFS radiances were processed with SeaDAS v4.5 to derive 8-day Chla composites for the period of each BMT voyage. Chlorophyll concentrations at transect sample locations were estimated using the median binning procedure described for SST. Validation of SeaWiFS Chla retrievals in the New Zealand region indicates regional retrieval errors are 35% (consistent with the nominal target accuracy of the SeaWiFS mission) but suggests biases are water mass dependent [Richardson et al., 2004]. The correlation between nitrate prediction errors and remotely sensed Chla was characterized for the subtropical and frontal (S2 and S3) and subantarctic (S4) water masses accordingly. [52] Nitrate prediction errors are illustrated as a function of observed (remote-sensing 8-day composite) Chla concentration in the left-hand panels of Figure 6. A linear regression model explains 30 80% of the variance in the nitrate prediction residuals, and these correlations are significant at the 1% confidence level in all water masses. [53] The regression relations derived for water masses S2 and S4 have been applied to the subtropical and STF (S2 and S3) and subantarctic (S4) water masses, respectively, to estimate the chlorophyll-corrected nitrate concentrations dno 3 0 : dno 3 0 ¼ dno 3 þ d 0 þ d 1 :Chla where (d 0, d 1 ) are equal to (1.1, 3.25) for subtropical and STF waters and (2.5, 8.04) for subantarctic waters. The corresponding chlorophyll-corrected nitrate prediction errors illustrated in the right hand panels of Figure 6 and tabulated in Table 4. [54] Although the corrections are derived using and applied to the same data sets, and may not be representative of predictive accuracy for independent data sets, the results are nonetheless encouraging. The chlorophyll correction reduces the seasonal prediction biases in all water masses ð4þ 9of13

10 Figure 6. Scatterplots of nitrate prediction errors (NPE) versus remotely sensed chlorophyll and nitrate prediction errors after the chlorophyll correction described in section has been applied to the Biophysical Mooring Transect data set. Nitrate prediction errors greater than 4 mm are associated with misclassified subantarctic waters (small dots) and have been excluded when estimating the linear regression coefficient for the S3 class. significantly, chlorophyll-corrected nitrate predictions explain 80 90% of the observed variation in nitrate concentrations, and RMS nitrate prediction errors in the subtropical (S2) water mass are reduced to 0.4 mm. [55] When these same corrections are applied to predictions using monthly mean remote-sensing SST composites (see Table 4), RMS prediction errors are also substantially improved, although SST-based prediction errors are higher by mm in the S2 and S4 classes, compared to predictions using the in situ temperature measurements (prediction errors are equal in the S3 class, where the effects of water-mass misclassification make a substantial contribution to the overall error budget). [56] These results suggest that the inclusion of Chla as a predictor is the key to making seasonally unbiased predictions of nitrate concentrations in the subtropical and frontal waters of the New Zealand region, where the temporal variation of surface chlorophyll concentrations is essentially in phase with the temporal variation of biological nitrate uptake. More extensive in situ sampling, potentially including measurements of dissolved iron, silicate, and chloro- Table 4. Summary of the Correlation (r 2 ) Between Nitrate Prediction Errors (Using the Observed In Situ Temperature Record) and Remotely Sensed Chlorophyll, and Nitrate Prediction Error Characteristics After a Chlorophyll Correction has Been Applied to Nitrate Predictions for the Biophysical Mooring Transect Data Set a Class N r 2 RMSE FEV S (0.47) 0.93 S (1.58) 0.84 S (1.10) 0.84 a Values in brackets are the RMS errors for predictions using monthly mean remote-sensing SST in conjunction with the chlorophyll correction. 10 of 13

11 Table 5. Summary of the Median Nitrate-Depletion Temperatures (NDT) in the Latitude Bands S and S Between 150 E and 160 W Reference NDT, C S S Reported Value Depth Range Method of Estimation This Study Mixed layer Cubic regression root Kamykowski et al. [2002] a z 1000 m. Median T, nitrate 5 mm Switzer et al. [2003] z 1000 m. Cubic regression root Switzer et al. [2003] z 1000 m. Percentile-based T, nitrate 5 mm This Study Mixed layer Median T, nitrate 5 mm This Study z 1000 m. Median T, nitrate 5 mm This Study Mixed layer Lower quartile T, nitrate 0.1 mm phyll concentrations, will be required to elucidate the reason(s) for high nitrate variability and improve predictive accuracy within the HNLC waters southeast of New Zealand. However, it is possible that surface chlorophyll concentrations may act as a predictive proxy for limiting nutrient availability. This has yet to be demonstrated but will be addressed in upcoming work to extend the regression models to include Chla as a predictor. 4. Comparison With Other Published Regional and Global Studies 4.1. Characterization of Predictive Accuracy [57] Mixed-layer nitrate prediction errors have been reported for regression models for the extratropical North Atlantic [Garside and Garside, 1995] and North Pacific [Goes et al., 1999, 2000]. [58] The North Atlantic region considered in the study of Garside and Garside [1995] (35 65 N, W) is characterized by light and nitrate limitation of phytoplankton growth and is thus comparable to New Zealand subtropical (and possibly STF) waters [Longhurst, 1998]. Garside and Garside [1995] report a RMS prediction error of 1.0 mm for their regression data set. [59] The spatial sampling of the extratropical regression set of Goes et al. [1999, 2000] spans the region N, E and S, E, covering a diverse range of biogeochemical provinces, including the oligotrophic North Pacific tropical gyre, the Kuroshio and Oyashio current systems and the HNLC Western Pacific subarctic gyre and subantarctic water masses. They report a regression set RMS prediction error of 2.2 mm. The sampling of the independent (validation) data set used by Goes et al. [2000] is more restricted in geographic range, sampling the region N, 125 E 115 W of the North Pacific Ocean on 11 trans-pacific voyages [Nojiri et al., 1999]. They report a RMS error of 1.74 mm for predictions based on monthly mean remotely sensed SST and Chla for this independent data set. [60] The magnitude of these errors will depend on the fraction of nitrate variance explained by model predictors, the ambient nitrate concentrations, and the inherent spatial, seasonal, and/or interannual variability in the temperaturenitrate covariance in the region of study [Garside and Garside, 1995; Chavez et al., 1996; Henson et al., 2003] and on the spatiotemporal sampling characteristics of the regression and validation data sets, and clearly, we cannot distinguish between these different factors. Nonetheless, at face value, there seems to be no significant difference between the magnitude of nitrate prediction errors for the extratropical North Atlantic, North Pacific (1 2 mm), and the errors we report for the New Zealand region, particularly when water mass sampling characteristics are taken into account. Error estimates reported in the literature for independent predictions of mixed-layer nitrate concentrations in the equatorial region also cover a similar range ( mm [Gong et al., 1995; Chavez et al., 1996]). [61] Given the magnitude of these errors, the question still remains as to whether the regression models can accurately predict interannual variations in seasonal nitrate concentrations and whether predictions are sufficiently accurate to be of use for the estimation of mixed-layer nitrate budgets or in biological modeling. For example, if nitrate half saturation constants are of the order of 1 mm or less (cf. estimates reported by Eppley et al. [1969] for marine phytoplankton) then errors of 1 mm in estimated nitrate concentrations will lead to large errors in the inferred growth rate as nitrate concentrations become limiting Nitrate-Depletion Temperatures [62] The spatial patterns of NDTs derived in this study and illustrated in Figure 3 are qualitatively consistent with those derived in the square analyses of Kamykowski et al. [2002] and Switzer et al. [2003] for subtropical and frontal waters in the New Zealand region; all studies show a marked decrease in NDT with increasing latitude south and a secondary variation with longitude (in particular, NDT at a given latitude decreases by 2 4 C east of 180 E) within our study domain. Quantitative agreement between our cubic root NDT estimates for subtropical and frontal waters and the results of Kamykowski et al. [2002] and Switzer et al. [2003] is poor. Median values of the NDT estimates for the latitude bands S and S between 150 E and 160 W are summarized for the three studies in Table 5 and show the NDT predicted by our regression model to be systematically higher by 4 8 C. As discussed in section 2.5, our regression model NDT estimates may overestimate minimum observed NDT by 1 3 C, but this is still not sufficient to account for the systematic discrepancy between the various NDT estimates. [63] In contrast to our analysis, which only considers data within the mixed layer, the studies of Kamykowski et al. [2002] and Switzer et al. [2003] are both based on the analysis of Kamykowski and Zentara [1986] of NODC data in the upper 1000 meters of the water column. This choice of vertical sampling is expected to lead to lower cubic root and percentile-based NDT estimates [Kamykowski, 1987]. We have explicitly calculated the median temperatures of observations satisfying the threshold criterion of Kamykowski and Zentara [1986] (5 mm) in the upper 11 of 13

12 1000 meters of the water and the mixed layer using our regression data set. These estimates are reported in Table 5 and may be compared directly with the tabulated NDT estimates reported by Kamykowski et al. [2002]. While the threshold definition appears to be the principal factor governing the median-based NDT estimates, the use of data sampling the upper 1000 meters of the water column leads to a further reduction in the estimated NDT by 1 C. The median temperature NDT estimates are relatively insensitive to inclusion/exclusion of data from the S4 water mass class because these observations rarely satisfy the threshold criterion. [64] NDT reported by Kamykowski et al. [2002] and Switzer et al. [2003] based on percentile analyses for the subantarctic waters east of New Zealand (13 and 15 C) imply the occurrence of seasonal nitrate depletion. However, our observations show no evidence of nitrate depletion in this water mass at these temperatures. These errors in model NDT predictions are almost certainly due to the use of a simple and coarse-scale geographic discretization which fails to account for the different water masses present within the grid cell spanning this region. We believe these NDT estimates actually characterize subtropical and frontal waters within the grid cell because, as noted above, observations from the S4 water mass class rarely satisfy the threshold criterion. [65] These results and discrepancies have important implications for the inference of nutrient availability based on the sign of the difference between estimated NDT and observed SST, as envisaged by Kamykowski et al. [2002] and Switzer et al. [2003]. The NDT estimates given in Table 5 for the S and S bands may be compared with the observed data for the (S1 and S2) and S3 classes and with the lower quartile of observed mixedlayer NDTs tabulated in the last row of Table 5. For a significant subset of observations in the data sets presented here, the NDT estimates of Kamykowski et al. [2002] and Switzer et al. [2003] are not indicative of nitrate depletion, that is, there are a range of temperatures greater than the estimated NDT where observed nitrate concentrations generally exceed detection limits. As discussed above, this is also true of their NDT estimates for the HNLC subantarctic water mass (S4) east of southern New Zealand. Conversely, there is also a significant subset of observations where nitrate is depleted at temperatures less than the NDT estimates based on the cubic roots of our mixed-layer regression model. Definition of a robust measure of nitratedepletion temperature is clearly not trivial, and interpretation of SST NDT differences in terms of nutrient availability needs to be carefully validated with independent in situ measurements. 5. Conclusions and Further Work [66] We have derived climatological annual temperaturenitrate regression relationships for mixed-layer waters of the New Zealand region which take account of the complex physical, chemical, and biological oceanography of the region and validated predictions using three independent in situ data sets. RMS prediction errors for the regression models range from 0.9 to 1.8 mm in subtropical waters, 1.6 to 1.9 mm in the Subtropical Front, and 1.4 to 2.5 mm in subantarctic waters and are comparable with errors reported in the literature for the North Atlantic and North Pacific. Furthermore, regression model predictions are more accurate than the CARS nitrate climatology for subtropical and subantarctic surface waters to the east of southern New Zealand because of systematic seasonal biases in the nitrate climatology. [67] However, the regression models, as implemented, have three identifiable and significant sources of error (systematic seasonal biases in nitrate predictions, unmodeled nitrate variability in subantarctic waters, and water mass misclassification), which currently limit predictive accuracy and hence compromise quantitative estimates of the mixed-layer nitrate budget for the New Zealand region. Our detailed analysis of NDT in the New Zealand region also indicates regression model estimates of NDT do not give an adequate description of observed NDT in subtropical and STF waters, and previously published NDT estimates incorrectly predict the occurrence of seasonal nitrate depletion in HNLC subantarctic waters east of New Zealand. [68] Thus, despite comparable accuracy with regression models for other regions, we conclude that improvements in model accuracy, and demonstrated skill in predicting observed interannual variability in nitrate concentrations, are required before applying our models to the entire study domain. Future work should address the known sources of error in the current regression model by introducing Chla as a predictor and investigating the use of remotely sensed SST gradients to locate surface temperature fronts and reduce the climatological water mass classification errors. Model validation should be extended to subtropical waters in the north and west of the study domain, beginning with data obtained on four recent NIWA voyages, and a detailed validation of predictions of interannual variability in nitrate concentrations should be undertaken using time series data from the ongoing BMT and Munida transect programs. [69] While the New Zealand region is undoubtedly a sparsely sampled and complex oceanographic region, many of the issues raised in this study are relevant to other regions of the world s oceans (and to productive oceanic frontal systems in particular) and highlight the importance of detailed regional validation of regression models and associated derived parameters (NDT and new production estimates) using spatially and temporally resolved in situ nutrient data sets. [70] Acknowledgments. The authors thank all the scientists who have made their nutrient measurements in this data-sparse region of the planet accessible to the wider research community; without their contribution, this work would not have been possible. We particularly thank Jeff Dunn (CSIRO) for providing CSIRO nutrient data sets and for his careful review of this manuscript. We also thank our colleagues Matt Walkington, George Payne, Phil Sutton, Steve Chiswell, Cliff Law, Graham Rickard, Michael Uddstrom, and Ken Richardson for useful discussions and for their ongoing contributions to data acquisition, processing and archive, and three anonymous referees whose comments improved this manuscript. This research was funded by the New Zealand Foundation for Research, Science and Technology contracts CO1X0223 and C01X0501. References Arrigo, K. (2005), Marine microorganisms and global nutrient cycles, Nature, 437, Banse, K. (1996), Low seasonality of low concentrations of surface chlorophyll in the subantarctic water ring: Underwater irradiance, iron or grazing?, Prog. Oceanogr., 37, of 13