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Quantifying Daytime Heating Biases in Marine Air Temperature Observations from Ships

Quantifying Daytime Heating Biases in Marine Air Temperature Observations from Ships APRIL 2023 C R O PPE R E T A L . 427 Quantifying Daytime Heating Biases in Marine Air Temperature Observations from Ships a a,b a a THOMAS E. CROPPER , DAVID I. BERRY , RICHARD C. CORNES , AND ELIZABETH C. KENT National Oceanography Centre, Southampton, United Kingdom World Meteorological Organization, Geneva, Switzerland (Manuscript received 22 July 2022, in final form 6 January 2023) ABSTRACT: Marine air temperatures recorded on ships during the daytime are known to be biased warm on average due to energy storage by the superstructure of the vessels. This makes unadjusted daytime observations unsuitable for many applications including for the monitoring of long-term temperature change over the oceans. In this paper a physics- based approach is used to estimate this heating bias in ship observations from ICOADS. Under this approach, empirically determined coefficients represent the energy transfer terms of a heat budget model that quantifies the heating bias and is applied as a function of cloud cover and the relative wind speed over individual ships. The coefficients for each ship are derived from the anomalous diurnal heating relative to nighttime air temperature. Model coefficients, cloud cover, and relative wind speed are then used to estimate the heating bias ship by ship and generate nighttime-equivalent time series. A variety of methodological approaches were tested. Application of this method enables the inclusion of some daytime observations in climate records based on marine air temperatures, allowing an earlier start date and giving an increase in spatial coverage compared to existing records that exclude daytime observations. SIGNIFICANCE STATEMENT: Currently, the longest available record of air temperature over the oceans starts in 1880. We present an approach that enables observations of air temperatures over the oceans to be used in the creation of long-term climate records that are presently excluded. We do this by estimating the biases inherent in daytime tem- perature reports from ships, and adjust for these biases by implementing a numerical heat-budget model. The adjust- ment can be applied to the variety of ship types present in observational archives. The resulting adjusted temperatures can be used to create a more spatially complete record over the oceans, that extends further back in time, potentially into the late eighteenth century. KEYWORDS: Climate; Diurnal effects; Surface temperature; Data quality control; In situ atmospheric observations; Ship observations 1. Background and motivation bias adjustment of DMAT, and if this adjustment can be deter- mined accurately the sampling and coverage of MAT will be Marine air temperature (MAT) observations from ships improved throughout the record. form a long-term climate record used to construct gridded Global mean surface temperature (GMST) anomaly data- data products as either the principal data source (Berry and sets, combining observations over land, ice, and ocean, have Kent 2009, 2011; Kent et al. 2013; Cornes et al. 2020; Junod used SST in lieu of MAT for their ocean component (Lenssen and Christy 2020) or for bias adjustment of sea surface tem- et al. 2019; Morice et al. 2021; Huang et al. 2020), including in perature (SST) products (Huang et al. 2017; Kennedy et al. the sixth Intergovernmental Panel on Climate Change Assess- 2019). These gridded products only use MAT observed during ment Report (Gulev et al. 2021). GMST is used instead of nighttime (NMAT) to exclude data affected by solar heating global surface air temperature (GSAT) for three main of the instrument and local ship environment during daytime reasons: there are more (all-hours) SST observations than (DMAT). Using only NMAT approximately halves the num- NMAT; quantification of SST measurement bias and uncer- ber of available observations and limits the temporal extent tainties is more mature than for MAT (Kennedy et al. 2019); of any MAT-based dataset as early observations were often and the belief that SST anomalies are more reliable than only recorded during the daytime (Fig. 1a). For example, two MAT at large spatial scales (Kent and Kennedy 2021). It was recently published NMAT datasets begin in 1880 (CLASSnmat; also asserted that large-scale anomalies of SST and MAT Cornes et al. 2020) and 1900 (UAHNMAT; Junod and Christy display similar variability and trends (Huang et al. 2017), 2020). Extending the MAT record further back in time requires although this is increasingly being questioned (e.g., Cowtan et al. 2015; Richardson et al. 2016; Rubino et al. 2020). Here we demonstrate a method to estimate the daytime heating Denotes content that is immediately available upon publica- biases in MAT observations on a ship-by-ship basis that can tion as open access. be applied throughout the observed record. The ultimate goal is to use these adjusted data to create a GSAT record based on air temperature over land, ice, and ocean. This will facili- Corresponding author: Thomas E. Cropper, thomas.cropper@ noc.ac.uk tate comparison of the observed surface temperature record DOI: 10.1175/JTECH-D-22-0080.1 Ó 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 428 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 FIG. 1. Sampling characteristics of MAT observations from ship reports in ICOADS (Freeman et al. 2017). (a) The 1784–2020 percentage of MAT observations recorded annually during daytime (DMAT, black line, left-hand axis), the red dashed line indicates 50% daytime obser- vations. The solid blue line (right-hand axis) is the annual total number of MAT observations, and the dotted blue line is the number of MAT observations associated with a ship track of 12 or more reports, with diurnal sampling, and including only observations with associated cloud and relative wind speed (V) observations. Free text comments indicate the annual average number of MAT observations for select periods (or the total amount for 1784–1853). (b) Stacked plot of the percent of MAT observations with a corresponding cloud and/or V value. The red area indicates reports with both cloud and V; the blue area indicates reports with neither. Reports with either cloud or V, but not both, are in- dicated in green and yellow, respectively. The dotted line indicates MAT with V but without cloud when the green color overrides. When yellow is visible, lack of cloud information is the major constraint on applying the heating bias model introduced in section 2a; when green is visible, lack of V is the constraint. (c) Stacked plot of the percentage of MAT observations with an associated present weather code (WW; green) and with WW code indicating precipitation (red). The dashed line shows the percentage of extant WW indicating precipitation. with the output of climate models (Jones 2020), which most related bias on 17 ships extracted from the VOSClim database straightforwardly provide estimates of GSAT rather than (Berry and Kent 2005). In the construction of the NOC Surface GMST. Flux and Marine Meteorological Dataset (Berry and Kent 2009, 2011)the BKT model was used to adjust the MAT obser- vations obtained from the International Comprehensive Ocean– 2. Methods Atmosphere Dataset (ICOADS; Freeman et al. 2017)for the period 1973–2014. However, in order to simplify the calculations a. The Berry et al. (2004) model in that analysis, a fixed annual set of coefficients was applied Berry et al. (2004, hereafter BKT) developed a model to across all ships. Here we develop coefficients ship by ship to give quantify heating-related biases in MAT, accounting for the an adjustment for heating bias that reflects the characteristics of energy accumulation and release by the superstructure of a particular ship. ships. The BKT model was developed and tested using tem- We define several measures of temperature in Eqs. (1)–(3), perature values recorded on board the Ocean Weather Ship which are illustrated in Fig. 2: T is the true air temperature; air Cumulus during 1988 and later used to examine exposure- T is the measured air temperature; T is the background ship nt APRIL 2023 C R O PPE R E T A L . 429 TABLE 1. Empirical coefficients; V is relative wind speed (m s ). a) Coefficient Definition Min Max 22 x A a /mc 0.0001 0.1 1 s s 20 x x V (A /mc)h c m Oct 22 Oct 24 Oct 26 Oct 28 Oct 30 x 0.0001 10 b) x 222 x (A /mc)h 0.0001 10 5 c o 0 energy transfer component (Q ), shown by BKT to account LW Oct 22 Oct 24 Oct 26 Oct 28 Oct 30 for a maximum ;3% of the estimated heating bias. Assuming Date d(T )/dt ’ 0, Eq. (4) becomes air FIG.2. (a) T (black line, circles show individual observations), ship dDT err T (T 2DT ) (blue), and T (red) for the ship Raphael dur- adj ship BKT nt mc 1 (h 1 h )A DT 5 a A R (a 1 b sinu)sinu: m o c err s s top i i dt ing October 1884 and (b) DT (black) and DT (blue, dark diur BKT (7) shading corresponds to 61 standard deviation of the DT value BKT from the 60-member ensemble and light shading corresponds to Substituting the coefficients given in Table 1 into Eq. (7) gives 62 standard deviations). dDT err x 1 (x V 1 x )DT 5 x [R (a 1 b sinu)sinu], 3 5 err 1 top i i dt nighttime air temperature (see section 2b); DT is the change err (8) in measured temperature due to ship heating; DT is an esti- diur mate of DT ; DT is the estimate of the temperature dif- err BKT where V is relative wind speed (m s ) and the empirical coef- ference from the BKT model; and T is the measured air adj ficients x represent terms of the energy budget model 1,3,4,5 temperature adjusted using the BKT model: (Table 2). We have redefined the coefficients x and x to in- 3 5 T 5 T 1DT ’ T 1DT , (1) corporate and exclude x (used in the original BKT defini- ship air err air diur 2 tion), so cooling depends on (x V 1 x ) and heating on x . 3 5 DT 5 T 2 T , (2) Expansion of the sinu terms in Eq. (8) and further substitu- diur ship nt tions (Table 2) gives T 5 T 2DT : (3) adj ship BKT dDT err 2 1 h (DT ) 5 h 1 h cos(f) 1 h cos (f), (9) 1 err 2 3 4 dt The BKT model relates T and T (bothmeasuredinKelvin) air ship to the heat exchange, Eq. (4): where f is hour angle in radians. The solution to Eq. (9), gives the value of the heating error at any time during daylight d(T ) ship mc 5 Q 1 Q 1 Q 1 Q : (4) hours (for a full description of the solution, see BKT): SW LW Conv Cond dt h h a h 2 3 1 In this equation m is the mass (kg) and c the specific heat DT 5 1 1 sin(f) 1 cos(f) err;day 2 h h 1 a a 21 21 1 1 capacity (J kg K ) of the sensor environment (that part of the ship that affects the measurement), t is time (s), Q is the 2 2 SW 4a h cos(f) sin(f) h cos (f) 1 4 1 1 1 1 shortwave irradiance [Eq. (5)], and Q and Q are the Conv Cond 2 2 h 1 4a 2a 4a 2h 1 1 rates of heat transfer between the ship and the atmosphere through convection and conduction [all in W m ,Eq. (6)]: 1 k exp(2h t), (10) int 1 Q 5 a A R (a 1 b sinu)sinu, (5) SW s s top i i where a is 2p/12. The integrating factor k can be deter- int mined assuming the sensor environment is in equilibrium at Q 1 Q 5 (T 2 T )A (h 1 h ): (6) Conv Cond air ship c m o sunrise (dDT /dt ; 0) such that diur Here, a is the solar absorptivity of the sensor environment, TABLE 2. Substitutions used in solving the BKT model; dec is A is the surface area normal to the direction of the incoming the solar declination and the k terms use latitude in radians. direct solar radiation (m ), R is the solar radiation at the top Parameter Substitution top of the atmosphere (we use 1368 W m ), u is the solar ele- vation, a and b are cloud-cover-dependent coefficients (index 4 i i h x V 1 x 3 5 i indicates categories of total cloud cover quantities by oktas; h x R (ak 1 ak ) 1 top 1 1 h x R (ak 1 2bk k ) from Dobson and Smith 1988), h and h are the convective 3 1 top 2 1 2 m o 22 21 h x R (bk ) and conductive heat transfer coefficients (W m K ), and 1 top 2 2 k sin[lat sin(dec)] A is the surface area of the sensor environment (m ). Follow- k cos[lat cos(dec)] ing Berry and Kent (2005) we exclude the small thermal ∆T (°C) T (°C) 430 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 2 [Eq. (5)]become a and b as specific coefficients are avail- i,lat i,lat h 4a h cos(f ) sin(f ) h cos (f ) 2 4 sr sr 1 sr k 52 1 1 able for 108 latitudinal bands. Presently the BKT model imple- int 2 2 2 h 4a 1 h 2a 4a mentation requires the solar parameterization to be in the same form as the okta model, precluding the use of, for exam- 1 ah h 3 1 1 1 sin(f ) 1 cos(f ) , (11) ple, the parameterization of Aleksandrova et al. (2007). 2 sr sr 2h a 1 h a 1 1 Other than adjusting nine oktas to eight when the ICOADS present weather code indicates precipitation (Aleksandrova where f is the hour angle at the time of sunrise. At night the sr et al. 2018), we do not make any adjustments to the ICOADS heating error is cloud record. Considering long-term temporal trends, biases likely remain due to heterogeneous recording practices and DT 5 (T ) exp(2h t ), (12) err;night err;ss 1 ss conversions across the diversity of ICOADS source data. For example, cloud observations pre-1949 (when cloud recording where t is the time elapsed since sunset. ss changed from tenths to oktas) may be biased low due to being Using Eq. (10) (daytime) or Eq. (12) (nighttime) DT at BKT double adjusted if the original observation was in oktas (Gulev any location and time can be calculated using the coefficients and Aleksandrova 2020). x along with cloud cover and V. 1,3,4,5 d. Optimization b. Estimation of the temperature error due to ship heating The optimization selects values for the x coefficients that min- Both the true diurnal variation of T and the heating error air imize the difference between DT and DT using Eqs. (10) diur BKT are poorly known. BKT estimated the heating error (DT )in err and (12), and using several different cost functions. Coefficients two ways: as the MAT anomaly from the local midnight to are derived for selected individual ships, but could also be ap- sunrise mean and as the T 2 SST difference. The former is ship plied across a group of ships thought to have similar DT diur likely to overestimate DT as it incorporates the true diurnal err characteristics. cycle of T , while the latter is likely to be an underestimate. air The solution uses the L-BFGS-B (Byrd et al. 1995) solver Given the difficulty of making an adjustment that accounts in R (an option in the optim function; R Core Team 2019) for the real diurnal cycle of T , a pragmatic approach was air with lower and upper coefficient limits from Table 1. We min- taken to estimate DT [Eq. (2)], and hence the adjustment diur imize six different cost functions to evaluate the BKT model [DT , from Eqs. (10) and (12)] relative to an estimated BKT solutions. Each cost function tests different aspects of the background nighttime temperature (T ). First, an estimate of nt goodness of fit and the spread across the cost functions is the expected diurnal SST anomaly associated with every value wider giving more realistic estimates of fit uncertainty: of T was calculated as a function of cloud cover and wind ship speed following Morak-Bozzo et al. (2016) and subtracted 1) The residual root-mean-square error (RMSE), from T . Nighttime values were then calculated using the ship 2 RMSE 5 (1/n)∑ (DT 2DT ) , the RMSE k51 diur BKT k k normal definition of 1 h after sunset to 1 h after sunrise gives the simplest measure of the fit. (Bottomley et al. 1990). These nighttime averages were as- 2) Weighted RMSE (RMSE ) only using MAT observation signed to the time of each sunrise and were linearly interpo- times between 3 and 8 h after sunrise. RMSE gives lated over the 24-h period for each ship (T ). This approach nt weight only to hours where DT values are expected to BKT allows the construction of climate records from a combination be largest. of adjusted all-hours MAT with unadjusted NMAT. 3) RMSE , where the RMSE is calculated from bin means c. Solar parameterization of data in 2 m s V and local-hour intervals. 4) RMSE ,as RMSE but with 5 m s V and 2-hourly inter- V V The BKT model uses cloud-cover-dependent coefficients to 5 2 vals. Both RMSE and RMSE are designed to greater V V estimate solar radiation based on location, date, and time. 2 5 weight the importance of minimizing the (DT 2DT ) diur BKT BKT used coefficients from the Dobson and Smith (1988) residual through the day and across values of V. okta model, which were derived from a limited geographical 5) RMSE 5 (1 2 l)RMSE 1 l(|DW 2 2|), where DW is DW region. Using the same okta model as Dobson and Smith the Durbin–Watson statistic and l is a scaling factor that (1988), we generate a set of updated coefficients. To do this, we set to 0.3. RMSE , is used to down-weight solutions DW we used data from the Surface Solar Radiation dataset–Heliosat where the residual displays autocorrelation. version 2.1 (Pfeifroth et al. 2019), which covers most of the 6) RMSE 5 (1 2 l)RMSE 1 l(KS), where KS is the KS Atlantic (658S–658N, 658W–658E). We collocate the 30-min Kolmogorov–Smirnov statistic. This cost function gives sampling interval of satellite instantaneous incoming solar radi- greater weight to solutions where the cumulative sums of ation values with ICOADS cloud observations for the period daytime values of DT and DT are small. diur BKT 1983–2017 and use this information to generate updated okta model coefficients (https://git.noc.ac.uk/glosat_tc/okta_model). An ensemble of these cost functions is used to test different as- The resulting coefficients produce a less peaked solar cycle than pects of the structure of the residual (DT 2DT )toensure diur BKT the original Dobson and Smith coefficients and reduce the over- a reasonable fit throughout the day and across all cloud-cover all RMSE of estimated to satellite incoming solar radiation by and relative wind speed combinations. Avoiding unphysical start- ;10% for data not included in the fit. The a and b terms ing coefficient combinations improves efficiency and helps to i i APRIL 2023 C R O PPE R E T A L . 431 TABLE 3. Sixteen ships selected from ICOADS to illustrate the results of fitting the BKT model. Deck refers to the original source data collection in ICOADS. Metadata contain information that could be readily obtained via an Internet search of the original call sign or name of the ship. The ship U.S. Navy 12388 samples at 0800, 1200, and 2000 local hour, a common feature of currently available WWII-era ships. Ship Year Hourly sampling frequency Deck Metadata USS Constitution 1854 2 721 Sail, wood USS Despatch 1858 2 701 Screw steamer USS Merrimac 1858 2 721 Steam frigate Mary 1884 2 704 Unknown Panay of Salem 1884 2 704 Sail Raphael 1884 2 704 Sail, wood Chosen Maru 1916 4 762 Cargo, steel, screw steamer Kanagawa Maru 1916 4 762, 706 Passenger, steel, screw steamer U.S. Navy 12388 1942 3 times daily 195 Unknown U.S. naval ship U.S. hourlies 2129 1955 1 116, 117 Unknown Merchant Marine 0805 1955 3 116, 117 Unknown Kajtum 1975 6 927 Cargo ship Westfalen 1995 3 926, 892, 888 Passenger/cargo ship Cape Azalea 2014 1 992 Bulk carrier Polar Resolution 2014 1 992 Oil tanker Alliance St. Louis 2020 1 798, 992 Vehicle carrier avoid local minima so we use a pool of ;350 precalculated sets Figure 3 shows the mean DT , DT , and residuals diur BKT (DT 2DT ) using the best-fit set of coefficients for each of starting coefficients to initialize the fit. For each ship, we ran- diur BKT cost function (i.e., six lines) for the ship Mary (Figs. 3a–d), domly select 10 sets of starting coefficients and 5 subsets of 70% split across local hour of the day, cloud cover, 2 m s intervals of available days. This gives an ensemble of 300 sets of coeffi- of V,and 108 latitude bins. Following BKT we use a target accu- cients (10 starting values, 5 data subsets, and 6 cost functions), racy of 60.28C. Figure 3 shows that across the input parameters and any convergence failures are rerun until there are 50 sets of of the BKT model (time/position, cloud cover, and V), the heat- coefficients per cost function. Unless otherwise stated, hereafter ing bias is removed, with bin-mean residuals that are generally the DT value is the ensemble mean taken from 60 realizations BKT within 60.28C, and the bin-mean local-hour average residuals of the DT using the 10 best-fit time series from each of the 6 BKT are always within the 60.28C target. However, for this ship the cost functions. BKT model appears to underadjust for clear skies (0 okta) and a V of 22–24 m s , although these bins are poorly sampled 3. Results (14 observations for 0 oktas and 45 and 16 observations for the 22 and 24 m s bins, respectively). a. Fitting to individual ships Figures 4a–c display the DT , DT , and residuals diur BKT To illustrate the application of the BKT model, we show (DT 2DT ) across all 16 ships as a function of the num- diur BKT results from 16 ships covering different time periods, sam- ber of hours since sunrise. DT can be ,08C, as MAT values diur pling frequencies, and original input sources (Table 3). close to sunrise will be cooler than the nighttime mean MAT. The data for these ships were obtained from the ICOADS DT is always above 08C, and this is reflected in the nega- BKT (Freeman et al. 2017) archive: release 3.0.0 up to 2014 and tive residuals for hours 0–1 and $18. Aside from the 28–34, release 3.0.1 thereafter. Quality checking has been applied 21 46, and 50 m s wind speed bins and 608N latitude bin, the to the data prior to model fitting (appendix). The reports bin-mean residuals (Figs. 4c–f) are all within 60.28C. The from these 16 ships contain all of the variables required to pattern of a relative DT 2DT underadjustment for diur BKT fit the adjustment model, and all have reported data over at hours 3–5 and 9–14 (Fig. 4c) appears consistent regardless of least 150 days. Collectively, these ships provide a global whether a single cost function is used or a different sample of sample of data between 608Sand 608N, with 64% of obser- ships is selected (not shown). Possible causes are inaccurate vations in the tropics (308N–308S), 26% in the Northern estimates of solar radiation [Eq. (5)] or systematic errors in Hemisphere, and 10% in the Southern Hemisphere. Longi- our estimate of DT . diur tudinally, there are 31% of observations in the Atlantic The mean overall DT 2DT residual for each individ- diur BKT Ocean, 29% in the Pacific Ocean, 18% in the Indian Ocean, ual ship is always within 60.28C, with 11 out of 16 ships within 17% in the South China Sea and adjoining gulfs/seas, with 60.058C. The largest residual (0.148C) is found for the U.S. 3% in the Mediterranean Sea and remainder (2%) of obser- Navy 12388 ship. The WWII period is one of the more diffi- vations from minor ocean basins. cult periods to apply the BKT model correction, due to the Figure 2 shows the diurnal adjustment for the ship Raphael dur- limited number of observations from which determine T ,as nt ing October 1884. Figure 2a shows T , T ,and T . Figure 2b well as the occurrence of and a warm bias in nighttime obser- ship nt adj shows the estimates of DT and DT . vations over 1942–46 (Cornes et al. 2020). diur BKT 432 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 a) b) c) d) 0 5 10 15 20 02468 0 5 10 15 20 25 −40 −20 0 20 40 Local Hour Cloud (Okta) V (m/s) Latitude FIG.3.The mean DT (solid blue line), DT (dashed lines), and residual (dotted lines) for the ship Mary (Table 3) grouped by diur BKT (a) local hour (every 2 h), (b) cloud cover (one okta intervals), (c) 2 m s intervals of V,and (d) 10 latitude bins. Individual dashed and dotted lines represent the best-fitting DT from each of the six cost functions described in section 2d. The horizontal red lines indicate BKT 08 and 60.28C limits. Each bin contains at least 100 observations, except for 0 and 7 oktas, 18 and .20 m s ,and 408 latitude. To determine the relative improvement of MAT data (Fig. 4c), as expected. The RMSE reduction (DT cf. diur after applying the BKT model adjustment, DT and DT 2DT ) ranges from 15% (U.S. Navy 12388, diur diur BKT DT 2DT should be compared. First, it is clear that 1.538–1.358C) to 53% (Kajtum,2.458–1.138C), with a mean diur BKT the spread of DT values (Fig. 4a) is greater than the of 28% across all 16 ships. The RMSE reduction signifi- diur spread for both DT (Fig. 4b)and DT 2DT cantly correlates (r 5 0.92) with the magnitude of DT . BKT diur BKT diur a) b) c) 0 4 8 12162024 048 12 16 20 24 048 12 16 20 24 Hours After Sunrise Hours After Sunrise Hours After Sunrise d) e) f) 0 123 456 7 8 0 1020304050 −60 −40 −20 0 20 40 60 Okta V (m/s) Latitude FIG. 4. Boxplots displaying the bin mean (solid line), bin mean 61 standard deviation (box limits), and 5th and 95th percentiles (whiskers) for (a) DT and (b) DT as grouped by the number of hours after sunrise. (c)–(f) The DT 2DT residual when diur BKT diur BKT grouped by (c) the number of hours after sunrise, (d) cloud cover, (e) 2 m s intervals of V,and (f) 108 latitude bins. All 16 ships from Table 3 are included and the DT is taken as the ensemble mean across 60 realizations of the DT (the 10 best-fit realizations from BKT BKT each of the 6 cost functions described in section 2d). The horizontal solid red and dark-red dashed lines indicate zero and 60.28C limits, respectively. The box widths correspond to the square root of the sample size in each bin. MAT (deg.C) MAT (deg.C) −0.2 0.0 0.2 0.4 0.6 0.8 1.0 −4 −2 0 2 4 −2 −1 0 1 2 3 4 5 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 MAT (deg.C) MAT (deg.C) −4 −2 0 2 4 −2 −1 0 1 2 3 4 5 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 MAT (deg.C) MAT (deg.C) −4 −2 0 2 4 −3 −2 −1 0 1 2 3 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 APRIL 2023 C R O PPE R E T A L . 433 a) USS Constitution | 1854 b) USS Despatch | 1858 c) USS Merrimac | 1858 d) Raphael | 1884 14 13 13 13 e) Mary | 1884 f) Panay of Salem | 1884 g) Kanagawa Maru | 1916 h) Chosen Maru | 1916 13 13 13 13 i) US Navy 12388 | 1942 j) US Hourlies −129 | 1955 k) Merchant Marine 0805 | 1955 l) Kajtum | 1975 13 13 14 14 m) Westfalen | 1995 n) Cape Azalea | 2014 o) Polar Resolution | 2014 p) Alliance St. Louis | 2020 13 14 13 13 04 8 12 16 20 0 4 8 12 16 20 04 8 12 16 20 04 8 12 16 20 Local Hour FIG. 5. The mean (solid line), standard deviation range (darker shading), and 5th–95th-percentile range (lighter shading) for DT for BKT the 16 different ships (Table 3) under fixed environmental conditions of 15 m s V, four oktas cloud cover, 2208 longitude, Julian day 150, and variable latitudes 258N (red), 508N (green), and 658N (blue). The vertical line is at 1300 local time and the number in the upper left of each panel indicates the peak heating hour at 258N. It is not expected that DT will exactly match DT . Re- around the peak heating hours, and the uncertainty range BKT diur siduals will include the effects of any model misfit, errors in V, across different ships will relate to the magnitude of the DT diur cloud cover, or the parameterization of solar radiation and and the environmental conditions, which will depend on the other nonsystematic differences such as weather effects. The region in which the ship was operating. Figure 5 illustrates the magnitude and variability of the residuals, and the percentage importance of obtaining a BKT model solution for individual changes, will depend on the relative sizes of the adjustment ships, but also suggests that coefficients can be estimated for required and these other factors. groups of similar ships (see sections 3c and 3e). Figure 5 illustrates values of DT under fixed environ- If a ship contains observations where it was not possible to BKT mental conditions and for selected latitudes for each ship, us- determine T , but there are sufficient T observations for nt nt ing the 60 ensemble member BKT model coefficients for each that ship to fit the BKT model, then every observation with a ship. Under these conditions, DT in terms of amplitude corresponding cloud and V can be adjusted since sets of BKT BKT and timing is similar for some ships (e.g., the pairing of the model coefficients can be determined. USS Merrimac and Kanagawa Maru), and different for b. Estimating missing cloud and V values others. To adjust the Kajtum using the coefficients generated for the Chosen Maru would leave the Kajtum still retaining a Depending on the observation source, MAT will not always large MAT diurnal cycle, whereas the inverse operation be accompanied by cloud and wind observations. Figure 1 shows would generate a physically unrealistic diurnal cycle for the the proportion of potentially adjustable MAT observations using Chosen Maru. Uncertainties across the ships are largest the BKT model has been decreasing since a sustained peak in ∆T BKT 434 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 a) b) c) d) Raw Raw w/ Stock Coeffs V Infill Okta Infill V & Okta Infill V & Okta Infill w/ Stock 0 5 10 15 20 02 468 0 102030 4050 −60 −20 20 60 Hours After Sunrise Okta V (m/s) Latitude FIG 6. (a)–(d) The bin-mean DT 2DT residual and (e)–(h) the bin mean of the 60-member standard deviation of the DT 2DT diur BKT diur BKT residual. Six different approaches to defining the DT were used: the “normal” approach using raw observational data (black line BKT with circles), using infilled cloud (magenta line), V (green line), both cloud and V (blue line with circles) alongside fitting the DT BKT using “stock” coefficient combinations for raw observational data (black line with crosses) and infilled cloud and V (blue line with crosses). the 1980s, likely due to increasing contributions from automatic resulting in the same hourly rounded (0.18C) values of the weatherstationsinICOADSinthe modern era (Freeman et al. DT throughout the day. This results in a stock coefficient da- BKT 2017). taset of 2500 coefficients, suitable for adjustment of data from As a means to examine the impact of infilling data on the widely differing ships. The 2500 different possible DT values BKT BKT model adjustment (explored in section 3d), we generate can be calculated and the coefficients selected using the same the empirical histogram of clouds on a 18 spatial grid at set of cost functions used for optimization. DT values can be BKT monthly resolution (using ICOADS data from 1961 to 1990). determined following the same approach in section 2d allowing We can then sample cloud cover values from this climatologi- efficientadjustmentoflarge datasets. cal histogram to generate ensembles of cloud cover estimates d. BKT adjustment and uncertainty using “stock” for MAT with missing cloud cover, which will vary across a 18 coefficients and climatological infilling grid and month. Similarly for V, we sample wind speed (ws) values from the Rayleigh distribution, with the scale parame- The impact of infilling missing cloud and V values (section 3b) ter set as ws/ p, and direction sampled from the climatologi- and fitting the model using a pool of stock coefficients in lieu of cal distribution of the 16-point compass direction. To generate running the optimization (section 3c)isshown in Fig. 6. Figure 6a V, we further add a random directional component from the shows that the mean uncertainty value (defined as one stan- uniform distribution (622.49 ) to the coarse-resolution wind dard deviation of the 60-member DT 2DT ensemble diur BKT direction and then use the observed ship speed and value to spread) is at a minimum when using raw observation data and recalculate a sampled V. fitting via optimization, with largest uncertainty values during the peak heating hours of 6–12 h after sunrise. The uncertainty c. Bulk application of the BKT model using “stock” increases slightly when using raw observation data and the coefficient combinations stock coefficients (black line with crosses), and further in- The optimization of model coefficients is computationally creases when infilling V and cloud cover (green and magenta intensive and impractical for application to every ship in lines). The greatest increase in uncertainty comes from replac- ICOADS. To avoid this the optimization was applied to over ing observation data with climatological infilling of both V and 10 000 ships in ICOADS during the period 1854–2020, gener- cloud. Using either optimized (section 2b)orstock coefficients ating a collection of “stock” coefficients (without using infilled (section 3c)when infilling both variables makes little differ- cloud and V). Many of these coefficient combinations were ence (both blue lines). The greater increase in uncertainty similar, so we reduced the number of stock coefficients. We when infilling cloud only (magenta line) as opposed to V only first reduced the number of the coefficients by removing du- (green line) is logical in the context of the BKT model plicate values across the four x coefficients when rounding to [Eq. (10)] as the okta value scales the incoming solar radiation, two significant figures. We then calculated the hourly BKT ad- and that sets the initial magnitude of DT . This pattern typi- BKT justment value for a selection of spatial locations, environmen- cally holds true when assessing the uncertainty change against tal conditions, and days, and removed coefficient combinations bins of cloud cover, V, and latitude, though some bin values Standard Deviation (deg.C) 0.0 0.1 0.2 0.3 0.4 0.5 Standard Deviation (deg.C) 0.0 0.1 0.2 0.3 0.4 0.5 Standard Deviation (deg.C) 0.0 0.1 0.2 0.3 0.4 0.5 Standard Deviation (deg.C) 0.0 0.1 0.2 0.3 0.4 0.5 APRIL 2023 C R O PPE R E T A L . 435 a) b) 2.0 400 1.5 1.0 0.5 0.0 0.000 0.002 0.004 0.006 812 16 200 4 Ratio between heating and cooling terms Local Hour c) 03 05 07 09 11 13 15 17 Day FIG. 7. (a) Density plot of the ratio between the BKT model heating and cooling terms (i.e., x /x V 1 x )for 1 3 5 each cost function as selected by either the 83-member ensemble using the 1854–70 grouping (blue) or the 59-member ensemble using pre-1854 ships (green). (b) The magnitude and uncertainty of DT under the same fixed environ- BKT mental conditions as in Fig. 5 at 258N. (c) The DT time series (black dashed line) for the ship HMS Favorite during diur December 1831, with T for the pre-1854 ensemble (solid green line) where shading intensity corresponds to 61–2 BKT standard deviations. The T for the 1854–70 grouping is shown without shading for comparison (solid blue line). BKT differ. Climatological infilling of both parameters typically We trial two attempts to adjust the pre-1854 data. First, doubles the uncertainty compared to using raw data and opti- data from all ships between 1854 and 1870 are used as the mizing (Fig. 6). The relatively minor increase in uncertainty pre-1854 analog period. Each stock coefficient combination is when using stock coefficients and raw data gives us confidence given an identification number, and the number of times each in the en masse application of the BKT model using this set of stock coefficient occurs within the 60-member ensemble approach. for a ship in the 1854–70 period occurs is counted. From this, a break in the most frequently occurring coefficients was identi- e. Application to pre-1854 ships fied at n 5 83, which generated an ensemble of 83 different If it is not possible to generate any T values for a ship, realizations from the stock coefficients that are then applied to nt DT cannot be estimated [Eq. (2)] and the BKT model can- the pre-1854 ships. The mean of the DT is determined from diur BKT not be fit using the methodology we outline in section 2d.A these83sets ofcoefficients and the standard deviation of the DT value can be determined using stock coefficients, but DT values becomes the uncertainty range. Second, for pre- BKT BKT the chosen sets of coefficients have to be determined via ana- 1854 ships with over 50 DT observations, we generate cloud diur log, based an expected DT profile for the particular ship. and V valuesasin section 3b, which enables the BKT model to diur Before ca. 1854 there are increasingly fewer NMAT observa- be fitas in section 3c, resulting in a 59 member ensemble size. tions (Fig. 1a), and ships that do sample the diurnal cycle are Figure 7a presents a density plot of the ratio between the unlikely to have cloud and V observations available (Fig. 1b). heating and cooling terms of the BKT model. This allows a Stock coefficients enable an estimation of the DT to be broad approximation of the exposure and heating bias of a BKT made without a DT target. As the accuracy of the adjust- ship. The 1854–70 ensemble is characterized by most ships’ ra- diur ment cannot be directly assessed this way, the quality of the tio being below ;0.002, which after Fig. 4 in Berry and Kent adjustment will be based on the efficacy of the grouping of (2005), is an appropriate range for good ships with a low heat- the ships. For example, we can expect that most ships pre- ing bias. The pre-1854 ensemble distribution is more uni- 1854 are wooden-hulled sailing ships, with nonstandard formly spread, indicative of more ships with larger heating observing practices (i.e., differences between countries and in- biases. This is reflected in Fig. 7b, using the same fixed envi- dividual ships). It would therefore be desirable to obtain a set ronmental conditions as Fig. 5; the DT is shown to be BKT of coefficients that have been successfully applied to analog larger (and less certain) for the pre-1854 ensemble. The im- ships during the following years. Good analogs are difficult to pact on a MAT time series using either ensemble is shown in derive during the early 1850s as the global shipping fleet transi- Fig. 7c, alongside the DT .For the HMS Favorite during diur tioned from sail to steam. However, the 1853 Brussels Marine December 1831, it is clear that the pre-1854 ensemble (Fig. 7c) Conference (Maury 1853) led to an increased standardization captures the evolution of the DT more appropriately than the diur of measuring practices and hence the metadata in ICOADS/ 1854–70 ensemble (Fig. 7d)asthe DT often falls out of the diur digitized records could enable selection of ships in the decades uncertainty range for the latter. following 1854 that are the most appropriate counterparts to En masse application of the pre-1854 ensemble of coeffi- the assumptions listed above. cients to the pre-1854 data would result in larger values of Density ∆T | ∆T BKT err ∆T BKT 436 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 DT as opposed to using the 1854–70 ensemble. The pur- sources are digitized, and/or metadata tied to existing obser- BKT pose of the comparison here is not to identify the better over- vations are utilized. all choice, but to highlight that it is possible to achieve b. Data issues and quality control sensible heating bias adjustments to the early data. Rather than a broadscale adjustment, specific BKT model coefficient Relatively strict quality control procedures have been ap- plied (appendix) to ensure the analysis uses data that accu- groupings could be made for different ICOADS decks or rately portray the measured diurnal cycle. source IDs, and as for newly digitized data as they become The diurnal-cycle-based quality control routine (appendix) available. Utilizing this analog approach to the heating bias identified data from a number of ships in the 1880s that adjustment is not limited to pre-1854, and could be used passed the climatology-based QC checks but that had a ;12-h throughout the full ICOADS period. offset. Without removal or adjustment these data would ad- versely affect NMAT datasets. Furthermore we were able to 4. Summary and discussion identify ships suspected of making measurements in cabins, by analysis of the peak hour of DT (appendix). Overall, diur a. General application of the BKT model this shows that there is still much to be learned about MAT In this paper we have extended the method developed by observations and diurnal-cycle-based assessments are likely to BKT for the correction of diurnal heating biases in ship-based remain a useful tool in improving the long-term records air temperature measurements. From our estimate of this (Cornes et al. 2020; Chan and Huybers 2021). A further unre- heating bias, we are able to generate MAT time series for in- solved issue is whether some reported ICOADS wind and di- dividual ships, T (Fig. 2), that substantially reduces the adj rection values are the true wind and direction, or relative DT , leaving a mean residual within 60.28C(Fig. 4). Results err values uncorrected for ship trajectory (Gulev 1999). focus on a sample of 16 ships, but the approach is applicable c. Precipitation and weather codes to all ship-based observations in ICOADS and ultimately will be used in the construction of improved estimates of global The presence of precipitation invalidates the energy trans- surface air temperature trends. fer assumptions of the BKT model. When the recording of Our DT estimate [Eq. (2)], based on the difference be- diur the present weather (WW) code is systematically high (.95% tween MAT and the underlying NMAT trend, minus the cli- during the 1960–70s, green color in Fig. 1c), the percent of matological SST cycle from buoys as defined in Morak-Bozzo WW observations indicating precipitation is ;10% (red color et al. (2016), is likely an overestimate of the true heating bias. in Fig. 1c). As the WW code is not always recorded with every The heating bias is difficult to disentangle from the true diur- MAT observation, it may not be possible to identify all obser- nal cycle as both depend on the incoming solar radiation. vations that may have been affected by precipitation. Further Application of the BKT model requires observations to be work is required to better identify affected observations and part of a ship-track time series, either through an extant iden- to understand the impact of precipitation on the heating bias. tifier or after application of a tracking methodology (Carella d. Systematic structure in diurnal residuals et al. 2017), to enable DT to be calculated. This can be diur ameliorated by improved tracking methods or ensuring ship The approach outlined here, across the 16 analyzed ships, identify information is preserved in metadata records as they reduces the mean hourly local time error in all-hours observa- are stored/digitized. tions (DT ’ DT ) to within 60.28C(DT 2DT ). err diur diur BKT For ships that lack accompanying cloud and V it is possible However, a systematic diurnal structure remains in the resid- to estimate the MAT daytime bias (Fig. 6)by infilling these uals of the BKT model adjustment (Fig. 4c). Further reduc- variables. The uncertainty in DT inflates to account for BKT tion in these residuals is likely to require an improved analysis the infilling. method. Examples of possible improvements might be better It is possible to achieve a removal of the daytime heating estimates of incoming solar radiation, potentially including a bias for ships without sampling across the diurnal cycle; this is diffuse term; reinstatement of the original x thermal transfer required for temporal extension of the MAT record further term (which would add dewpoint temperature as a data re- back in time than ca. 1854. For example, the English East quirement in applying the BKT model); or explicitly estimat- Indian Company ships (ICOADS Deck 248) mostly report a ing, or fitting the true diurnal cycle of MAT. single daily observation at local noon, which makes determin- e. The need for more complete data and metadata ing a nighttime value and DT estimate impossible. How- diur ever, in this paper we have demonstrated that if a sufficient The value in the recovery and digitization of MAT data, in number of analog ships can be identified, which are able to be terms of the marine contribution to extending the global tem- adjusted, the most commonly occurring BKT model coeffi- perature record, cannot be overstated. While much work has cients used in the adjustment of these ships can be used to been done in extracting historical observations from available generate an ensemble of DT for these older ships (Fig. 7), archives, e.g., Garc´ ıa-Herrera et al. (2005), extra value can be BKT enabling a backward temporal extension of the MAT record. prescribed to MAT observations that cover the full diurnal cy- Here, an outline for choosing analog ships was made, but this cle and have concomitant cloud and wind speed observations, can be refined in the future as data from newly recovered particularly for pre-1854. 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Quantifying Daytime Heating Biases in Marine Air Temperature Observations from Ships

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American Meteorological Society
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1520-0426
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10.1175/jtech-d-22-0080.1
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Abstract

APRIL 2023 C R O PPE R E T A L . 427 Quantifying Daytime Heating Biases in Marine Air Temperature Observations from Ships a a,b a a THOMAS E. CROPPER , DAVID I. BERRY , RICHARD C. CORNES , AND ELIZABETH C. KENT National Oceanography Centre, Southampton, United Kingdom World Meteorological Organization, Geneva, Switzerland (Manuscript received 22 July 2022, in final form 6 January 2023) ABSTRACT: Marine air temperatures recorded on ships during the daytime are known to be biased warm on average due to energy storage by the superstructure of the vessels. This makes unadjusted daytime observations unsuitable for many applications including for the monitoring of long-term temperature change over the oceans. In this paper a physics- based approach is used to estimate this heating bias in ship observations from ICOADS. Under this approach, empirically determined coefficients represent the energy transfer terms of a heat budget model that quantifies the heating bias and is applied as a function of cloud cover and the relative wind speed over individual ships. The coefficients for each ship are derived from the anomalous diurnal heating relative to nighttime air temperature. Model coefficients, cloud cover, and relative wind speed are then used to estimate the heating bias ship by ship and generate nighttime-equivalent time series. A variety of methodological approaches were tested. Application of this method enables the inclusion of some daytime observations in climate records based on marine air temperatures, allowing an earlier start date and giving an increase in spatial coverage compared to existing records that exclude daytime observations. SIGNIFICANCE STATEMENT: Currently, the longest available record of air temperature over the oceans starts in 1880. We present an approach that enables observations of air temperatures over the oceans to be used in the creation of long-term climate records that are presently excluded. We do this by estimating the biases inherent in daytime tem- perature reports from ships, and adjust for these biases by implementing a numerical heat-budget model. The adjust- ment can be applied to the variety of ship types present in observational archives. The resulting adjusted temperatures can be used to create a more spatially complete record over the oceans, that extends further back in time, potentially into the late eighteenth century. KEYWORDS: Climate; Diurnal effects; Surface temperature; Data quality control; In situ atmospheric observations; Ship observations 1. Background and motivation bias adjustment of DMAT, and if this adjustment can be deter- mined accurately the sampling and coverage of MAT will be Marine air temperature (MAT) observations from ships improved throughout the record. form a long-term climate record used to construct gridded Global mean surface temperature (GMST) anomaly data- data products as either the principal data source (Berry and sets, combining observations over land, ice, and ocean, have Kent 2009, 2011; Kent et al. 2013; Cornes et al. 2020; Junod used SST in lieu of MAT for their ocean component (Lenssen and Christy 2020) or for bias adjustment of sea surface tem- et al. 2019; Morice et al. 2021; Huang et al. 2020), including in perature (SST) products (Huang et al. 2017; Kennedy et al. the sixth Intergovernmental Panel on Climate Change Assess- 2019). These gridded products only use MAT observed during ment Report (Gulev et al. 2021). GMST is used instead of nighttime (NMAT) to exclude data affected by solar heating global surface air temperature (GSAT) for three main of the instrument and local ship environment during daytime reasons: there are more (all-hours) SST observations than (DMAT). Using only NMAT approximately halves the num- NMAT; quantification of SST measurement bias and uncer- ber of available observations and limits the temporal extent tainties is more mature than for MAT (Kennedy et al. 2019); of any MAT-based dataset as early observations were often and the belief that SST anomalies are more reliable than only recorded during the daytime (Fig. 1a). For example, two MAT at large spatial scales (Kent and Kennedy 2021). It was recently published NMAT datasets begin in 1880 (CLASSnmat; also asserted that large-scale anomalies of SST and MAT Cornes et al. 2020) and 1900 (UAHNMAT; Junod and Christy display similar variability and trends (Huang et al. 2017), 2020). Extending the MAT record further back in time requires although this is increasingly being questioned (e.g., Cowtan et al. 2015; Richardson et al. 2016; Rubino et al. 2020). Here we demonstrate a method to estimate the daytime heating Denotes content that is immediately available upon publica- biases in MAT observations on a ship-by-ship basis that can tion as open access. be applied throughout the observed record. The ultimate goal is to use these adjusted data to create a GSAT record based on air temperature over land, ice, and ocean. This will facili- Corresponding author: Thomas E. Cropper, thomas.cropper@ noc.ac.uk tate comparison of the observed surface temperature record DOI: 10.1175/JTECH-D-22-0080.1 Ó 2023 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). 428 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 FIG. 1. Sampling characteristics of MAT observations from ship reports in ICOADS (Freeman et al. 2017). (a) The 1784–2020 percentage of MAT observations recorded annually during daytime (DMAT, black line, left-hand axis), the red dashed line indicates 50% daytime obser- vations. The solid blue line (right-hand axis) is the annual total number of MAT observations, and the dotted blue line is the number of MAT observations associated with a ship track of 12 or more reports, with diurnal sampling, and including only observations with associated cloud and relative wind speed (V) observations. Free text comments indicate the annual average number of MAT observations for select periods (or the total amount for 1784–1853). (b) Stacked plot of the percent of MAT observations with a corresponding cloud and/or V value. The red area indicates reports with both cloud and V; the blue area indicates reports with neither. Reports with either cloud or V, but not both, are in- dicated in green and yellow, respectively. The dotted line indicates MAT with V but without cloud when the green color overrides. When yellow is visible, lack of cloud information is the major constraint on applying the heating bias model introduced in section 2a; when green is visible, lack of V is the constraint. (c) Stacked plot of the percentage of MAT observations with an associated present weather code (WW; green) and with WW code indicating precipitation (red). The dashed line shows the percentage of extant WW indicating precipitation. with the output of climate models (Jones 2020), which most related bias on 17 ships extracted from the VOSClim database straightforwardly provide estimates of GSAT rather than (Berry and Kent 2005). In the construction of the NOC Surface GMST. Flux and Marine Meteorological Dataset (Berry and Kent 2009, 2011)the BKT model was used to adjust the MAT obser- vations obtained from the International Comprehensive Ocean– 2. Methods Atmosphere Dataset (ICOADS; Freeman et al. 2017)for the period 1973–2014. However, in order to simplify the calculations a. The Berry et al. (2004) model in that analysis, a fixed annual set of coefficients was applied Berry et al. (2004, hereafter BKT) developed a model to across all ships. Here we develop coefficients ship by ship to give quantify heating-related biases in MAT, accounting for the an adjustment for heating bias that reflects the characteristics of energy accumulation and release by the superstructure of a particular ship. ships. The BKT model was developed and tested using tem- We define several measures of temperature in Eqs. (1)–(3), perature values recorded on board the Ocean Weather Ship which are illustrated in Fig. 2: T is the true air temperature; air Cumulus during 1988 and later used to examine exposure- T is the measured air temperature; T is the background ship nt APRIL 2023 C R O PPE R E T A L . 429 TABLE 1. Empirical coefficients; V is relative wind speed (m s ). a) Coefficient Definition Min Max 22 x A a /mc 0.0001 0.1 1 s s 20 x x V (A /mc)h c m Oct 22 Oct 24 Oct 26 Oct 28 Oct 30 x 0.0001 10 b) x 222 x (A /mc)h 0.0001 10 5 c o 0 energy transfer component (Q ), shown by BKT to account LW Oct 22 Oct 24 Oct 26 Oct 28 Oct 30 for a maximum ;3% of the estimated heating bias. Assuming Date d(T )/dt ’ 0, Eq. (4) becomes air FIG.2. (a) T (black line, circles show individual observations), ship dDT err T (T 2DT ) (blue), and T (red) for the ship Raphael dur- adj ship BKT nt mc 1 (h 1 h )A DT 5 a A R (a 1 b sinu)sinu: m o c err s s top i i dt ing October 1884 and (b) DT (black) and DT (blue, dark diur BKT (7) shading corresponds to 61 standard deviation of the DT value BKT from the 60-member ensemble and light shading corresponds to Substituting the coefficients given in Table 1 into Eq. (7) gives 62 standard deviations). dDT err x 1 (x V 1 x )DT 5 x [R (a 1 b sinu)sinu], 3 5 err 1 top i i dt nighttime air temperature (see section 2b); DT is the change err (8) in measured temperature due to ship heating; DT is an esti- diur mate of DT ; DT is the estimate of the temperature dif- err BKT where V is relative wind speed (m s ) and the empirical coef- ference from the BKT model; and T is the measured air adj ficients x represent terms of the energy budget model 1,3,4,5 temperature adjusted using the BKT model: (Table 2). We have redefined the coefficients x and x to in- 3 5 T 5 T 1DT ’ T 1DT , (1) corporate and exclude x (used in the original BKT defini- ship air err air diur 2 tion), so cooling depends on (x V 1 x ) and heating on x . 3 5 DT 5 T 2 T , (2) Expansion of the sinu terms in Eq. (8) and further substitu- diur ship nt tions (Table 2) gives T 5 T 2DT : (3) adj ship BKT dDT err 2 1 h (DT ) 5 h 1 h cos(f) 1 h cos (f), (9) 1 err 2 3 4 dt The BKT model relates T and T (bothmeasuredinKelvin) air ship to the heat exchange, Eq. (4): where f is hour angle in radians. The solution to Eq. (9), gives the value of the heating error at any time during daylight d(T ) ship mc 5 Q 1 Q 1 Q 1 Q : (4) hours (for a full description of the solution, see BKT): SW LW Conv Cond dt h h a h 2 3 1 In this equation m is the mass (kg) and c the specific heat DT 5 1 1 sin(f) 1 cos(f) err;day 2 h h 1 a a 21 21 1 1 capacity (J kg K ) of the sensor environment (that part of the ship that affects the measurement), t is time (s), Q is the 2 2 SW 4a h cos(f) sin(f) h cos (f) 1 4 1 1 1 1 shortwave irradiance [Eq. (5)], and Q and Q are the Conv Cond 2 2 h 1 4a 2a 4a 2h 1 1 rates of heat transfer between the ship and the atmosphere through convection and conduction [all in W m ,Eq. (6)]: 1 k exp(2h t), (10) int 1 Q 5 a A R (a 1 b sinu)sinu, (5) SW s s top i i where a is 2p/12. The integrating factor k can be deter- int mined assuming the sensor environment is in equilibrium at Q 1 Q 5 (T 2 T )A (h 1 h ): (6) Conv Cond air ship c m o sunrise (dDT /dt ; 0) such that diur Here, a is the solar absorptivity of the sensor environment, TABLE 2. Substitutions used in solving the BKT model; dec is A is the surface area normal to the direction of the incoming the solar declination and the k terms use latitude in radians. direct solar radiation (m ), R is the solar radiation at the top Parameter Substitution top of the atmosphere (we use 1368 W m ), u is the solar ele- vation, a and b are cloud-cover-dependent coefficients (index 4 i i h x V 1 x 3 5 i indicates categories of total cloud cover quantities by oktas; h x R (ak 1 ak ) 1 top 1 1 h x R (ak 1 2bk k ) from Dobson and Smith 1988), h and h are the convective 3 1 top 2 1 2 m o 22 21 h x R (bk ) and conductive heat transfer coefficients (W m K ), and 1 top 2 2 k sin[lat sin(dec)] A is the surface area of the sensor environment (m ). Follow- k cos[lat cos(dec)] ing Berry and Kent (2005) we exclude the small thermal ∆T (°C) T (°C) 430 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 2 [Eq. (5)]become a and b as specific coefficients are avail- i,lat i,lat h 4a h cos(f ) sin(f ) h cos (f ) 2 4 sr sr 1 sr k 52 1 1 able for 108 latitudinal bands. Presently the BKT model imple- int 2 2 2 h 4a 1 h 2a 4a mentation requires the solar parameterization to be in the same form as the okta model, precluding the use of, for exam- 1 ah h 3 1 1 1 sin(f ) 1 cos(f ) , (11) ple, the parameterization of Aleksandrova et al. (2007). 2 sr sr 2h a 1 h a 1 1 Other than adjusting nine oktas to eight when the ICOADS present weather code indicates precipitation (Aleksandrova where f is the hour angle at the time of sunrise. At night the sr et al. 2018), we do not make any adjustments to the ICOADS heating error is cloud record. Considering long-term temporal trends, biases likely remain due to heterogeneous recording practices and DT 5 (T ) exp(2h t ), (12) err;night err;ss 1 ss conversions across the diversity of ICOADS source data. For example, cloud observations pre-1949 (when cloud recording where t is the time elapsed since sunset. ss changed from tenths to oktas) may be biased low due to being Using Eq. (10) (daytime) or Eq. (12) (nighttime) DT at BKT double adjusted if the original observation was in oktas (Gulev any location and time can be calculated using the coefficients and Aleksandrova 2020). x along with cloud cover and V. 1,3,4,5 d. Optimization b. Estimation of the temperature error due to ship heating The optimization selects values for the x coefficients that min- Both the true diurnal variation of T and the heating error air imize the difference between DT and DT using Eqs. (10) diur BKT are poorly known. BKT estimated the heating error (DT )in err and (12), and using several different cost functions. Coefficients two ways: as the MAT anomaly from the local midnight to are derived for selected individual ships, but could also be ap- sunrise mean and as the T 2 SST difference. The former is ship plied across a group of ships thought to have similar DT diur likely to overestimate DT as it incorporates the true diurnal err characteristics. cycle of T , while the latter is likely to be an underestimate. air The solution uses the L-BFGS-B (Byrd et al. 1995) solver Given the difficulty of making an adjustment that accounts in R (an option in the optim function; R Core Team 2019) for the real diurnal cycle of T , a pragmatic approach was air with lower and upper coefficient limits from Table 1. We min- taken to estimate DT [Eq. (2)], and hence the adjustment diur imize six different cost functions to evaluate the BKT model [DT , from Eqs. (10) and (12)] relative to an estimated BKT solutions. Each cost function tests different aspects of the background nighttime temperature (T ). First, an estimate of nt goodness of fit and the spread across the cost functions is the expected diurnal SST anomaly associated with every value wider giving more realistic estimates of fit uncertainty: of T was calculated as a function of cloud cover and wind ship speed following Morak-Bozzo et al. (2016) and subtracted 1) The residual root-mean-square error (RMSE), from T . Nighttime values were then calculated using the ship 2 RMSE 5 (1/n)∑ (DT 2DT ) , the RMSE k51 diur BKT k k normal definition of 1 h after sunset to 1 h after sunrise gives the simplest measure of the fit. (Bottomley et al. 1990). These nighttime averages were as- 2) Weighted RMSE (RMSE ) only using MAT observation signed to the time of each sunrise and were linearly interpo- times between 3 and 8 h after sunrise. RMSE gives lated over the 24-h period for each ship (T ). This approach nt weight only to hours where DT values are expected to BKT allows the construction of climate records from a combination be largest. of adjusted all-hours MAT with unadjusted NMAT. 3) RMSE , where the RMSE is calculated from bin means c. Solar parameterization of data in 2 m s V and local-hour intervals. 4) RMSE ,as RMSE but with 5 m s V and 2-hourly inter- V V The BKT model uses cloud-cover-dependent coefficients to 5 2 vals. Both RMSE and RMSE are designed to greater V V estimate solar radiation based on location, date, and time. 2 5 weight the importance of minimizing the (DT 2DT ) diur BKT BKT used coefficients from the Dobson and Smith (1988) residual through the day and across values of V. okta model, which were derived from a limited geographical 5) RMSE 5 (1 2 l)RMSE 1 l(|DW 2 2|), where DW is DW region. Using the same okta model as Dobson and Smith the Durbin–Watson statistic and l is a scaling factor that (1988), we generate a set of updated coefficients. To do this, we set to 0.3. RMSE , is used to down-weight solutions DW we used data from the Surface Solar Radiation dataset–Heliosat where the residual displays autocorrelation. version 2.1 (Pfeifroth et al. 2019), which covers most of the 6) RMSE 5 (1 2 l)RMSE 1 l(KS), where KS is the KS Atlantic (658S–658N, 658W–658E). We collocate the 30-min Kolmogorov–Smirnov statistic. This cost function gives sampling interval of satellite instantaneous incoming solar radi- greater weight to solutions where the cumulative sums of ation values with ICOADS cloud observations for the period daytime values of DT and DT are small. diur BKT 1983–2017 and use this information to generate updated okta model coefficients (https://git.noc.ac.uk/glosat_tc/okta_model). An ensemble of these cost functions is used to test different as- The resulting coefficients produce a less peaked solar cycle than pects of the structure of the residual (DT 2DT )toensure diur BKT the original Dobson and Smith coefficients and reduce the over- a reasonable fit throughout the day and across all cloud-cover all RMSE of estimated to satellite incoming solar radiation by and relative wind speed combinations. Avoiding unphysical start- ;10% for data not included in the fit. The a and b terms ing coefficient combinations improves efficiency and helps to i i APRIL 2023 C R O PPE R E T A L . 431 TABLE 3. Sixteen ships selected from ICOADS to illustrate the results of fitting the BKT model. Deck refers to the original source data collection in ICOADS. Metadata contain information that could be readily obtained via an Internet search of the original call sign or name of the ship. The ship U.S. Navy 12388 samples at 0800, 1200, and 2000 local hour, a common feature of currently available WWII-era ships. Ship Year Hourly sampling frequency Deck Metadata USS Constitution 1854 2 721 Sail, wood USS Despatch 1858 2 701 Screw steamer USS Merrimac 1858 2 721 Steam frigate Mary 1884 2 704 Unknown Panay of Salem 1884 2 704 Sail Raphael 1884 2 704 Sail, wood Chosen Maru 1916 4 762 Cargo, steel, screw steamer Kanagawa Maru 1916 4 762, 706 Passenger, steel, screw steamer U.S. Navy 12388 1942 3 times daily 195 Unknown U.S. naval ship U.S. hourlies 2129 1955 1 116, 117 Unknown Merchant Marine 0805 1955 3 116, 117 Unknown Kajtum 1975 6 927 Cargo ship Westfalen 1995 3 926, 892, 888 Passenger/cargo ship Cape Azalea 2014 1 992 Bulk carrier Polar Resolution 2014 1 992 Oil tanker Alliance St. Louis 2020 1 798, 992 Vehicle carrier avoid local minima so we use a pool of ;350 precalculated sets Figure 3 shows the mean DT , DT , and residuals diur BKT (DT 2DT ) using the best-fit set of coefficients for each of starting coefficients to initialize the fit. For each ship, we ran- diur BKT cost function (i.e., six lines) for the ship Mary (Figs. 3a–d), domly select 10 sets of starting coefficients and 5 subsets of 70% split across local hour of the day, cloud cover, 2 m s intervals of available days. This gives an ensemble of 300 sets of coeffi- of V,and 108 latitude bins. Following BKT we use a target accu- cients (10 starting values, 5 data subsets, and 6 cost functions), racy of 60.28C. Figure 3 shows that across the input parameters and any convergence failures are rerun until there are 50 sets of of the BKT model (time/position, cloud cover, and V), the heat- coefficients per cost function. Unless otherwise stated, hereafter ing bias is removed, with bin-mean residuals that are generally the DT value is the ensemble mean taken from 60 realizations BKT within 60.28C, and the bin-mean local-hour average residuals of the DT using the 10 best-fit time series from each of the 6 BKT are always within the 60.28C target. However, for this ship the cost functions. BKT model appears to underadjust for clear skies (0 okta) and a V of 22–24 m s , although these bins are poorly sampled 3. Results (14 observations for 0 oktas and 45 and 16 observations for the 22 and 24 m s bins, respectively). a. Fitting to individual ships Figures 4a–c display the DT , DT , and residuals diur BKT To illustrate the application of the BKT model, we show (DT 2DT ) across all 16 ships as a function of the num- diur BKT results from 16 ships covering different time periods, sam- ber of hours since sunrise. DT can be ,08C, as MAT values diur pling frequencies, and original input sources (Table 3). close to sunrise will be cooler than the nighttime mean MAT. The data for these ships were obtained from the ICOADS DT is always above 08C, and this is reflected in the nega- BKT (Freeman et al. 2017) archive: release 3.0.0 up to 2014 and tive residuals for hours 0–1 and $18. Aside from the 28–34, release 3.0.1 thereafter. Quality checking has been applied 21 46, and 50 m s wind speed bins and 608N latitude bin, the to the data prior to model fitting (appendix). The reports bin-mean residuals (Figs. 4c–f) are all within 60.28C. The from these 16 ships contain all of the variables required to pattern of a relative DT 2DT underadjustment for diur BKT fit the adjustment model, and all have reported data over at hours 3–5 and 9–14 (Fig. 4c) appears consistent regardless of least 150 days. Collectively, these ships provide a global whether a single cost function is used or a different sample of sample of data between 608Sand 608N, with 64% of obser- ships is selected (not shown). Possible causes are inaccurate vations in the tropics (308N–308S), 26% in the Northern estimates of solar radiation [Eq. (5)] or systematic errors in Hemisphere, and 10% in the Southern Hemisphere. Longi- our estimate of DT . diur tudinally, there are 31% of observations in the Atlantic The mean overall DT 2DT residual for each individ- diur BKT Ocean, 29% in the Pacific Ocean, 18% in the Indian Ocean, ual ship is always within 60.28C, with 11 out of 16 ships within 17% in the South China Sea and adjoining gulfs/seas, with 60.058C. The largest residual (0.148C) is found for the U.S. 3% in the Mediterranean Sea and remainder (2%) of obser- Navy 12388 ship. The WWII period is one of the more diffi- vations from minor ocean basins. cult periods to apply the BKT model correction, due to the Figure 2 shows the diurnal adjustment for the ship Raphael dur- limited number of observations from which determine T ,as nt ing October 1884. Figure 2a shows T , T ,and T . Figure 2b well as the occurrence of and a warm bias in nighttime obser- ship nt adj shows the estimates of DT and DT . vations over 1942–46 (Cornes et al. 2020). diur BKT 432 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 a) b) c) d) 0 5 10 15 20 02468 0 5 10 15 20 25 −40 −20 0 20 40 Local Hour Cloud (Okta) V (m/s) Latitude FIG.3.The mean DT (solid blue line), DT (dashed lines), and residual (dotted lines) for the ship Mary (Table 3) grouped by diur BKT (a) local hour (every 2 h), (b) cloud cover (one okta intervals), (c) 2 m s intervals of V,and (d) 10 latitude bins. Individual dashed and dotted lines represent the best-fitting DT from each of the six cost functions described in section 2d. The horizontal red lines indicate BKT 08 and 60.28C limits. Each bin contains at least 100 observations, except for 0 and 7 oktas, 18 and .20 m s ,and 408 latitude. To determine the relative improvement of MAT data (Fig. 4c), as expected. The RMSE reduction (DT cf. diur after applying the BKT model adjustment, DT and DT 2DT ) ranges from 15% (U.S. Navy 12388, diur diur BKT DT 2DT should be compared. First, it is clear that 1.538–1.358C) to 53% (Kajtum,2.458–1.138C), with a mean diur BKT the spread of DT values (Fig. 4a) is greater than the of 28% across all 16 ships. The RMSE reduction signifi- diur spread for both DT (Fig. 4b)and DT 2DT cantly correlates (r 5 0.92) with the magnitude of DT . BKT diur BKT diur a) b) c) 0 4 8 12162024 048 12 16 20 24 048 12 16 20 24 Hours After Sunrise Hours After Sunrise Hours After Sunrise d) e) f) 0 123 456 7 8 0 1020304050 −60 −40 −20 0 20 40 60 Okta V (m/s) Latitude FIG. 4. Boxplots displaying the bin mean (solid line), bin mean 61 standard deviation (box limits), and 5th and 95th percentiles (whiskers) for (a) DT and (b) DT as grouped by the number of hours after sunrise. (c)–(f) The DT 2DT residual when diur BKT diur BKT grouped by (c) the number of hours after sunrise, (d) cloud cover, (e) 2 m s intervals of V,and (f) 108 latitude bins. All 16 ships from Table 3 are included and the DT is taken as the ensemble mean across 60 realizations of the DT (the 10 best-fit realizations from BKT BKT each of the 6 cost functions described in section 2d). The horizontal solid red and dark-red dashed lines indicate zero and 60.28C limits, respectively. The box widths correspond to the square root of the sample size in each bin. MAT (deg.C) MAT (deg.C) −0.2 0.0 0.2 0.4 0.6 0.8 1.0 −4 −2 0 2 4 −2 −1 0 1 2 3 4 5 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 MAT (deg.C) MAT (deg.C) −4 −2 0 2 4 −2 −1 0 1 2 3 4 5 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 MAT (deg.C) MAT (deg.C) −4 −2 0 2 4 −3 −2 −1 0 1 2 3 −0.2 0.0 0.2 0.4 0.6 0.8 1.0 APRIL 2023 C R O PPE R E T A L . 433 a) USS Constitution | 1854 b) USS Despatch | 1858 c) USS Merrimac | 1858 d) Raphael | 1884 14 13 13 13 e) Mary | 1884 f) Panay of Salem | 1884 g) Kanagawa Maru | 1916 h) Chosen Maru | 1916 13 13 13 13 i) US Navy 12388 | 1942 j) US Hourlies −129 | 1955 k) Merchant Marine 0805 | 1955 l) Kajtum | 1975 13 13 14 14 m) Westfalen | 1995 n) Cape Azalea | 2014 o) Polar Resolution | 2014 p) Alliance St. Louis | 2020 13 14 13 13 04 8 12 16 20 0 4 8 12 16 20 04 8 12 16 20 04 8 12 16 20 Local Hour FIG. 5. The mean (solid line), standard deviation range (darker shading), and 5th–95th-percentile range (lighter shading) for DT for BKT the 16 different ships (Table 3) under fixed environmental conditions of 15 m s V, four oktas cloud cover, 2208 longitude, Julian day 150, and variable latitudes 258N (red), 508N (green), and 658N (blue). The vertical line is at 1300 local time and the number in the upper left of each panel indicates the peak heating hour at 258N. It is not expected that DT will exactly match DT . Re- around the peak heating hours, and the uncertainty range BKT diur siduals will include the effects of any model misfit, errors in V, across different ships will relate to the magnitude of the DT diur cloud cover, or the parameterization of solar radiation and and the environmental conditions, which will depend on the other nonsystematic differences such as weather effects. The region in which the ship was operating. Figure 5 illustrates the magnitude and variability of the residuals, and the percentage importance of obtaining a BKT model solution for individual changes, will depend on the relative sizes of the adjustment ships, but also suggests that coefficients can be estimated for required and these other factors. groups of similar ships (see sections 3c and 3e). Figure 5 illustrates values of DT under fixed environ- If a ship contains observations where it was not possible to BKT mental conditions and for selected latitudes for each ship, us- determine T , but there are sufficient T observations for nt nt ing the 60 ensemble member BKT model coefficients for each that ship to fit the BKT model, then every observation with a ship. Under these conditions, DT in terms of amplitude corresponding cloud and V can be adjusted since sets of BKT BKT and timing is similar for some ships (e.g., the pairing of the model coefficients can be determined. USS Merrimac and Kanagawa Maru), and different for b. Estimating missing cloud and V values others. To adjust the Kajtum using the coefficients generated for the Chosen Maru would leave the Kajtum still retaining a Depending on the observation source, MAT will not always large MAT diurnal cycle, whereas the inverse operation be accompanied by cloud and wind observations. Figure 1 shows would generate a physically unrealistic diurnal cycle for the the proportion of potentially adjustable MAT observations using Chosen Maru. Uncertainties across the ships are largest the BKT model has been decreasing since a sustained peak in ∆T BKT 434 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 a) b) c) d) Raw Raw w/ Stock Coeffs V Infill Okta Infill V & Okta Infill V & Okta Infill w/ Stock 0 5 10 15 20 02 468 0 102030 4050 −60 −20 20 60 Hours After Sunrise Okta V (m/s) Latitude FIG 6. (a)–(d) The bin-mean DT 2DT residual and (e)–(h) the bin mean of the 60-member standard deviation of the DT 2DT diur BKT diur BKT residual. Six different approaches to defining the DT were used: the “normal” approach using raw observational data (black line BKT with circles), using infilled cloud (magenta line), V (green line), both cloud and V (blue line with circles) alongside fitting the DT BKT using “stock” coefficient combinations for raw observational data (black line with crosses) and infilled cloud and V (blue line with crosses). the 1980s, likely due to increasing contributions from automatic resulting in the same hourly rounded (0.18C) values of the weatherstationsinICOADSinthe modern era (Freeman et al. DT throughout the day. This results in a stock coefficient da- BKT 2017). taset of 2500 coefficients, suitable for adjustment of data from As a means to examine the impact of infilling data on the widely differing ships. The 2500 different possible DT values BKT BKT model adjustment (explored in section 3d), we generate can be calculated and the coefficients selected using the same the empirical histogram of clouds on a 18 spatial grid at set of cost functions used for optimization. DT values can be BKT monthly resolution (using ICOADS data from 1961 to 1990). determined following the same approach in section 2d allowing We can then sample cloud cover values from this climatologi- efficientadjustmentoflarge datasets. cal histogram to generate ensembles of cloud cover estimates d. BKT adjustment and uncertainty using “stock” for MAT with missing cloud cover, which will vary across a 18 coefficients and climatological infilling grid and month. Similarly for V, we sample wind speed (ws) values from the Rayleigh distribution, with the scale parame- The impact of infilling missing cloud and V values (section 3b) ter set as ws/ p, and direction sampled from the climatologi- and fitting the model using a pool of stock coefficients in lieu of cal distribution of the 16-point compass direction. To generate running the optimization (section 3c)isshown in Fig. 6. Figure 6a V, we further add a random directional component from the shows that the mean uncertainty value (defined as one stan- uniform distribution (622.49 ) to the coarse-resolution wind dard deviation of the 60-member DT 2DT ensemble diur BKT direction and then use the observed ship speed and value to spread) is at a minimum when using raw observation data and recalculate a sampled V. fitting via optimization, with largest uncertainty values during the peak heating hours of 6–12 h after sunrise. The uncertainty c. Bulk application of the BKT model using “stock” increases slightly when using raw observation data and the coefficient combinations stock coefficients (black line with crosses), and further in- The optimization of model coefficients is computationally creases when infilling V and cloud cover (green and magenta intensive and impractical for application to every ship in lines). The greatest increase in uncertainty comes from replac- ICOADS. To avoid this the optimization was applied to over ing observation data with climatological infilling of both V and 10 000 ships in ICOADS during the period 1854–2020, gener- cloud. Using either optimized (section 2b)orstock coefficients ating a collection of “stock” coefficients (without using infilled (section 3c)when infilling both variables makes little differ- cloud and V). Many of these coefficient combinations were ence (both blue lines). The greater increase in uncertainty similar, so we reduced the number of stock coefficients. We when infilling cloud only (magenta line) as opposed to V only first reduced the number of the coefficients by removing du- (green line) is logical in the context of the BKT model plicate values across the four x coefficients when rounding to [Eq. (10)] as the okta value scales the incoming solar radiation, two significant figures. We then calculated the hourly BKT ad- and that sets the initial magnitude of DT . This pattern typi- BKT justment value for a selection of spatial locations, environmen- cally holds true when assessing the uncertainty change against tal conditions, and days, and removed coefficient combinations bins of cloud cover, V, and latitude, though some bin values Standard Deviation (deg.C) 0.0 0.1 0.2 0.3 0.4 0.5 Standard Deviation (deg.C) 0.0 0.1 0.2 0.3 0.4 0.5 Standard Deviation (deg.C) 0.0 0.1 0.2 0.3 0.4 0.5 Standard Deviation (deg.C) 0.0 0.1 0.2 0.3 0.4 0.5 APRIL 2023 C R O PPE R E T A L . 435 a) b) 2.0 400 1.5 1.0 0.5 0.0 0.000 0.002 0.004 0.006 812 16 200 4 Ratio between heating and cooling terms Local Hour c) 03 05 07 09 11 13 15 17 Day FIG. 7. (a) Density plot of the ratio between the BKT model heating and cooling terms (i.e., x /x V 1 x )for 1 3 5 each cost function as selected by either the 83-member ensemble using the 1854–70 grouping (blue) or the 59-member ensemble using pre-1854 ships (green). (b) The magnitude and uncertainty of DT under the same fixed environ- BKT mental conditions as in Fig. 5 at 258N. (c) The DT time series (black dashed line) for the ship HMS Favorite during diur December 1831, with T for the pre-1854 ensemble (solid green line) where shading intensity corresponds to 61–2 BKT standard deviations. The T for the 1854–70 grouping is shown without shading for comparison (solid blue line). BKT differ. Climatological infilling of both parameters typically We trial two attempts to adjust the pre-1854 data. First, doubles the uncertainty compared to using raw data and opti- data from all ships between 1854 and 1870 are used as the mizing (Fig. 6). The relatively minor increase in uncertainty pre-1854 analog period. Each stock coefficient combination is when using stock coefficients and raw data gives us confidence given an identification number, and the number of times each in the en masse application of the BKT model using this set of stock coefficient occurs within the 60-member ensemble approach. for a ship in the 1854–70 period occurs is counted. From this, a break in the most frequently occurring coefficients was identi- e. Application to pre-1854 ships fied at n 5 83, which generated an ensemble of 83 different If it is not possible to generate any T values for a ship, realizations from the stock coefficients that are then applied to nt DT cannot be estimated [Eq. (2)] and the BKT model can- the pre-1854 ships. The mean of the DT is determined from diur BKT not be fit using the methodology we outline in section 2d.A these83sets ofcoefficients and the standard deviation of the DT value can be determined using stock coefficients, but DT values becomes the uncertainty range. Second, for pre- BKT BKT the chosen sets of coefficients have to be determined via ana- 1854 ships with over 50 DT observations, we generate cloud diur log, based an expected DT profile for the particular ship. and V valuesasin section 3b, which enables the BKT model to diur Before ca. 1854 there are increasingly fewer NMAT observa- be fitas in section 3c, resulting in a 59 member ensemble size. tions (Fig. 1a), and ships that do sample the diurnal cycle are Figure 7a presents a density plot of the ratio between the unlikely to have cloud and V observations available (Fig. 1b). heating and cooling terms of the BKT model. This allows a Stock coefficients enable an estimation of the DT to be broad approximation of the exposure and heating bias of a BKT made without a DT target. As the accuracy of the adjust- ship. The 1854–70 ensemble is characterized by most ships’ ra- diur ment cannot be directly assessed this way, the quality of the tio being below ;0.002, which after Fig. 4 in Berry and Kent adjustment will be based on the efficacy of the grouping of (2005), is an appropriate range for good ships with a low heat- the ships. For example, we can expect that most ships pre- ing bias. The pre-1854 ensemble distribution is more uni- 1854 are wooden-hulled sailing ships, with nonstandard formly spread, indicative of more ships with larger heating observing practices (i.e., differences between countries and in- biases. This is reflected in Fig. 7b, using the same fixed envi- dividual ships). It would therefore be desirable to obtain a set ronmental conditions as Fig. 5; the DT is shown to be BKT of coefficients that have been successfully applied to analog larger (and less certain) for the pre-1854 ensemble. The im- ships during the following years. Good analogs are difficult to pact on a MAT time series using either ensemble is shown in derive during the early 1850s as the global shipping fleet transi- Fig. 7c, alongside the DT .For the HMS Favorite during diur tioned from sail to steam. However, the 1853 Brussels Marine December 1831, it is clear that the pre-1854 ensemble (Fig. 7c) Conference (Maury 1853) led to an increased standardization captures the evolution of the DT more appropriately than the diur of measuring practices and hence the metadata in ICOADS/ 1854–70 ensemble (Fig. 7d)asthe DT often falls out of the diur digitized records could enable selection of ships in the decades uncertainty range for the latter. following 1854 that are the most appropriate counterparts to En masse application of the pre-1854 ensemble of coeffi- the assumptions listed above. cients to the pre-1854 data would result in larger values of Density ∆T | ∆T BKT err ∆T BKT 436 J OUR N A L O F A T M O S P H E R I C A N D O C E A N I C T E C H N O L OGY VOLUME 40 DT as opposed to using the 1854–70 ensemble. The pur- sources are digitized, and/or metadata tied to existing obser- BKT pose of the comparison here is not to identify the better over- vations are utilized. all choice, but to highlight that it is possible to achieve b. Data issues and quality control sensible heating bias adjustments to the early data. Rather than a broadscale adjustment, specific BKT model coefficient Relatively strict quality control procedures have been ap- plied (appendix) to ensure the analysis uses data that accu- groupings could be made for different ICOADS decks or rately portray the measured diurnal cycle. source IDs, and as for newly digitized data as they become The diurnal-cycle-based quality control routine (appendix) available. Utilizing this analog approach to the heating bias identified data from a number of ships in the 1880s that adjustment is not limited to pre-1854, and could be used passed the climatology-based QC checks but that had a ;12-h throughout the full ICOADS period. offset. Without removal or adjustment these data would ad- versely affect NMAT datasets. Furthermore we were able to 4. Summary and discussion identify ships suspected of making measurements in cabins, by analysis of the peak hour of DT (appendix). Overall, diur a. General application of the BKT model this shows that there is still much to be learned about MAT In this paper we have extended the method developed by observations and diurnal-cycle-based assessments are likely to BKT for the correction of diurnal heating biases in ship-based remain a useful tool in improving the long-term records air temperature measurements. From our estimate of this (Cornes et al. 2020; Chan and Huybers 2021). A further unre- heating bias, we are able to generate MAT time series for in- solved issue is whether some reported ICOADS wind and di- dividual ships, T (Fig. 2), that substantially reduces the adj rection values are the true wind and direction, or relative DT , leaving a mean residual within 60.28C(Fig. 4). Results err values uncorrected for ship trajectory (Gulev 1999). focus on a sample of 16 ships, but the approach is applicable c. Precipitation and weather codes to all ship-based observations in ICOADS and ultimately will be used in the construction of improved estimates of global The presence of precipitation invalidates the energy trans- surface air temperature trends. fer assumptions of the BKT model. When the recording of Our DT estimate [Eq. (2)], based on the difference be- diur the present weather (WW) code is systematically high (.95% tween MAT and the underlying NMAT trend, minus the cli- during the 1960–70s, green color in Fig. 1c), the percent of matological SST cycle from buoys as defined in Morak-Bozzo WW observations indicating precipitation is ;10% (red color et al. (2016), is likely an overestimate of the true heating bias. in Fig. 1c). As the WW code is not always recorded with every The heating bias is difficult to disentangle from the true diur- MAT observation, it may not be possible to identify all obser- nal cycle as both depend on the incoming solar radiation. vations that may have been affected by precipitation. Further Application of the BKT model requires observations to be work is required to better identify affected observations and part of a ship-track time series, either through an extant iden- to understand the impact of precipitation on the heating bias. tifier or after application of a tracking methodology (Carella d. Systematic structure in diurnal residuals et al. 2017), to enable DT to be calculated. This can be diur ameliorated by improved tracking methods or ensuring ship The approach outlined here, across the 16 analyzed ships, identify information is preserved in metadata records as they reduces the mean hourly local time error in all-hours observa- are stored/digitized. tions (DT ’ DT ) to within 60.28C(DT 2DT ). err diur diur BKT For ships that lack accompanying cloud and V it is possible However, a systematic diurnal structure remains in the resid- to estimate the MAT daytime bias (Fig. 6)by infilling these uals of the BKT model adjustment (Fig. 4c). Further reduc- variables. The uncertainty in DT inflates to account for BKT tion in these residuals is likely to require an improved analysis the infilling. method. Examples of possible improvements might be better It is possible to achieve a removal of the daytime heating estimates of incoming solar radiation, potentially including a bias for ships without sampling across the diurnal cycle; this is diffuse term; reinstatement of the original x thermal transfer required for temporal extension of the MAT record further term (which would add dewpoint temperature as a data re- back in time than ca. 1854. For example, the English East quirement in applying the BKT model); or explicitly estimat- Indian Company ships (ICOADS Deck 248) mostly report a ing, or fitting the true diurnal cycle of MAT. single daily observation at local noon, which makes determin- e. The need for more complete data and metadata ing a nighttime value and DT estimate impossible. How- diur ever, in this paper we have demonstrated that if a sufficient The value in the recovery and digitization of MAT data, in number of analog ships can be identified, which are able to be terms of the marine contribution to extending the global tem- adjusted, the most commonly occurring BKT model coeffi- perature record, cannot be overstated. While much work has cients used in the adjustment of these ships can be used to been done in extracting historical observations from available generate an ensemble of DT for these older ships (Fig. 7), archives, e.g., Garc´ ıa-Herrera et al. (2005), extra value can be BKT enabling a backward temporal extension of the MAT record. prescribed to MAT observations that cover the full diurnal cy- Here, an outline for choosing analog ships was made, but this cle and have concomitant cloud and wind speed observations, can be refined in the future as data from newly recovered particularly for pre-1854. 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Journal of Atmospheric and Oceanic TechnologyAmerican Meteorological Society

Published: May 1, 2023

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