Geophysical Research Letters

Sea surface salinity constrains rainfall estimates over tropical oceans



[1] Uncertainties in the monthly mean estimates of precipitation are the largest over oceanic regions with the heaviest rainfall. Using the adjoint sensitivity analysis and 4d variational assimilation of sea surface salinity (SSS) into an ocean model, we show that rainfall estimation errors in the regions of heavy precipitation could be reduced by taking SSS observations into account. Inverse analysis of SSS in the Bay of Bengal also indicates that the monthly mean rainfall of the Global Precipitation Climatology Project (GPCP) is more consistent with SSS and river runoff data than other precipitation climatologies.

1. Introduction

[2] Tropical rains account for more than half of the global precipitation, with 40% of the rainfall confined to a few distinct regions with the annual mean rates exceeding 2 m/yr. These regions of heavy precipitation (RHP) are mainly associated with Intertropical Convergence Zones and occupy less than 7% of the Earth's surface. Most of the rainfall in RHPs falls into the World Ocean leaving a clear signature in SSS with typical variations of 0.2–0.5 psu [Delcroix et al., 1996]. Freshening of the oceanic surface mixed layer in RHPs strongly affects ocean-atmosphere heat flux through formation of the barrier layers [Lukas and Lindstrom, 1991] and modifies the upper ocean circulation. Therefore, good knowledge of the freshwater exchange over the oceans on seasonal and longer time scales, is essential for advancing climate modeling and prediction. Monthly mean precipitation climatologies are of particular importance because they are widely used as a reference state in climate studies and as a spin-up forcing for ocean models.

[3] Existing rainfall climatologies can be roughly divided into two classes: those based purely on observations and reanalysis climatologies. Among the former, the most widely used are the Comprehensive Ocean-Atmosphere Data Set (COADS) [Da Silva et al., 1994]; GPCP; [Huffman et al., 1997; Adler et al., 2003], and Climate Prediction Center Merged Analysis of Precipitation (CMAP [Xie and Arkin, 1997]). CMAP and GPCP cover the satellite period starting in 1979 and basically differ in the methods of data processing. The Tropical Rainfall Measuring Mission (TRMM) satellite was specifically targeted to improve the accuracy of rainfall observations in tropics but accumulated only 8 years of data.

[4] Reanalysis climatologies, such as NCEP/NCAR (NCEP1 [Kistler et al., 2001]), NCEP/-DOE (NCEP2 [Kanamitsu et al., 2002]), and ECMWF[Kallberg, 2003] are based on data assimilation into atmospheric models and exhibit larger precipitation errors than observational climatologies do [e.g., Trocolli and Kallberg, 2004]). Comparison of the observational climatologies shows, however, that considerable errors exist in these products as well (Figure 1). Yin et al. [2004] have shown, for example, that spatial correlation between the global 23-year mean GPCP and CMAP products is only 0.36 over the ocean as opposed to 0.94 over land. Monthly mean rainfall uncertainties can be as large as 3–8 mm/day in some of the RHPs over tropical oceans. As an example, the rms difference between several precipitation products is close to 2.7 mm/day in the Bay of Bengal during the monsoon season (Figure 1).

Figure 1.

An ensemble of annual mean precipitation climatologies in the Bay of Bengal (m/yr) with area-mean accumulated rainfall shown in the upper right. Seasonal cycle of the ensemble-mean rainfall (bold line) and the corresponding r.m.s. variance (thin line) are given in the data plot.

[5] Significant errors over the oceans could be attributed to many factors. First, calibration of the satellite retrieval algorithms is impeded by extremely sparse in situ observations. Gauge data on islands significantly differ from open-ocean buoy data due to orographic and land effects; even the atoll data included into the CMAP product are being questioned [Gruber et al., 2000]. Second, due to high spatio-temporal intermittence of the rainfall, sampling errors of gauge observations are large enough to prevent fine tuning of the satellite retrieval algorithms [Bowman, 2005]. Finally, satellite algorithms involve many poorly known parameters such as drop size distribution, whose variability over large spatial and temporal scales may cause systematic errors in rainfall climatologies. As a consequence, efforts to improve global precipitation products always encounter regional problems. For instance, Yuter et al. [2005] compared TRMM V5 and V6 retrievals and noted poorer performance of the latest V6 algorithm in RHPs over the Tropical Pacific and the Bay of Bengal. It is quite likely that these drawbacks are caused by the unknown local variability of the algorithm parameters which cannot be adjusted uniformly over the globe unless some additional constraints are available.

[6] In this study we make an attempt to improve monthly precipitation climatology in a monsoon driven RHP by employing SSS data as a constraint. Because SSS and rainfall are related through complex upper ocean dynamics, we first estimate SSS errors induced by uncertainties in precipitation and other components of the atmospheric forcing and compare these errors with errors in SSS observations. In Section 3 SSS data from the World Ocean Atlas [Conkright et al., 1998; Boyer et al., 2002] are used to correct rainfall climatologies in the Bay of Bengal during the summer monsoon. Finally, a possibility of improving the rainfall estimates in RHPs by incorporating SSS observations is discussed.

2. Methodology

2.1. Inverse Model

[7] The nonlinear reduced gravity model specifically designed for simulation of the upper tropical ocean [Han and McCreary, 2001; Perigaud et al., 2003] is used to project the seasonal cycle of atmospheric forcing and river runoff ℛ onto the evolution of the ocean state. In the inverse formulation of the model [Yaremchuk et al., 2005] the monthly mean river runoff ℛm, m = 1, …, 12 and precipitation errors δequation imagem(x) are treated as unknowns whose values are determined from SSS data S*m by minimization the cost function

equation image

where ɛS2 is the SSS error variance, Sm is the monthly mean model SSS hindcast, and A is the area of the model domain. The second term in square brackets (equation image) penalizes the magnitudes of the rainfall error fields δequation imagem(x) = equation imageξnmEnm(x) expanded in eigenvectors Enm of the corresponding error covariance matrices equation image, σequation image2 being their eigenvalues. The precipitation error covariance matrices equation image are estimated for every month by averaging over the ensemble of six precipitation climatologies outlined in Section 1.

[8] First guess model solutions are forced by the monthly-mean fields of shortwave and longwave radiation Qs,lm, air temperature Tm, specific humidity hm, wind stress τm, and precipitation equation imagem from COADS [Da Silva et al., 1994]. Additional assimilation runs are performed using other preciptation climatologies (CMAP, GPCP, NCEP1,2 and University of Arizona (UA [Zeng, 1999]) as a first guess. The first guess initial S(x, 0) and open boundary Sm(∂A) values of salinity are extracted from the model solution in a larger domain [Yaremchuk et al., 2005] whereas the first guess monthly-mean river runoff ℛm and precipitation errors δequation imagem are set to zero. Model forcings are determined at each time by linear interpolation between the neighboring monthly values. Optimization is performed using the constrained version of the quasi-Newtonian descent algorithm of Byrd et al. [1995]. The cost function gradient is computed using the adjoint code.

2.2. Error Analysis

[9] Availability of the adjoint code allows to perform sensitivity and error analysis of the model solutions [e.g., Thacker, 1989]. These computations are important for assessing the amount of information on the freshwater fluxes that is present in SSS field under the model constraints.

[10] Given an optimized model solution, one can assume that error perturbations of the forcing fields are small compared to their optimal values, so that the perturbed solution does not deviate far from the optimal one and SSS error dynamics could be well approximated by the tangent model equation image, linearized in the vicinity of the optimal state: δS(x, t) = equation image. Here δℱ is the vector of error perturbations of the model forcings δℱ = {δℛm, δequation imagem, δTm, δhm, δQl,sm, δS(x, 0), δSm(∂A)}. If the error covariance equation image of δℱis known, then the SSS error covariance equation imageS can be computed as equation image, where equation image is the operator of the adjoint model.

[11] Since computation of equation imageS is prohibitive we limit ourselves to calculation of twelve error variances σm2 of the monthly mean SSS values equation imagem averaged over the model domain

equation image

σm2 is expressed in terms of the forcing covariance as σm2 = equation image. If equation image is diagonal, then σm2 can be estimated at the expense of a single run of the adjoint model by first computing the vector of sensitivities equation image and then taking the square of equation image. Furthermore, the SSS error variance σm2 can be represented as the sum of contributions σS2(ℛ), σS2(equation image) … from the various components of model forcing, including the initial and boundary conditions.

[12] This type of SSS error decomposition, although approximate, may shed some light upon a possible impact of SSS data on the overall accuracy of rainfall observations: If the freshwater flux errors significantly contribute to σm2, and the error of SSS observations ɛS2 is not much larger than σm2, then the rainfall climatologies are likely to be constrained by inverse SSS modeling.

3. Results

3.1. SSS Errors

[13] A rough estimate of σm could be obtained from a simple “instantaneuos mixing” model of an ocean with a mixed layer depth h and salinity S, whose SSS variations are related to evaporation E, precipitation P and other processes F by St = (S/h)(EP) + F. A model of this type was used by Delcroix et al. [1996] who analysed in situ SSS observations in the Tropical Pacific and obtained an estimate of h = 24 m for the mean effective mixed layer depth in the regions of high precipitation. Their result indicates importance of the barrier layer formation processes in the tropical RHPs and suggests that 9 cm of monthly rainfall may cause on the average a 0.13 psu reduction in SSS. In other words, a 3 mm/day uncertainty in the RHP rainfall rate projects to 0.13 psu salinity error. Similarly, the 20 W/m2 error in the latent heat flux [Gleckler and Weare, 1996] could be converted into 1.1 mm/day error in evaporative mass flux at the ocean surface. These simple estimates show that precipitation errors in tropical RHPs are likely to provide a considerable contribution into σS that is comparable with the accuracy ɛS = 0.1 psu of the future satellite SSS observations [Yueh et al., 2001].

[14] To refine these estimates, we perform the above described error analysis of the model-simulated monthly mean SSS averaged over the Bay of Bengal. All forcing error variances (except for the river runoff) are assumed independent on spatial coordinates. On the annual average the following values were used: σequation image = 1.8 mm/day, στ = 1.2 Nm−2, σT = 0.5°C, σh = 3 · 10−4 kg m−3, σQ = 15 Wm−2, σS(x,0) = σS(∂A) = 0.2 psu. River runoff errors were taken from the study of Yaremchuk et al. [2005].

[15] Contributions to the uncertainty of the September-mean A-averaged SSS are shown in Figure 2. It is obvious that during the heavy rainfall season (May–September) SSS errors are mostly determined by the uncertainties in rainfall and river runoff. A significant contribution of δℛ and δequation image persists through the annual cycle, accounting for more than 50% of the September-mean SSS error variance. This result indicates that SSS observations may have a noticeable impact on precipitation errors under the inverse formulation of the numerical model.

Figure 2.

Monthly values of the error contributions to the September-mean model SSS. Vertical bars are the time integrals providing the overall partitioning of the September-mean SSS error. Errors in radiative fluxes, initial and boundary conditions contribute less than 7% to the net SSS error (not shown).

3.2. Precipitation Errors

[16] Figure 3a shows the spatial structure of the August-mean rainfall error δequation image retrieved from the WOA SSS. Two basic features seen in Figures 3a and 3b are 1–2 mm/day overestimation of the mean August rainfall in the southwest and 0.5–1.5 mm/day underestimation in the northeastern Bay. This error pattern persists through July–October and also characterizes corrections to the CMAP (Figure 3b) and COADS precipitation climatologies.

Figure 3.

Optimized August-mean rainfall errors (mm/day) for (a) GPCP and (b) CMAP climatologies. (c) Percentage of the stratiform and (d) convective cloud cover over the Bay in August (ISCCP climatology available at

[17] It is likely that error distributions shown in Figures 3a and 3b have a certain degree of realism because of their robustness and correlation with the type of cloud cover (Figures 3b and 3c). The region of negative rainfall errors in the southwest has a higher percentage of low (stratiform) clouds, whereas the underestimated region in the northeast is dominated by high (convective type) cloud cover. The qualitative correlation of the error field with the cloud cover (rain type) is consistent with a known notion that satellite retrieval algorithms tend to overestimate weak rains associated with stratiform clouds and underestimate heavy rainfall of convective origin [Kim et al., 2004; Hu et al., 2006]. This suggests that the error fields shown in Figures 3a and 3b originate from the rainfall information implicitly present in the SSS field.

[18] In November–April, when the monthly mean rainfall and its error drop more than 4 times (Figure 1), correlation of the SSS-retrieved rainfall errors δequation image with cloud cover vanishes. This could be explained by the fact that during that period the SSS field becomes less sensitive to much smaller rainfall variations and information on δequation image is lost on the background of errors in other forcing components.

[19] Analysis of the COADS, CMAP, UA, NCEP1, and NCEP2 rainfall corrections δequation image shows that their amplitudes tend to be larger than that of GPCP error field, indicating that these climatologies are less consistent with the WOA surface salinity in the framework of the employed dynamical constraints. Table 1 characterizes precipitation climatologies by three indices: a) normalized magnitude of the precipitation error field equation image; b) normalized misfit with the WOA SSS ��S; and c) rms difference R* between the SSS-optimized river runoff and the runoff from the Global Runoff Data Center [Dai and Trenberth, 2002], normalized by the corresponding variance. As it is seen from Table 1, GPCP climatology is also capable to provide the least misfit with river runoff data and is seemingly the best in terms the overall ranking. In particular, Table 1 shows that GPCP climatology is somewhat “better” than CMAP, a notion consistent with indications exposed in some of the recent studies [Gruber et al., 2000; Yin et al., 2004].

Table 1. Rankings of the Precipitation Climatologies With Respect to the Magnitude of SSS-Optimized Rainfall Corrections equation image; Misfit with SSS Data ��S; and Misfit With River Runoff Data R*a
  • a

    The bottom row shows overall ranking as the mean of the three indices, normalized by the GPCP value.

equation image0.1140.1010.0970.1280.0980.101

[20] Reanalysis-based climatologies are characterized by lower ranking compared to the observationally-based ones.

4. Conclusions

[21] In this study we employed an upper-ocean model of intermediate complexity to analyze SSS sensitivity to atmospheric forcing and made an attempt to improve monthly mean precipitation estimates during the monsoon season in the Bay of Bengal. Our analysis indicates that a) rainfall and river runoff variations provide a major contribution to SSS variability in tropical RHPs; b) SSS accuracy of 0.1–0.2 psu is sufficient to constrain monthly precipitation estimates in RHPs by assimilating SSS observations into numerical models of the upper ocean.

[22] In the analysis, model errors were assumed to be much smaller than the forcing errors. This assumption is justified by the model's ability to realistically simulate SSS field in the Indian Ocean [Yu and McCreary, 2004], to retrieve the seasonal cycle of river transports from SSS observations [Yaremchuk et al., 2005] and to produce corrections to rainfall climatologies that are consistent with independent cloud cover data. Assumptions of Gaussianity and linearity in the error analysis appear to be more restrictive, because relative errors in the forcing fields range within 10–30%.

[23] Our analysis underlines potential importance of the massive satellite SSS observations for better understanding the hydrological cycle: Numerical models of the upper ocean appear to be skillful enough to provide a reliable connection between SSS and rainfall, at least in the regions of heavy precipitation. Given this, and the accuracy of the rainfall and SSS measurements on monthly time scales, there exists an evident opportunity to advance both the rainfall/SSS satellite retrieval algorithms and our understanding of the global freshwater balance.


[24] This study was supported by NASA through grant NAG 5-10045 and by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) through its sponsorship of the International Pacific Research Center (IPRC). Helpful discussions with H. Annamalai and Jan Hafner are acknowledged. This manuscript is IPRC Contribution 385 and SOEST 6779.