Solar Cycles and the Equatorial Trough: An Alternate Conceptual Model

by Michael Wallace, Hydrologist

I have offered to write this guest essay to reflect recent talks I’ve presented to water resource professionals on hydroclimatology and Solar cycles. As an academic and hydrologic forecaster, I have followed an energy centric, reproducible data path to quantify correlations between solar cycles and atmospheric moisture patterns. I have anchored my study areas upon subdivisions of the hydrosphere, including the Equatorial Trough (ET) and its relative, the Intertropical Convergence Zone (ITCZ). I have exploited the lags to high correlations that I found to produce what appear to be some of the most accurate climate forecasts known.

In focusing on those objectives, I developed a body of work which initially relied upon linear regression between candidate parameters. As I continued to study that information along with other physical phenomena, I developed a more routine capacity to exercise and test my results to the global energy budget foundation sources in peer reviewed literature. In that testing, I found that I could not reconcile the actual data based magnitude of latent heat identified over our planet with the magnitude attributed to GHGs in the widely relied upon foundational sources. I ultimately developed a concern that the foundational energy budget by Trenberth et. al [1] does not appear to properly account for the magnitude of the latent heat component.

It may also be that the omitted latent energy can account for any or all of the global energy budget assigned currently to greenhouse gases. My academic research also indicates on many levels, including empiricism, linear regression, and physical equations of state, that Solar forcing is the driver of changes in latent heat concentration. Accordingly it appears that there is no need to invoke the GHG theory to explain any of the heat in the global atmosphere.

Origins of a new conceptual model for solar cycle forcing of the hydrosphere

Through advancing my Ph.D. studies, I have been researching the high lagged correlations between solar cycles, the equatorial trough and hydrologic moisture patterns in high altitude middle latitude catchments. As captured by some of my posts at WUWT over the past several years, and by other reports I have authored, my relevant work also branched out into topics of atmospheric ozone, ocean pH, radiant heat transfer, and cyclonic energy.

I have applied this work towards a number of projection and/or forecasting exercises for moisture and temperature at different domains of the atmosphere and hydrosphere. Many of these have shown better accuracy than prevailing models. Those prevailing models include the charts illustrated by Figure 1. That example from the West Wide Climate Assessment utilizes modern day emissions-based global circulation modeling (GCMs) ensembles with downscaling. Those were applied to a series of predictions of long term behaviors of several streamflow gages in the western US. In this example the Upper Rio Grande Watershed (URGW) is represented by flows through the Otowi Gage near Santa Fe.[2]

Figure 1. a. Western Climate Assessment projections for annual volume past Otowi Gage of the Upper Rio Grande in acre ft. Blue line added by Wallace as an annotation of the observations. source: US Bureau of Reclamation USBR Technical Memorandum No. 86-68210-2016-01 West-Wide Climate Risk Assessments: Hydroclimate Projections. Figure 33

b. The higher and sharper the error curve (red dots), the less accurate is the overall performance of the forecast exercise.

I’ve provided the blue observation overlay, which is the actual historical record for that gage in that figure because the authors did not. Their models could not “bear to compare” against observations. I found it helpful to independently produce an estimate of their errors through the scatterplot in red within that figure. Notably some of their results displayed relative errors over 1,000%. A figure at the end of this post features some of my forecasts for a nearby stream so that the reader can compare the relative skill. For those not familiar with this field of hydrology, those WWCA results are extremely poor by most standards. For example, as crude as they can be, the default auto correlation methods are much more accurate, as I explore in a paper in peer review.

Also the WWCA results are unacceptably opaque, by not disclosing poor accuracy. I was pursuing a possibly better set of ideas by early 2014 myself. My ideas revolved around higher transparency and better accuracy as two intertwined goals. By that time I was engaging in systematic time series analyses of streams of the Southwestern US (SWUS). I was the one of the first researchers to develop explicit quantitative correlation metrics between the Pacific Decadal Oscillation (PDO) and streams such as the Upper Rio Grande Watershed (URGW) in northern New Mexico [3]. This reference was never published in a peer reviewed journal, but it was cited by a Federal agency for some endangered species assessments[4].

Figures 2 through 4 are examples from work I produced and/or presented that year. Figure 2. demonstrates a strong graphically obvious correlation for a four year moving average between the PDO and the Upper Rio Grande in the southern Rocky Mountains of the SWUS. In those reports I cited prior relevant work as well.

Figure 2. Otowi Gage and PDO Index time series comparisons, 4 year trailing averages. Sources [5] and [6]

Figure 3. Correlations of Candidate Causal Parameters to Otowi Stream Flow Gage Record. Covering 3 different moving averages and 4 separate climate indexes PDO, AMO, ENSO, and GHG (Mauna Loa CO2 atmospheric concentration). Derived from sources [6], [5], [7], [8], and [9]

Figure 4. Southwestern US climate – ocean correlations, examined for 2014 study area a. Relative topography and observation locations b. Correlations of AMO (red dotted line) and PDO (green banded contours) to flows of the Otowi Gage in the URGW. All comparisons for 10 year trailing averages. Derived from sources [6], [5], and [7]


Figure 3 was developed as an example of the types of correlation patterns seen between the URGW Otowi Gage record I examined and major well known climate indexes, such as the PDO, the AMO, and ENSO. I also reported that the GHG forcing candidate had the lowest correlations of all [3]. A collaborator on a subset of reports appeared to develop similar independent estimates to some extent but that work as most of the others was not accepted for publication.

In any case, for the purposes of parsimony in my research, the comparisons approach of Figure 3 had triggered a flag for the low performing GHG candidate. From the remaining candidates, the URGW was found to lie at an intersection of high correlations to the PDO for moisture and to the AMO for temperature. Figure 4 describes these as an integrated correlation map. Since that time coverage has been expanded and resolution enhanced.

The Links between Solar Cycles, the Western Equatorial Pacific, and Middle Latitude High Altitude River Catchments

I followed up over the next several years working through so-called Auto Regression Moving Average (ARMA), and normal (sometimes multiple or sequential) linear regression styled lagged data time series explorations. I targeted continental moisture and temperature and related those at selected locations around the planet. I worked from an assumption that the optimal places to look for Solar hydrologic connections were high altitude streamflow gages in middle latitudes of each hemisphere. My focus converged again around my resident region of the SWUS, along with its proposed teleconnection to the greatest concentration of atmospheric moisture on the planet hovering over the Western Equatorial Pacific (WEP) within the already widely recognized Equatorial Trough (ET).

For the production of Figure 5 I developed a MATLAB application to work with European satellite reanalysis data (ERAI) for the full atmosphere. I concentrated on a few signatures, Z (the weight of the full atmosphere), Temperature, Atmospheric Moisture, as proxied by Evaporation minus Precipitation (EP) , Zonal (Latitudinal) and Meridional (Longitudinal) fluxes of the sensible and latent energies, including moisture flux, and its Divergence of Latent Energy (LEDIV).

Figure 5. Current Study Regime for Dissertation, Including Circulation and Contours of Geopotential Height Z

The example of Figure 5 includes contours for Geopotential Height Z, as developed for the full atmospheric thickness. As noted, Z is basically the weight of the atmosphere. This content is for the full 432 months of data from 1979 through 2014. The vast light oval patches surrounding the equator are gyres. Vertically, they somewhat extend into the atmosphere and into the oceans. Magenta streamlines show the flows are directed from E to W. The opposite prevails elsewhere for the most part as shown by blue streamlines.

The figure includes other annotations that relate to my presentation and study focus. The rectangular blue boundary outlines the greatest co-concentration of both ocean temperature and atmospheric moisture on the planet. In addition to other acronyms used over the years, that footprint has been termed the Western Equatorial Pacific (WEP). That was the location where I began to compare the Sun’s 11 year cycle in Total Solar Irradiance (TSI) to changes there and along the adjacent gyres.

I searched through greater numbers of streamflow gages from around the Earth. I documented some results which also suggested that upper altitude catchment streams of the middle latitudes oscillate together, so long as they are in the same hemisphere. Figure 6 illustrates preliminary confirmation within the Northern Hemisphere. The chart includes three streams from the Southern Rocky Mountains in black, one from north of that cluster in Green and one from a Himalayan catchment in red.

Figure 6. Selected Flows in Elevated Catchments such as the Rocky Mountains and the Himalayas sources in a document in peer review

The solar cycle signature expresses high multiyear correlations with multiple parameters associated with the WEP. Figure 7 indicates the convection from the surface (as represented inversely by a trade wind inverse proxy the TWWP), the outgoing longwave radiation (OLR) from the top of the atmosphere (TOA), and the latent heat (LEDIV) across the ET with some consistency.

Figure 7. Comparison of a Solar Cycle Time Series to components of the Hot Tower overlying the WEP. All are Standardized Five Year Trailing Averages.

Also the well known ENSO parameter, the Southern Oscillation Index (SOI) (as opposed to the ONI parameter(s)) is in partial synchrony with these other time series. Moreover from its bottom to its TOA, the WEP expresses a lagged synchrony to the TSI, at least for this 5 year trailing average.

In other words, for the Equatorial Trough, across the WEP, it is found that the OLR, the TWWP and the Latent Heat signatures appear to directly register a synchronous lagged solar correlation. It also happens that the WEP is roughly synonymous with the Atmospheric Wet Pool, AWP, which is attributed as the world’s greatest concentration of atmospheric moisture[10]. In my reports I noted that moisture and latent heat patterns are closely linked through the exponential Clausius Clapeyron relation. It is commonly understood that EP patterns may show some consistency with latent heat patterns, in the context of circulation. It is also notable that many of these WEP parameters are included within the ENSO pantheon, even though the ONI index is the commonly cited.

Figure 8 shows that the correspondence between the LEDIV and OLR signatures across the WEP footprint are strong even at a monthly resolution. This again raises an obvious question of whether most of the radiant heat leaving the Earth’s atmosphere can be accounted for by latent heat alone. In that perspective it is noted that the right axis demonstrates that the LEDIV energy reaches higher absolute values than attributed by Trenberth et. al. [1]

Figue 8. LEDIV and OLR monthly signatures associated with the WEP footprint source [11].

Through images such as Figure 9., I could further see that the LEDIV signature shared a textured contour pattern to the atmospheric moisture wave patterns I had featured in past WUWT posts. In this representation of the 5 year trailing average of LEDIV for the span covering 2009 through 2014 the approach is inverted from a convention. Here the deeper the color of green and the deeper that surface, the more negative the magnitude of the LEDIV value. And the deeper the color of red and the higher that surface, the more positive is the magnitude of the LEDIV value. Most LEDIV data values range from -250 W/m2 to +250 W/m2. That happens to roughly compare with the Trenberth value for OLR [1] but not with their values for latent heat.

Figure 9. LEDIV surface (W/m2) 5 year trailing average at end of 2014 source [11]

Figure 9 may premier an alternate and more exuberant topography of heat transport across our planet. In any case, being data-based and mapped, it can be compared against the various competing models for what is driving our climate. For whatever it is worth, I have embraced a forced damped harmonic energy budgeting approach to explore the causalities of this data. I think that approach is compatible in principal with these ubiquitous wave patterns.

Figure 10 is adapted from an associated work of mine in peer review at this time and features a solar cycle dominated forcing notion. This is the concept of regionalized raising and lowering of the WEP atmospheric surfaces (both a moisture proxy and a full atmosphere pressure) along the Equatorial Trough across the West Pacific in a damped, lagged response (via circulation paths) to a rising and lowering of an exclusive solar forcing agent, the TSI. As the figure suggests, changes in TSI transform the atmospheric signature in part through the well known linear relation exemplified by the Geopotential Height Z kg/m via the Hypsometric Equation, and also through the well known Clausius Clapeyron relation of significant fluctuations in the moisture due to changes in Temperature regionalized over the WEP footprint.

Figure 10. Concept of Solar Driven Climate Forcings and Outcomes over the Western Equatorial Pacific

In my reports I have related these WEP signature changes in OLR, EP, and LEDIV, to the so called atmospheric Hot Tower [12] tropical features which can rise and fall over time (see inset photo of Figure 10). As the upper portion of such cloud formations expand into the stratosphere, they accordingly block more and more OLR. As the cloud convection processes amplify, so does the relative magnitude of a vertical atmospheric mass and energy flux. That energy is represented by the latent heat of condensation, captured by the LEDIV parameter. As that vertical flux amplifies, the horizontal flux components of the trade wind air above the WEP drop in magnitude. These processes repeat continuously across this footprint according to cycles which are significantly correlated to sunspot number cycles.


Reproducible and practical simplifications for energy budgeting within the hydrosphere are goals and explain why I have favored devoting attention to the WEP, which lies within the Equatorial Trough, as the likely strongest signature for energy on the planet. I have reported some of the interesting correlations between the atmospheric moisture and the geopotential height patterns shown my web site here and here which draw from ERAI data.

In comparison to energy budgeted by Trenberth et al (2009) and featured in Figure 11, the actual LEDIV values identified in Figure 8 indicate much higher relative portions of the energy budget. Accordingly these observations pose a challenge to the Trenberth energy budget. In that reference, only 80 W/m2 are allocated for condensation or evaporation. Now it seems that the latent energies of the hydrosphere can account for much more than the tiny boxes assigned by Trenberth et al. and annotated by the green outline in Figure 11. Given the actual dominance featured here of the LEDIV energy allocation, perhaps the entire right third of the Trenberth budget figure, namely the tan arrows, could be simply discarded. If that were done, and the latent energy features were re-assigned from ERAI data, then all would balance and simplify.

Figure 11. Global Energy Flow Budget adapted from TrenberthFig. 1. “The global annual mean Earth’s energy budget for the Mar 2000 to May 2004 period (W m–2). The broad arrows indicate the schematic flow of energy in proportion to their importance. ” Green box outline added.

As noted in Figure 11, the Trenberth energy budget reports only 80 W/m2 for any type of latent energy. Other data sources, including the NASA page featured in Figure 12, along with the ERAI sources I use, report much higher latent heat energy values reaching sometimes above a relative value of 250 W/m2. The NASA page is interesting also in its depiction of the relative component of radiant energy that is presumably impacted by GHGs. The net thermal radiation from this resource is only 17%. which is the limiting fraction of the global energy budget which IR active atmospheric molecules (GHGs) can apply.

Figure 12. Global Energy Flow Budget adapted from NASA resource Source [16]


I continue to explore the Solar connections as well as other related mechanisms of these patterns. Some are believed to be a result of prevailing upper and lower atmosphere moisture transport patterns according to Hadley and Walker circulation processes. In general, the Hadley circulation is a primarily meridional, nearly global circulation pattern where upper atmospheric air and moisture migrate from the equator towards upper latitudes, approaching each pole and then subside into the lower atmosphere. The relative energy transport of the Hadley meridional circulation is balanced by additional geostrophic momentum and heat signatures. Those include the climatological scaled angular momentums of the subtropical gyres of the ocean and of the atmosphere. Gyres can exert a dominant impact in their respective regions over such scales, as suggested by focused studies. For example, Rhines and Young explore the significant momentum, dimensions, profiles, and solute and energy transports within paired major atmospheric and ocean gyres [13], while authors including Zhang and Chen [10] and Qui and Chen [14] describe in equivalent scope but independently, the interwoven masses of the Atmospheric Warm Pool (AWP) and ocean parcels.

There is clearly still much for almost any to learn about these circulatory mechanisms and I feel that I have only begun to scratch that surface. As part of the stochastic investigations, I’ve developed Figures 13 and 14, which explore two 5 year trailing averages of global LEDIV for the full atmosphere from the ERAI data source, with a focus over the WEP. Those frames were selected for their relation to drought patterns I review in the southwestern US (SWUS). Again among other things, it appears that the LEDIV dominates the Earth’s emission signature. These energy magnitude contours are also consistent with other independent sources [15]

Figure 13. LEDIV 5 year trailing average W/m^2 1980 through 1985

Left with legend, Right augmented color for contrast with streamlines for full atmosphere. Source UCAR ERAI Source: [11]


Figure 14. LEDIV 5 year trailing average W/m^2 2009 through 2014

Left with legend, Right augmented color for contrast with streamlines for full atmosphere. Source UCAR ERAI Source: [11]

I have also included Figure 15 and Animation 1 as an example of a WEP lag based forecast for a stream close to the URGW. The chart compares my three year advance forecasts to observations. It also includes some projections of mine based on anticipated sunspot numbers which extends the forecast to the year 2022. This may be the first successful multi year streamflow forecast exercise to date by any. In any case because of the transparency of this forecast, the projections can continue to be scored for fidelity to resulting observations until that time.

Figure 15 and Animation 1. Observations versus Forecasts for the Pecos River near Pecos, New Mexico File name MWAStream4slowrate.gif

As this narrative indicates, in simply trying to advance my research and methodology, I’ve found it necessary to produce data based content which challenges established notions of GHG contributions to the global energy budget. It may be a detour to state but I continue to learn in related fields, and I expect that greenhouse gases follow fundamental thermodynamic constraints for IR active atmospheric molecules. Accordingly the gaps in the Earth’s IR emission spectra may be simply a common “extinction” pattern indicated by the Beer Lambert Law. Accordingly the re-emission of photons from greenhouse gases is likely to occur at ever longer wavelengths, thereby unimpeded by the overlying atmosphere. I’ll keep reading, but all from my view still needs to be reconciled with this latent heat quantile as well as the moisture related signatures I have profiled.

In Summary, I have followed a data and energy centric path to quantify new correlations between solar cycles and atmospheric moisture patterns. I have exploited the lags to produce linear regression based projections which can be scored with time. In focusing on those objectives, I became more familiar with the global energy budget publications that relate to latent and sensible heat. I have developed a concern that the widely relied upon, foundational energy budget by Trenberth et. al [1] does not appear to properly account for the magnitude of the latent heat component. It may also be that latent energy, as a primary variable, can account for any or all of the global energy budget assigned currently to greenhouse gases. The data I have explored continues to challenge some other greenhouse gas causality notions, including their poor correlations to droughts of the SWUS, and common knowledge about IR active gases. My preliminary successes with linear regression, Solar cycle based multi year streamflow forecasts points to a productive area of future research and applications.


[1] Trenberth, K.E., J.T. Fasullo, and J. Kiehl, 2009, “EARTH’S GLOBAL ENERGY BUDGET”, ARTICLES, American Meteorological Society March 2009

[2] US Bureau of Reclamation USBR Technical Memorandum No. 86-68210-2016-01 West-Wide Climate Risk Assessments: Hydroclimate Projections. Figure 33

[3] Wallace, M. G. 2014. The relative impact of the Pacific Decadal Oscillation upon the hydrology of the Upper Rio Grande and adjacent watersheds in the southwestern United States. Michael Wallace & Associates White Paper, Albuquerque, New Mexico. llation_Upon_the_Hydrology_of_the_Upper_Rio_Grande_and_Adjacent_Watersheds_in _the_Southwestern_United_States._3_4_5.

[4] Accessed November 18, 2016 by US Department of the Interior, Fish and Wildlife Service for their publication: “Final Biological and Conference Opinion for Bureau of Reclamation, Bureau of Indian Affairs, and Non-Federal Water Management and Maintenance Activities on the Middle Rio Grande, New Mexico”  Fish and Wildlife Service  at file


[6] USGS 2014 08313000, Rio Grande At Otowi Bridge, NM accessed online at

[7](AMO ARCHIVE): NOAA/ESRL/PSD1 2014, and Zhang, Y., J.M. Wallace, D.S. Battisti, 1997

[8] (ENSO ARCHIVE): also

[9](GHG ARCHIVE): NOAA-ESRL Mauna Loa CO2 Data. 2014,

[10] Zhang, C. and Chen, G. 2008. The atmospheric wet pool: Definition and comparison with the oceanic warm pool. Chinese Journal of Oceanology and Limnology, 26, 440–449.

[11] ERAI ARCHIVE at files ‘, ‘ ‘, ‘ ‘ see Dee, D. P., Uppala, S. M., Simmons, A. J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M. A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A. C. M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A. J., Haimberger, L., Healy, S. B., Hersbach, H., Hólm, E. V., Isaksen, L., Kållberg, P., Köhler, M., Matricardi, M., McNally, A. P., Monge-Sanz, B. M., Morcrette, J.-J., Park, B.-K., Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.-N. and Vitart, F. (2011), The ERA-Interim reanalysis: configuration and performance of the data assimilation system. Q.J.R. Meteorol. Soc., 137: 553–597. doi: 10.1002/qj.828

[12] Houze, R. A. 2003. From hot towers to TRMM: Joanne Simpson and advances in tropical convection research. Meteorological Monographs, 29, 37–37

Brown, P. and K. Caldiera, 2017 “Greater future global warming inferred from Earth’s recent energy budget” NATURE 552, 45-50

[13] Rhines, P.B. and W.R. Young, 1982. A theory of wind-driven circulation. I. Mid-ocean gyres. Journal of Marine Research 40 Supplement. 559-596.

[14] Qui, B. and S. Chen, 2012. Multidecadal sea level and gyre circulation variability in the Northwestern Tropical Pacific Ocean. Journal of Physical Oceanography. 42, 193-206.

[15] OAFlux Project Technical Report (OA-2008-01) example at Multidecade Global Flux Datasets from the Objectively Analyzed Air-sea Fluxes (OAFlux) Project: Latent and Sensible Heat Fluxes, Ocean Evaporation, and Related Surface Meteorological Variables

Woods Hole Oceanographic Institution


[17] USGS 2014 08378500 Pecos River near Peco, NM accessed online at


a work in progress please see first instance and perhaps comments

SWUS SouthWest US
WEP Western Equatorial Pacific
PDO Pacific Decadal Oscillation
ENSO El Niño Southern Oscillation
AMO Atlantic Mulidecadal Oscillation
SOI Southern Oscillation Index
ET Equatorial Trough
Z Geopotential Height
LEDIV Latent Energy Divergence
OLR Outgoing Longwave Radiation
ERAI European Reanalysis of Satellite Data
EP Evaporation minus Precipitation
TSI Total Solar Irradiance
TWWP Trade Winds of the Western equatorial Pacific
ONI ENSO parameter of temperature at a specific footprint of eastern equatorial Pacific
AWP Atmospheric Wet Pool
ITCZ Inter Tropical Convergence Zone
URGW Upper Rio Grande Watershed

via Watts Up With That?

January 11, 2018 at 03:00AM

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